Integration of Fuzzy Analytic Hierarchy Process into multi-objective Computer Aided Molecular Design

Accepted Manuscript Title: Integration of Fuzzy Analytic Hierarchy Process into Multi-objective Computer Aided Molecular Design Authors: Jecksin Ooi, Michael Angelo B. Promentilla, Raymond R. Tan, Denny K.S. Ng, Nishanth G. Chemmangattuvalappil PII: DOI: Reference:

S0098-1354(17)30416-7 https://doi.org/10.1016/j.compchemeng.2017.11.015 CACE 5959

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

7-7-2017 12-10-2017 14-11-2017

Please cite this article as: Ooi, Jecksin., Promentilla, Michael Angelo B., Tan, Raymond R., Ng, Denny KS., & Chemmangattuvalappil, Nishanth G., Integration of Fuzzy Analytic Hierarchy Process into Multi-objective Computer Aided Molecular Design.Computers and Chemical Engineering https://doi.org/10.1016/j.compchemeng.2017.11.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Integration of Fuzzy Analytic Hierarchy Process into Multiobjective Computer Aided Molecular Design Jecksin Ooia, Michael Angelo B. Promentillab, Raymond R. Tanb, Denny K. S. Nga, Nishanth

a

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G. Chemmangattuvalappila Department of Chemical and Environmental Engineering/ Centre of Excellence for Green

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Technologies, The University of Nottingham Malaysia Campus, Broga Road, 43500 Semenyih, Selangor, Malaysia b

Centre for Engineering and Sustainable Development Research, De La Salle University,

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2401 Taft Avenue, 0922 Manila, Philippines

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HIGHLIGHTS

Novel methodology for multiobjective molecular design



Integrate Fuzzy Analytic Hierarchy Process in molecular design



Consideration of different classes of property targets in molecular design



Application example in solvent design for oil extraction

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Abstract

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

In this paper, a novel Computer Aided Molecular Design (CAMD) framework is developed to solve multi-objective molecular design problems. CAMD can be formulated as a multi-

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objective optimisation problem when there are multiple target properties to be optimised simultaneously. A major obstacle faced by multi-objective CAMD problems is the difficulty in assigning weighting factors to the target properties, since the relative importance of these factors is not always defined. It is particularly difficult to compare target properties which belong to different categories, such as physicochemical, safety, health and environmental 1

properties, on a common scale. This paper presents a systematic CAMD algorithm built on Fuzzy Analytic Hierarchy Process (FAHP) to deal with the ambiguity involved in evaluating the weights of target properties in multi-objective CAMD problem. Instead of using exact numerical values, FAHP approach expresses the pairwise comparison of target properties through triangular fuzzy numbers, which allow the degree of confidence of decision maker

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to be quantified. Hence, the proposed approach can address the uncertainties arising from

ambiguity involved during value judgement elicitation in multi-objective CAMD problems.

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The solutions generated provide a better balance of performance for a set of identified target

properties. The proposed methodology is illustrated through a case study on designing a

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better solvent for extracting residual oil from palm pressed fibre.

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Keywords: Computer Aided Molecular Design (CAMD), Fuzzy Analytic Hierarchy Process

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(FAHP), multi-objective optimisation, multi-objective molecular design

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Nomenclature

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CAMD = Computer Aided Molecular Design AHP = Analytic Hierarchy Process

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FAHP = Fuzzy Analytic Hierarchy Process

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lo g K o c = Soil sorption coefficient

ORCs = Organic Rankine Cycles

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TFN = Triangular fuzzy number IPCCWN = Inter-plant chilled and cooling water network GCM = Group contribution method C i = Contribution of the first-order group of type-i

2

D

= Contribution of the second-order group of type-j

j

E k = Contribution of the third-order group of type-k

N i = Number of occurrence of the first-order group of type-i

j

= Number of occurrence of the second-order group of type-j

O k = Number of occurrence of the third-order group of type-k

= Value of target property

L

= Lower bound of product specification

U

= Upper bound of product specification

vp

A

vp

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IEX = Explosiveness based index IFL = Flammability based index

U

p

N

V

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= Target property

p

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ISI = Inherent Safety Index

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NFPA = National Fire Protection Association

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IOHI = Inherent Occupational Health Index IEL = Exposure limit index

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IAH = Acute health hazards 𝐼𝑆𝐻𝐼,𝑤 = Total weighted penalty score for safety and health aspects of molecules I = Binary integer variable wi / w

j

= solution ratio

3

A

= Fuzzy pairwise comparison matrix

aˆ i j

= Fuzzy number

Lˆ i j

= lower bound of triangular fuzzy number

ij

= modal value of triangular fuzzy number

Uˆ i j =

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Mˆ

upper bound of triangular fuzzy number

w

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𝛿𝑐 = degree of confidence = optimal priority vector

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λ = consistency index

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GT= Total number of groups selected

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v i = valence of group i

w m = weighting factor

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F w e ig h te d s u m = Overall objective function

= normalised target property operator

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 pm

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 p = target property operator

p m in



p m ax

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

= minimum value of target property operator = maximum value of target property operator

PPF = Palm pressed fibre TAGs = Triglycerides δ = Hildebrand solubility parameter 4

Rcarotene = difference of Hildebrand solubility parameter between solvent and carotene T b = boiling point

F p = Flashpoint 

= Viscosity

rat acute toxicity

L C 5 0 = Fathead

= Bioconcentration factor

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BCF

= Photochemical oxidation potential

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PCO

minnow toxicity

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L D 5 0 = Oral

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= Molecular weight

w

A

M

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σ = surface tension

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lo g K o w = Octanol-water partition coefficient

PEL = Permissible exposure limit

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LEL = Lower explosion limit

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UEL = Upper explosion limit

LFL = Lower flammability limit

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UFL = Upper flammability limit D AB

vA



= Diffusivity of oil in solvent B

= Molar volume of oil = Association factor for solvent

5

1. Introduction During the past three decades, Computer Aided Molecular Design (CAMD) has become a successful tool for addressing some challenges in the design and selection of molecules for various applications, such as solvent design, polymer design and refrigerant design (Austin et al., 2016). CAMD is a reverse engineering approach, aimed at generating molecules with a

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set of predefined target properties and using molecular building blocks (Harper and Gani, 2000). CAMD techniques can provide a promising systematic route to design molecules.

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In conventional practice, the target properties of a molecule usually include physical and thermodynamic properties such as boiling point and viscosity. More recently, safety, health

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and environmental (SHE) aspects have also become important due to progressively stricter

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SHE regulations in most countries. Chemical industries have thus been prompted to use

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molecules with desirable product functionality but do not pose major hazards to humans and

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the environment. When multiple target properties need to be optimised simultaneously, CAMD problem can be formulated as a multi-objective optimisation problem. Such problems

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can be solved using different strategies. Preference-based methods and solution-generating methods are the two commonly used categories for solving multi-objective optimisation

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problem (Diwekar, 2003). Goal programming is the most common preference-based method,

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whereas the -constraint method and weighting methods are the two common solutiongenerating methods. In goal programming, the decision maker needs to define an a priori goal for each objective, and subsequently solve the model to minimise the total deviation

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from goals. On the other hand, the -constraint method generates a set of Pareto optimal solutions from which a final solution can be selected; however, the method itself does not provide further basis for selecting a final solution from the Pareto set. By comparison, the weighting method can identify a unique optimal solution for actual implementation.

6

In the weighting method, the weight of each objective is specified before solving the multiobjective optimisation as an equivalent single-objective problem. The main drawback of the method is the inherent subjectivity in specifying values of the weighting factor. In addition, it is also difficult to evaluate the relative importance of target properties that belong to different categories, such as physical, safety, health and environmental aspects.. Hence, there will be

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uncertainties arising from ambiguity involved during judgement elicitation. This step becomes problematic in the absence of a systematic procedure to evaluate the relative

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importance of the properties. In such cases, the assigned weights will then provide no insight

into the underlying multi-objective CAMD problem. It is particularly important to address

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this issue, as good alternatives may be eliminated due to faulty weighting. Moreover, even

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slightly different weighting factors of objectives can generate different optimal molecules. To

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overcome this limitation, a procedure that enables the user to systematically evaluate the

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relative importance between properties must be integrated into the CAMD framework. In this work, Fuzzy Analytic Hierarchy Process (FAHP) approach is proposed to quantify the

involved in the problem.

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subjective opinion of decision makers in eliciting the relative importance of each property

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FAHP is an extension of the classical Analytic Hierarchy Process (AHP), a decision analysis

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technique which structures the decision-making problem in a hierarchical manner. Both methods are capable of comparing qualitative and quantitative criteria in a systematic manner through a decomposition strategy. In the conventional AHP approach, Saaty (1980)

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developed a fundamental 9-point scale to help a decision maker to assess pairwise comparison. The intensity of absolute scale assigned can express the relative importance of two criteria. Although the discrete numerical scale of AHP has the benefit of simplicity, in its basic form it cannot successfully manage the uncertainty of subjective opinions involved during the pairwise comparison. This is because the point estimate represented by a single 7

numerical value cannot model the degree of confidence that a decision maker puts in a particular judgement. In order to eliminate this limitation, FAHP approach allows the uncertainty and vagueness of decision makers’ opinion to be captured through fuzzy set theory (Zadeh, 1965). Fuzzy set theory is a well-known framework that can account for uncertainty and vagueness in human reasoning and decision-making. In the FAHP approach,

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a fuzzy scale is used to express the preference or relative importance of target properties,

instead of allocating the exact numerical numbers in pairwise comparison. Hence, FAHP

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approach both relative importance and the confidence level to be captured during pairwise comparison. For these reasons, FAHP approach is a potential solution to address the

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ambiguity involved in assigning the relative weights of target properties in multi-objective

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CAMD problem. The following sections present a summary of current state of the art in

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CAMD and FAHP approach.

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1.1 Computer Aided Molecular Design (CAMD)

CAMD technique has developed as a promising tool in chemical product design due to its

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ability to predict, estimate and design molecules with a set of predefined target properties and

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molecular building blocks (Harper and Gani, 2000). As stated by Papadopoulos and Linke (2006), it is important to formulate CAMD problem as a multi-objective optimisation

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problem to capture the relationship between all the physicochemical properties and SHE aspects of a molecule. Different approaches have been proposed for this purpose. For instance, an iterative step-wise methodology has been proposed by Pistikopoulos and Stefanis

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(1998) to design environmentally benign solvents which can achieve optimal separation performance at minimum cost. In their work, a methodology for environmental impact minimisation (MEIM), which considers environmental properties and economics at the design stage, has been incorporated into CAMD framework. Likewise, Papadopoulos and Linke (2006) have developed a novel multi-objective CAMD methodology for identifying 8

Pareto optimal solvents for liquid-liquid extraction and gas absorption processes based on multiple environmental indices and technical performance metrics. The proposed work allows the solvent design information to be incorporated into process synthesis. However, the proposed methodology does not guarantee that the generated Pareto points are evenly distributed into solvent solution space. In practice, there is a need to identify a unique

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optimum solution on the Pareto front. Papadopoulos et al., (2010) then further applied the

multi-objective CAMD methodology to design and identify the optimal working fluids which

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possess desirable physicochemical characteristic as well as having favourable environmental,

safety and economic performance for a low temperature Organic Rankine Cycles (ORCs).

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Also, Ng et al., (2014) have proposed a novel methodology to solve a multi-objective

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molecular design problem by incorporating fuzzy and bilevel optimisation into CAMD

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techniques. In his work, soil sorption coefficient (log Koc) together with vapour pressure and

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molar volume of the solvent are optimised simultaneously to design an amine-based solvent which exerts favourable performance and environmental characteristics. Recently,

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Papadopoulos et al., (2016) developed a systematic two-stage procedure to determine and choose a set of promising solvents for chemical absorption of carbon dioxide. In their work,

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reactivity, thermodynamic behaviour and sustainability criteria have been chosen as performance criteria in the solvent design. In another contribution, a single-stage chemical

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product design framework employing CAMD technique has been proposed by Ten et al., (2016) to design molecules which satisfy a set of desired properties and pose a low hazard

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risk to the environment and community. The measurement of safety and health indicators are based on the molecular properties that have effects on both aspects. Furthermore, CAMD technique has recently adapted to design sustainable solvents to extract residual oil from palm pressed fibres (PPF) (Khor et al., 2017). In order to design solvents which are safe for the

9

food industry, safety and health properties are optimized simultaneously together with physical properties. 1.2 Fuzzy Analytic Hierarchy Process (FAHP) FAHP is a variant of the widely known AHP, which was first developed by Saaty (1977). AHP approach structures a problem in a hierarchical form, with decision-making objective at

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the top, criteria and/or sub-criteria at the intermediate levels, and the alternatives at the bottom. AHP approach utilises a decomposition strategy based on the principle that it is more

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accurate and easier for a human decision maker to compare two criteria at a time instead of comparing multiple criteria simultaneously. At the same time, in AHP, each layer in the

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hierarchy is initially solved separately; the final step of the methodology allows the

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components to be synthesized into a coherent decision. In AHP, the criteria or alternatives are

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compared in a pairwise manner based on discrete numerical scales which is a fundamental 9-

M

point scale proposed by Saaty (1980). In addition, AHP also has the advantage of allowing the judgement on both qualitative and quantitative criteria to be performed on the same scale

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of analysis. However, the process of eliciting the relative importance of two criteria is usually complex and uncertain. It is often difficult to give exact numerical values which reflect the

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true character of human thinking in pairwise comparison (Chen and Fan, 2011). As

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previously mentioned, AHP approach utilises discrete numerical scales which makes it alone difficult to handle the fuzziness or ambiguity of subjective opinions that occurr during pairwise comparison. To overcome this limitation, the FAHP method is developed.

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Fuzzy set theory has proven to be an effective framework for dealing with vagueness and uncertainty (Zadeh, 1965). It was developed to provide a framework that mimics human reasoning for many decision problems (Tseng et al., 2009). Triangular fuzzy numbers (TFNs) are often used due to their simplicity, since their membership functions can be characterized using only three numbers. The FAHP method translates linguistic judgements into TFNs, 10

organized in fuzzy pairwise comparison matrices. FAHP has been widely applied in various fields of application. For example, the extended analysis method proposed by Chang (1996) to derive the crisp weighting factor from TFNs has been applied by Yang et al., (2011) in prioritizing environmental issues in offshore oil and gas operations. Besides, Tan et al., (2014) have proposed a FAHP methodology for process engineering problems which involve

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multiple criteria and alternatives. This methodology can determine a set of crisp weighting factors from scaled fuzzy judgements. In recent years, FAHP approach has also been applied

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in synthesizing inter-plant chilled and cooling water network (IPCCWN) (Leong et al., 2016). In this contribution, a two-stage procedure which involves fuzzy optimisation and FAHP

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method have been developed for generating alternative IPCCWN designs and selecting the

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most optimum network design based on qualitative and quantitative criteria. Note that the

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above examples have shown that FAHP method is well suited to solving complex real-world

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decision-making problems which involve subjective evaluation. In this work, FAHP approach

2. Methodology

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is extended into multi-objective CAMD problems.

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The main purpose of this work is to present a novel multi-objective CAMD methodology for systematic allocation of weighting factors to each target property the problem. The

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integration of FAHP approach into multi-objective CAMD framework can account for the inherent vagueness and uncertainty arising from the determination of weighting factors of each property. By using the proposed methodology, a molecule that gives the best balance of

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performance in terms of physicochemical properties as well as SHE aspects can be designed. The proposed framework is summarised in the following steps, illustrated in Figure 1:

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Step 1: Determine design objective for CAMD problem

Step 2: Identify and analyze target properties

Step 3: Determine property prediction model

Step 4: Select safety and health indices

Is property prediction model available for target property?

No

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Develop statistical property prediction model

Yes

Perform disjunctive programming

Is the safety and health index score depend on property value?

Yes

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No

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Step 5: Determine limits for property constraint

A

N

Are there multiple target properties to be optimized?

No

Yes

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Step 6: Establish hierarchy model

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Step 7: Construct fuzzy pairwise comparison matrix

Step 8: Compute optimal priority vectors using NLP formulation

Is consistency index, λ value between 0-1?

No

Yes Step 9: Repeat step 7-8 for all hierarchy level and obtain overall weighting factors

Step 10: Molecular design stage

Enumerate molecular structure

Step 11: Define objective function and solve mathematical model

Figure 1: A multi-objective molecular design framework embedded with Fuzzy Analytic Hierarchy Process approach 12

2.1 Identification of design objective In the first step, the identification of design objective for CAMD problem is done by determining the needs of chemical product based on customers’ preferences, or from operating condition of industrial processes. Physical and thermodynamic properties are usually used to define the product specifications. Other than these properties, SHE criteria are

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also considered to ensure that the designed molecule also achieves favourable performance.

Safety and health performance of molecules can be characterised by appropriate indices,

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which will be further illustrated in Section 2.3. The desired target properties and criteria will then be selected as design objectives to ensure that the designed molecules simultaneously

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achieve the functionality and pose low safety, health and environmental hazard levels.

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2.2 Determination of property prediction model

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Once the product specifications and SHE targets are identified, the next step is the estimation

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of all identified target properties via property prediction models. Group contribution method (GCM) is one of the most common approaches in CAMD problems as only molecular

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structure of the pure component is needed to estimate physical and chemical properties

f ( p) 



N iC i  w  M j D j  z  O k E k

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i

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(Mattei et al., 2014). GCM equation is expressed by Equation (1) (Marrero and Gani, 2001):

j

(1)

k

where C i represents the contribution of the first-order group of type-i that occurs N i times, D

j

the contribution of the second-order group of type-j that occurs M

j

times and E k the

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contribution of the third-order group of type-k that has O k occurrences in a compound. The left-hand side of Equation (1) is the simple function f ( p ) of the target property p . In this work, first-order groups are applied as only simple-structured molecules are to be considered.

13

Empirical relationships and correlations can be used to estimate properties if no GCM available. Next, the upper and lower bounds of property constraints must be first determined to ensure the generated molecules will show similar physical characteristics as a conventional solvent. The target property ranges are identified based on product specifications, and is usually

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defined by process requirements or customers’ need. The product specification range can be

vp  Vp  vp

where

U

Vp

p  P

is the value of target property p,

L

vp

and

U

vp

(2)

represents the lower and upper limit of

U

L

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represented by Equation (2):

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2.3 Identification of safety and health indices

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product specification.

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Due to the growing number of industrial accidents, there is an increased emphasis on process safety in chemical industries. Safety hazards can be minimized by having milder process

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operating condition and replacing those hazardous materials with less harmful substances.

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Besides, occupational health should not be neglected as health hazards will often lead to chronic diseases after a prolonged exposure. The safety and health impact of a chemical

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product can be assessed by appropriate safety and health indices. Under safety aspects, two safety indices are applied in this work to evaluate the safety

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characteristics of the molecules, namely explosiveness based index (IEX) and flammability based index (IFL). The index score for IEX is obtained from Inherent Safety Index (ISI) (Heikkilä, 1999) whereas the scores for IFL are taken from National Fire Protection Association (NFPA) flammability rating (National Fire Protection Association, 2007). On the other hand, health indices such as exposure limit based index (IEL) and acute health hazards (IAH) are selected to assess the health performance of designed molecules. The index score for 14

IEL is taken from Inherent Occupational Health Index (IOHI) (Hassim and Hurme, 2010) whereas the index score for IAH is obtained from the NFPA health hazard rating (National Fire Protection Association, 2007). The penalty score for both safety and health indices are presented in Appendix 6.1. The total weighted penalty score for safety and health aspects of molecules (𝐼𝑆𝐻𝐼,𝑤 ) can be calculated by summing up all the sub-index values assigned to it,

weighting factor for each sub index will be determined by FAHP approach.

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𝐼𝑆𝐻𝐼,𝑤 = 𝑤𝐹𝐿 𝐼𝐹𝐿 + 𝑤𝐸𝑋 𝐼𝐸𝑋 + 𝑤𝐸𝐿 𝐼𝐸𝐿 + 𝑤𝐴𝐻 𝐼𝐴𝐻

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which is dictated by Eq. (3), where wi represents the weighting factor for sub-index i. The

2.4 Problem formulation

(3)

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Since the assignment of penalty score to a molecule is dependent on the property value, the

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disjunctive programming can be applied to translate the molecular properties into index

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scores which imply the hazard level of molecules (Ten et al., 2016b). Disjunctive

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programming is a modelling approach which applies discontinuous functions to trace the abrupt changes over a certain decision variable (El-Halwagi, 2011). For example, a score of

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IA will be assigned to a sub-index score if the corresponding property,

p sw itc h .

IA Ip    IB

value is equal to or

The sub-index score model is shown by Eq. (4):

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larger than

p

value is smaller

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than a certain property value whereas a score of IB is allocated when

p

p  p s w itc h

p  p s w itc h

(4)

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Binary integer variables are normally introduced to develop models for such cases which involve discontinuous function. Discontinuous functions can be transformed to the following mixed-integer formulation using a binary integer variable (I): I p  I A * I  I B * ( I  1)

(5)

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Subject to the following condition:  0 p  p s w itc h I    1 p  p s w itc h

(6)

To ascertain that the model allocates the correct value to I to fulfil condition (6), the

( p L  p sw itc h ) * I  p  p sw itc h  ( p U  p sw itc h ) * (1  I )

<

pL

p sw itch

and

pU

I   0 ,1

(7)

are lower and upper limits respective to any feasible value of

, the term

p  p s w itc h

becomes negative, forcing p

>

. When

p

to have value 1 to satisfy both p sw itch

,

I

is forced to be 0 to again

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equalities in the constraint (6). On the contrary, when

I

p

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where

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constraints written in Eq. (7) must be included:

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fulfil both equalities in constraint (6). The illustrative example for the formulation of

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disjunctive programming will be further discussed in section 3.3.

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Since there are multiple target properties as well as safety and health indices to be

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simultaneously optimised in the CAMD problem, FAHP approach is utilised to systematically determine a weighting factor for each property. The initial step is to model the

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decision problem as a hierarchy which is established in the way where the goal of the design problem is located at the top, followed by criteria and/or sub-criteria, and finally with the

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alternatives at the bottom (Saaty, 1980). The relationship between elements of one level with those of the level below can be illustrated with the use of a hierarchical framework.

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This step is then followed by performing pairwise comparisons based on expert judgement to derive the relative importance of criteria at a particular level. For example, the comparison between two main properties is carried out by asking the question: “How much more important is property A compared to property B with respect to a satisfaction of the goal of decision problem?” The intensity of importance of one property over the other property

16

within the same level with respect to a common property in the upper level is represented in the form of solution ratios (

wi / w

j

). The solution ratio

wi / w

j

denotes the relative

importance of property in ith row over the property in the jth column with respect to the specific element in the upper level. In a typical AHP problem, the 9-point scale (Saaty, 1980) wi / w

j

.

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is used to translate a linguistically expressed judgement into a numerical ratio

However, to capture the uncertainty and vagueness of judgement during the pairwise

the exact numerical value to approximate the solution ratio aˆ i j

represent the value judgement

  aˆ 2 n     1, 1, 1  

aˆ n 2



(8)

ED Lˆ i j

, modal value

Mˆ

aˆ i j

ij

is the fuzzy judgement which is

and upper bound

Uˆ i j ).

For instance,

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represented by TFN (lower bound

is identified to be more or less equally important, it is represented by the TFN < 1/1 +

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aˆ i j



w h e r e aˆ ji  1 / aˆ ij  1 / Lˆ ij ,1 / Mˆ ij , 1 / Uˆ ij

where A is the fuzzy pairwise comparison matrix,

if

, a fuzzy scale is used to

M

 1, 1, 1 

j

U N

aˆ 1 n

A

aˆ 1 2

wi / w

as TFN. The general form of a FAHP pairwise comparison

matrix can be expressed by Eq. (8).   1, 1, 1   aˆ 2 1 A     aˆ n 1 

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comparison, TFNs are used to extend the standard AHP 9-point scale. Thus, instead of using

𝛿𝑐 ,1 , 1 + 𝛿𝑐 > whereas if

aˆ i j

is identified to be more important over the other, it is

represented using the fuzzy scale written in Table 1. Note that 𝛿𝑐 is the degree of confidence

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of the decision maker, with a lower value suggests a higher degree of confidence, and viceversa. 𝛿𝑐 value of one, two and three indicate the high, moderate and low degree of confidence while eliciting the value judgement (Tan et al., 2014). Table 1: Summary of fuzzy scale (Tan et al., 2016) Fuzzy number,

aˆ i j

Linguistic scale for comparison of criteria 17

< 1/1 + 𝛿𝑐 ,1 , 1 + 𝛿𝑐 >

More or less equally important

< max (1, 3 – 𝛿𝑐 ), 3, min (9, 3 + 𝛿𝑐 )>

Moderately more important

< max (1, 5 – 𝛿𝑐 ), 5, min (9, 5 + 𝛿𝑐 )>

Strongly more important

< max (1, 7 – 𝛿𝑐 ), 7, min (9, 7 + 𝛿𝑐 )>

Very strongly more important

< max (1, 9 – 𝛿𝑐 ), 9, min (9, 9 + 𝛿𝑐 )>

Extremely more important

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The optimal priority vectors (𝑤) that approximate the solution ratio in pairwise comparison matrix are then computed using the nonlinear programming (NLP) formulation proposed by

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Promentilla et al., (2014), which is shown in Eq. (9): max 𝜆;

U

subject to:

N

𝜆(𝑀𝑖𝑗 − 𝐿𝑖𝑗 )(𝑤𝑗 ) − 𝑤𝑖 + 𝑤𝑗 𝐿𝑖𝑗 ≤ 0;

M

𝜆(𝑈𝑖𝑗 − 𝑀𝑖𝑗 )(𝑤𝑗 ) − 𝑤𝑖 + 𝑤𝑗 𝑈𝑖𝑗 ≤ 0;

A

𝜆(𝑀𝑗𝑖 − 𝐿𝑗𝑖 )(𝑤𝑖 ) − 𝑤𝑗 + 𝑤𝑖 𝐿𝑗𝑖 ≤ 0;

(9a)

(9b) (9c) (9d) (9e)

∑𝑛𝑚=1 𝑤𝑚 = 1; 𝑤𝑚 > 0

(9f)

PT

ED

𝜆(𝑈𝑗𝑖 − 𝑀𝑗𝑖 )(𝑤𝑖 ) − 𝑤𝑗 + 𝑤𝑖 𝑈𝑗𝑖 ≤ 0;

where 𝐿𝑖𝑗 is the lower bound, 𝑀𝑖𝑗 is the modal value lambda, 𝑈𝑖𝑗 is the upper bound and λ is

CC E

the consistency index, which indicate the degree of satisfaction of all computed weight ratios that would satisfy the initial fuzzy judgments. λ value shall range from 0 to 1. λ value of 0

A

denotes that the judgements are fulfilled at the boundaries whereas a value of 1 indicates perfect consistency (Tan et al., 2014). Therefore, by maximising λ, the most consistent set of weighting factors within the fuzzy bounds elicited from decision maker can be determined. However, if λ value falls out of the range, it implies a completely inconsistent pairwise

18

comparison and there will be no solution. In such case, it is necessary to elicit the judgement again. After obtaining the optimal priority vector of each property and sub-property, the final weighting factor of each sub-property, 𝑤𝑚 in the overall system are calculated by multiplying

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the priority vector of sub property with the priority vector of its main property. 2.5 Molecular design stage

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The subsequent step includes the selection of potential molecular building blocks based on the nature of the target molecules. Structural constraints are applied to ensure that the

molecule formed is structurally feasible. To design a molecule, the summation for the number

U

of occurrences for all selected groups must be greater than zero. This rule is explained

N

mathematically by Equation (10):



A

GT

Ni  0

(10)

M

i 1

ED

where N i is the number of occurrences of group i while GT is the total number of groups selected to generate the molecules. Besides, the octet rule of structural feasibility is applied to

GT

N i  2  vi   2 g

CC E



PT

ensure that a molecule has no free attachment. This rule is dictated in Equation (11):

(11)

i 1

where v i is the valence of group i and g is 1, 0, -1 or -2 for acyclic, monocyclic, bicyclic and

A

tricyclic compounds. In this work, simple-structured acyclic compounds and monocyclic compounds are considered. Hence, Equation (11) can be reduced to Equations (12) and (13) for acyclic and monocyclic compound respectively: GT



N i  2  vi   2

(12)

i 1

19

GT



N i  2  vi   0

(13)

i 1

2.6 Optimisation model Based on the identified design objective, CAMD problem is formulated as a multi-objective optimisation problem. Weighted sum method is applied to solve this multi-objective

IP T

optimisation model. Weighted sum method allows multiple objectives to be converted into an aggregated scalar objective function by first allocating each objective function with a

SC R

weighting factor, and then summing up all the contributors to obtain the overall objective function. However, all the target properties and sub-indices are depicted by different

U

measurement units and scales. Thus, normalisation step is important in bringing them to the

N

same magnitude.

A

The normalisation step can be carried out using Equations (14) and (15). Equation (14) is

M

applied to normalise target property or sub-indices that needs to be maximized whereas Equation (15) is used to normalise target property or sub-indices that needs to be minimized.



p 



p m ax

p m in



(14)

p m in

CC E



p

.

PT

 pm

operator,

ED

The normalised target property or sub-indices is then referred as normalised target property



p 

A



where  pm



p m ax

p m ax

p m in





and

p

(15)

p m in



p m ax

are the minimum and maximum value of target property operator.

will now have values ranging from 0 to 1. The consistent set of weighting factor

computed from FAHP approach together with

 pm

can then be used to represent the overall

objective function, which is shown in Equation (16): 20

F w e ig h te d s u m  w 1  p 1  w 2  p 2  ...  w m  p m

(16)

where F w e ig h te d s u m is the overall objective function and w m is the weighting factor for each normalised target property operator 

pm

.

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The design objective of this work is to maximize F w e ig h te d s u m . The solution with the highest F w e ig h te d s u m value will be the optimal molecule. After identifying a solution from the

SC R

optimisation model, an integer cut procedure is performed to obtain a ranked list of optimal

and near-optimal molecules. Using the proposed methodology, a more precise and consistent weighting factor is assigned to each target property as the relative importance of each target

U

property in molecular design can be systematically elicited.

A

N

3. Case study:

M

3.1 Problem statement

A case study by Khor et al., (2017) is revisited by considering physicochemical properties

ED

and SHE aspects as design criteria in the early decision-making stages. Palm pressed fibre (PPF) is a by-product produced from the palm oil milling process. According to Choo et al.,

PT

(1996), 5-7% of residual oil is retained in PPF after the oil extraction process. Residual oil

CC E

retained in PPF is enriched with 4500 – 8500 ppm of sterols, 2400 – 3500 ppm of vitamin E and 4000 – 6000 ppm of carotenoids (Choo et al., 1996). Vitamin E and carotenoids are commonly utilised in the food industry because of their antioxidant properties. In current

A

practice, solvent extraction is extensively applied to extract residual oil from PPF. Hexane has been the solvent of choice for extracting residual oil due to its low cost and high oil solubility (de Oliveira et al., 2013). Nonetheless, there is a growing interest in identifying alternative solvents to replace hexane because of several major drawbacks. For example, the high boiling point of hexane causes carotenoids to degrade at a faster rate. In addition, its 21

high flammability leads to higher operating cost as additional layers of protection must be installed in the plant. Furthermore, hexane is not suitable for edible oil extraction due to its adverse effects on human health after a long-term exposure. Fugitive emissions of hexane vapor also contribute to the formation of photochemical smog. Due to these limitations, this work focuses on improving the physical performance and SHE characteristics of solvent via

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multi-objective CAMD. Determination of design objective

their respective translated quantitative properties.

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Table 2 shows the summary of desirable qualitative attributes of the designed solvents and

Table 2: The desirable qualitative attributes of designed solvent with their respective translated quantitative properties

M

ED

Low flammability based index IFL

Low boiling point ( T b ) low viscosity (  ) and surface tension (  ) Small difference of Hildebrand solubility parameter (δ) between solvent and carotene (Rcarotene) High flashpoint ( F p )

PT

Safety aspects

Quantitative properties

U

N

Ensure good percolation and surface wetting which will lead to high rates of oil extraction (Bockisch, 1998) Ensure both carotene and triglycerides (TAGs) has high solubility in designed solvents

A

Physical attributes

Desirable qualitative attributes Reduce the degradation rates of carotene

Small difference between lower explosion limit (LEL) and upper explosion limit (UEL) Low exposure limit index IEL High permissible exposure limit (PEL) Low acute health hazard index IAH High oral rat LD50 Low aquatic toxicity High fathead minnow LC50 Minimise the formation of photochemical Low photochemical smog oxidation potential (PCO) Reduce accumulation of solvent in one Low soil sorption place coefficient (log Koc) Reduce the tendency of solvent to Low bioconcentration concentrate in aquatic organism factor (BCF)

CC E

Low explosiveness based index IEX

Health Aspects

A

Environmental Aspects

22

3.2 Identification of property prediction models The following step includes the determination of property prediction models for the identified target properties for the design problem. Tb, σ, µ, δ, Fp, PEL, Mw, LC50, LD50, PCO, log Kow and BCF are properties that can be estimated using GCM equations whereas log K oc, upper

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explosion limit (UEL) and lower explosion limit (LEL) can be calculated through empirical

SC R

correlations. GCM equations for the selected target properties are displayed in Appendix 6.2

lo g K o c can be estimated through the correlation given in terms of octanol-water partition

coefficient, lo g K o w . The correlation is expressed by the following equation (Seth et al., 1999): (17)

N

U

lo g K o c  1 .0 3 lo g K o w  0 .6 1

A

PEL can be calculated using the equation in Table 3 has a unit of mol/m3. However, the value

M

of PEL used for penalty score calculation has the unit of ppm. Thus, Equation. (17) can be

ED

used to convert the unit of PEL into ppm. P E L '  V g a s , s td  P E L  1 0 0 0

P E L ' has

the unit of ppm whereas

PT

where

(18)

V g a s , s td

is the molar volume of gas or vapour at

CC E

standard conditions (1 atm and 298 K), which has the value of 24.45 dm3/mol. From Table A.2, the difference between upper explosion limit (UEL) and lower explosion limit (LEL), which is denoted as S, can be used to calculate the explosiveness value. Both

A

UEL and LEL are used interchangeably with upper flammability limit (UFL) and lower flammability limit (LFL). Note that the limits can be calculated using the following correlations:

LFL 

100% 1  9 .0 4 5 4 C O

(19)

23

100%

UFL 

CO

is the oxygen stoichiometric coefficient in a reaction (Ma et al., 2013). Consider a

general compound

C x H yO z N w

C x H yO z N w ( g )  ( x 

4



z 2

)O 2 ( g )  x C O 2 ( g ) 

y 2

H 2O ( g ) 

w 2

N 2(g )

can then be calculated using the following equation:

Co  x 

y 4



SC R

CO

y

undergoes a complete combustion in the air:

z 2

(21)

IP T

where

(20)

1  1 .1 8 4 3 C O

(22)

U

The next step is to identify the upper and lower bounds of property constraint for solvent

N

design. Other than the property constraint, upper and lower limits are also introduced to target

A

properties such as Tb, Rcarotene as well as log Koc and BCF. This step is necessary to ensure

M

that the designed molecules will have a better performance than hexane.

ED

Table 3: Upper and lower bound of properties for solvent design Property

Tb (°C) Rcarotene(unit)

CC E

lo g K o c

PT

Fp (K)

log BCF

Lower Bound

Upper Bound

242

-

40

80

-

3.4

-

4.5

-

3.3

A

3.3 Disjunctive optimisation In this section, the application of disjunctive programming on the index scoring is demonstrated for explosiveness based index (IEX). Consider the following criteria:

24

1  2   3 4 

I EX

0  S  20 20  S  45

(23)

45  S  70 70  S  100

The explosiveness sub-index,

I EX

score may one, two, three or four depending on S value of I EX

functions

IP T

molecule. Binary integer variables have been used to model these functions.

can be translated to the following mixed-integer formulation using three integer variables I E X 2 and I E X 3 ):

SC R

( I EX 1 ,

I EX  I EX 1  I EX 2  I EX 3  1

S  20

0   1

S  45

0 I EX 3   1

S  70

A

(27)

In order to model conditions (25), (26) and (27) which allocate the values of

I EX 1 , I EX 2

and

be either 0 or 1 based on S value of molecule, the following constraints are considered:

CC E

I E X 3 to

(26)

M

S  45

S  70

(25)

ED

2

S  20

PT

I EX

N

0 I EX 1   1

U

Subject to the following conditions:

(24)

I E X 1   0 ,1

(28)

(0  4 5 ) * (1  I E X 2 )  S  4 5  (1 0 0  4 5 ) * I E X 2

I E X 2   0 ,1

(29)

(0  7 0 ) * (1  I E X 3 )  S  7 0  (1 0 0  7 0 ) * I E X 3

I E X 3   0 ,1

(30)

A

(0  2 0 ) * (1  I E X 1 )  S  2 0  (1 0 0  2 0 ) * I E X 1

25

3.4 Development of hierarchical model A three-level hierarchical decision structure is constructed for this case study and shown in Figure 2. The designed solvents should attain their functionalities while having favourable safety, health and environmental characteristics. Under physicochemical properties, there are four sub-properties naming boiling point (Tb), surface tension (σ), viscosity (µ) and

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Hildebrand solubility parameter (δ) difference between solvent and carotenoids (Rcarotene). IFL and IEX are the sub-indices chosen for safety aspects whereas IEL and IAH are the sub-indices

SC R

selected for assessing health criterion. There are four sub-properties under environmental criteria, such as aquatic toxicity (LC50), photochemical oxidation potential (PCO), soil

U

sorption coefficient (log Koc) and bioconcentration factor (BCF).

Physical Properties

µ

δcarotene

M

σ

Environmental Aspects

Health Aspects

IFL

IEX

IEL

IAH

LC50

PCO

log KOC

BCF

ED

Tb

Safety Aspects

A

N

Solvent Design for Oil Extraction

Figure 2: Hierarchical decision structure for this case study

PT

3.5 Computation of weighting factors from Decision Maker’s value judgement

CC E

The judgement in eliciting the relative importance of each criterion is identified from supporting literature or theory, which will be discussed in this section. The pairwise comparisons among criteria have been done as in standard AHP. However, the degree of

A

confidence is also being taken into account while eliciting the judgements. For instance, when comparing the relative importance between physical properties and safety aspects, questions asked are: “which criterion is more important and how much more important is it to satisfy the requirement in designing a solvent for extracting residual oil from PPF?” In addition, the decision maker can choose the degree of confidence when eliciting judgement, 26

such as having high, moderate or low confidence while assigning the intensity of important to the criteria. In this case study, the safety aspect is given the most priority compared to other aspects. This ensures that the designed solvents are inherently safe, and will not bring many adverse effects to the surrounding community if there is any unintentional release. Moreover, by using a less hazardous material in a process, the operational cost can be reduced as the

IP T

number of protection layers used in a plant can be minimised. Thus, the safety aspect of a

molecule is assumed to be moderately more important than physical properties taken together;

SC R

it is also considered to be strongly more important than environmental and health aspects of

the molecule. On the other hand, physical properties are assumed to be strongly more

U

important than environmental and health aspects of the molecules. In order to ensure that the

N

designed solvent will meet the environmental specifications, constraints are imposed on the environmental properties. Table 4 shows the assessment of the relative importance of main

M

A

criteria with respect to the main objective using a fuzzy scale. Note that the λ value is larger than zero, denoting that the judgement is consistent in this pairwise comparison matrix.

ED

Table 4: Fuzzy pairwise comparison matrix of main criteria for solvent design on oil extraction

1

CC E

Physical Properties

PT

Physical Properties

Environmental Aspects Safety Aspects

A

Health Aspects

Environmental Safety Aspects Aspects

Health Aspects

Priority Vector

(3, 5, 7)

(1/5, 1/3, 1)

(3, 5, 7)

0.3105

1

(1/7, 1/5, 1/3)

(1/2, 1, 2)

0.0844

1

(3, 5, 7)

0.5206

1

0.0844

λ = 0.3384

27

A similar question is asked when carrying out a pairwise comparisons between physical subproperties: “which is more important and how much more important is it with respect to a satisfaction of the physical properties of solvent?” The main goal in this case study is to design a solvent whereby carotene degradation rate will be lower during the solvent recovery process. The degradation rate of carotene can be minimised by lowering the boiling point of

IP T

solvent, Tb. Thus, Tb is assumed to be strongly more important than Rcarotene and moderately more important than surface tension and viscosity property. Surface tension and viscosity are

SC R

assumed to be more or less equally important with a high degree of confidence as both properties are crucial in improving solvent diffusivity. Also, surface tension and viscosity are

U

slightly more important than Rcarotene since it is important to ensure that the solvent is able to

N

first diffuse into the matrix of PPF followed by extracting the residual oil which is trapped in

A

the PPF matrix. High surface tension can also impede the penetration of designed solvent into

M

a matrix of PPF, whereas solvent with low viscosity is preferable since part of the extraction process is governed by capillary flow (Johnson and Lusas, 1983). In addition, the diffusion of

ED

residual oil from the matrix of PPF into the designed solvent can be modelled using Equation (32) (Tzia and Liadakis, 2003). From Equation (32), it clearly shows that diffusion of residual

18

( M

B

)

0 .5

T

where

D AB

is the diffusivity of oil in solvent B,

the temperature,  is the solution viscosity,

A

(32)

 vA

0 .6

CC E

D AB 

1 1 7 .3  1 0

PT

oil depends on the viscosity of solvent.

M

vA

B

is the molecular weight of solvent, T is

is the molar volume of oil and  is the

association factor for the solvent. The fuzzy pairwise comparison matrix of physical sub-properties is reported in Table 5. The elicited judgement is consistent since λ value is bigger than zero.

28

Table 5: Fuzzy pairwise comparison of physical sub-properties for solvent design on oil extraction Surface tension

Viscosity

Priority Vector

1

(3, 5, 7)

(1, 3, 5)

(1, 3, 5)

0.5213

1

(1/3, 1/2, 1)

(1/3, 1/2, 1)

0.1006

1

(1/2, 1, 2)

0.1891

1

0.1891

Solubility Surface tension Viscosity

SC R

λ = 0.8786

IP T

Boiling point

Boiling Point Rcarotene

Similar questions are also asked when performing the pairwise comparison for environmental sub-properties. The assumption made in this case study is that the environmental effect

U

caused by oil extraction from PPF using solvent will be similar to that from fresh plant

N

biomass or oilseeds. Moncada et al., (2016) have performed an environmental assessment of

A

the process of extracting essential oil from rosemary and oregano. Based on their report,

M

solvent extraction technology using hexane has the most harmful effect on the environment

ED

compared to supercritical fluid and water distillation technology. Similar results have been reported when calculating the potential environmental impact (PEI) per kilogram of these

PT

essential oils extracted using hexane. This is is attributed to the potential formation of photochemical smog and contribution to aquatic toxicity. Based on the results obtained for

CC E

rosemary oil, the PEI per kilogram of rosemary oil extracted for aquatic toxicity and photochemical oxidation potential is approximately 0.03 and 0.07, respectively (Moncada et

A

al., 2016). Hence, in order to generate a solvent which will significantly minimise the formation of photochemical smog, it is assumed that photochemical oxidation potential is strongly more important than aquatic toxicity.

On the other hand, aquatic toxicity is

considered to be moderately more important than log Koc and BCF. Besides, it is also important to ensure that the generated solvent will have low tendency to accumulate in one

29

place as degradation products with low biodegradability may persist in the environment. Since log Koc is a measure of the tendency of a solvent to accumulate in one place, while BCF is a measure of the tendency of a solvent to accumulate in aquatic organisms, both log Koc and BCF are assumed to be equally important while designing the molecules. In addition, upper bounds have been applied on both log koc and BCF to ensure that the designed solvent

IP T

is not bio-accumulative. The intensity of importance assigned to each property along with the degree of confidence is shown in Table 6.

log Koc

1

(1/7, 1/5, 1/3)

(2, 3, 4)

1

(5, 7, 9)

PCO log Koc

1

A

BCF

Priority Vector

(2, 3, 4)

0.1827

(5, 7, 9)

0.6583

(1/2, 1, 2)

0.0794

1

0.0794

M

λ = 0.3009

BCF

U

PCO

N

LC50

LC50

SC R

Table 6: Fuzzy pairwise comparison of environmental sub properties for solvent design on oil extraction

ED

When comparing the relative importance of flammability and explosiveness index, both indices are assumed to more or less equally important. This is because the flammable range

PT

of a material is indicated by the lower explosion limit (LEL) and the upper explosion limit (UEL). The terms lower flammability limit (LFL) and upper flammability limit (UFL) are

CC E

used interchangeably with LEL and UEL (National Fire Protection Association, 2007). It is equally important to prevent fire and explosion hazards in a plant. Table 7 shows that both flammability and explosiveness have equal relative weights after carrying out the fuzzy

A

pairwise comparison considering the degree of confidence of decision maker. Table 7: Fuzzy pairwise comparison of safety sub-index for solvent design on oil extraction

Flammability Explosiveness

Flammability

Explosiveness

Priority Vector

1

(1/3, 1, 3)

0.5

1

0.5 30

λ=1

Exposure limit and acute health hazard indices are assumed to be equally important with moderate confidence. The current permissible exposure limit for hexane in Malaysia is relatively low, at 50ppm TWA. Since hexane has high volatility, it is easily inhaled by a

IP T

human, leading to the risk of nerve when there is an increase in exposure time and level. Thus, while designing the alternative solvent to replace hexane, it is necessary to use a penalty

SC R

score for exposure limit. Hexane has relatively low acute toxicity towards rat through

ingestion where their oral rat LD50 is 28000 mg/kg. However, it is also important to consider

U

acute health hazard of a molecule during the design stage to ensure that the designed

N

molecule has low acute toxicity when being accidentally swallowed. The intensity of

A

importance assigned to each health sub-index along with the degree of confidence is shown in

M

Table 8.

Table 8: Fuzzy pairwise comparison of health sub-index for solvent design on oil extraction

Exposure limit

1

Priority Vector

(1/3, 1, 3)

0.5

1

0.5

CC E

λ=1

Acute health hazard

PT

Acute health hazard

ED

Exposure limit

The following steps include the calculation of final weighting factors of each sub-property in the overall system. It can be calculated by multiplying weighting factors of sub-property with

A

the weighting factor of its main property. The final weighting factors of target properties in the overall system for this case study are reported in Table 9. Table 9: Final weighting factors of target properties in the overall system Target Property

Final weighting factor

Boiling point

0.1618 31

Surface tension

0.0587

Viscosity

0.0587

LC50

0.0154

PCO

0.0556

log Koc

0.0067

BCF

0.0067

Flammability

0.2603

Explosiveness

0.2603

Exposure limit

0.0507

Acute health hazard

0.0507

IP T

0.0312

SC R

Solubility

U

3.6 Molecular design stage

N

The following step includes the selection of molecular building block based on the molecular

A

structure of the conventionally used solvents in oil extraction process. The chosen molecular

M

groups for this case study include C, CH, CH2, CH3, OH, COOH, CHO, CH-O, CH3CO, CH3O, CH2O, NH2 and CH2=CH. To ensure the formation of a structurally feasible molecule

ED

without having any free bonds, structural constraints expressed in Equation (10) and Equation (12) or Equation (13) are implemented. Equation (10) and Equation (12) are used for

PT

designing acyclic compounds whereas Equation (10) and Equation (13) are utilised for the

CC E

design of monocyclic compounds. 3.7 Optimisation model The target property models, as well as safety and health indices, are first transformed into

A

their property operators as shown in Appendix 6.3. The property operators are represented by the linear combinations of the number of occurrence for a molecular group of type-i and its corresponding contribution. After determining the property operators, property operators are normalised using Equation (14) or Equation (15) depending on whether the target property is to be minimised or maximised. 32

The overall objective function for this case study can be expressed by Equation (31): F w e ig h te d s u m  w 1  T  w 2    w 3    w 4  R b

 w8 BCF  w9 I

where w 1 , w 2 , …,

w1 2

 w10  I

F L

c a r o te n e

 w5 LC

 w11 I

EX

EL

50

 w 6  P C O  w 7  lo g K

 w12  I

oc

(31)

AH

are the weighting factors determined from FAHP approach.

IP T

The design objective now is to maximise the value of Fweightedsum. This optimisation model is a mixed integer linear programming (MILP) formulation, which allows the global optimum to

SC R

be readily identified without major computational difficulties. Integer cuts are then introduced to produce alternate optimal and near-optimal solutions.

U

3.8 Results and discussions

N

Both acyclic and monocyclic solvents are generated for this case study. Ten acyclic solvents

A

are listed as solvent A1- A10 whereas the ten monocyclic solvents are listed as solvent B1-

M

B10. The molecular structures of the top ten acyclic and monocyclic solvents are displayed in

CH3

H 3C O

O

H 3C

O

Solvent A1: Dimethoxymethane Solvent A2: Propionaldehyde

O

O

CH3

CC E

Solvent A6

PT

O

O

H 3C

CH3

H 2C O

O

Solvent A3: Acrolein

CH3

H 3C

A

H3C

Solvent B6: 2-(2,2-Dimethylpropryl)oxirane

O

H 3C

Solvent A8: Methyl Acetate

Solvent A9: Butyraldehyde

CH3

CH3

H3C H3C

O

Solvent A10: Ethyl Formate

CH3

O

O

CH3

Solvent B2: methylcyclohexane

O H3C

Solvent B4

Solvent B3

H3C

Solvent B7

O

CH3

CH3

H3C

CH3

H 3C

O

Solvent A7

Solvent B5

CH3

O

O CH3

CH3 Solvent A5: Isobutyraldehyde

Solvent A4: Butanone

O

H 3C CH2

O

H3C

O

CH3

H3C

CH3 Solvent B1: 1,2,4 trimethylcyclopentane

H 3C

H 3C

ED

Figure 3.

H3C

O

CH3 H3C

Solvent B8: epoxyhexane

Solvent B9: 1,1,3 Trimethylcyclopentane

H3C

Solvent B10: methoxycyclopentane

Figure 3: Molecular structure of the best ten acyclic and monocyclic solvents

33

Appendix 6.4 shows the properties of the best ten generated acyclic and monocyclic solvents. The generated solutions will be selected based on their rankings. Nevertheless, it should be noted that the generated ranking for each molecule is not absolute, since there will generally be uncertainties in values of target properties and prediction models. In this case, the rankings of molecules represent the potential solutions from a huge search space. When a molecule is

IP T

positioned at a higher ranking, it means that the molecule has a better potential for a specific application. Thus, in a later stage, the molecule can be selected for further verification

SC R

through experiments.

From the results, solvents A1 and B1 have the highest Fweightedsum values which make them

U

ranked the first among all the generated acyclic and monocyclic solvents. The properties of

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the designed molecules were then compared with that of hexane. The properties of hexane are

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shown in Appendix 6.6. The results showed that Tb of top three acyclic solvents (solvent A1

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to A3) and solvent A5, as well as all the ten monocyclic solvents, are lower than that of hexane. Besides, Rcarotene of all generated solvents is smaller than that of hexane which means

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that carotenoids can dissolve better in those generated solvents than in hexane. Based on the results, Solvent A1 and solvent B3 have the lowest Rcarotene values among the generated

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acyclic and monocyclic solvent. When compared the generated solutions with the existing

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solution in literature, it is found out that solvent A8 (methyl acetate) has been shown to be a suitable solvent for extracting oil from oilseeds. In addition, all the generated solvents have improved properties in terms of soil sorption as their log koc values are lower than that of

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hexane. In terms of safety aspects, although all the generated solvents are carrying the same safety sub-index (IFL and IEX) scores as that of hexane, their flashpoint properties, especially for acyclic solvents, are slightly better than that of hexane. Solvent A6 and solvent A10 will be the least flammable compared to the other generated solvents as their Fp values are significantly higher. From the point of view of health aspects, the generated monocyclic 34

solvents exert a better characteristic in terms of the permissible exposure limit. All the generated monocyclic solvents obtained a better IEL score compared to that of hexane. Besides, by comparing the overall ISHI scores, solvent B1 and solvent B2 exhibit better safety and health performance compared to all the generated solvents and hexane. In addition, the results were compared to the case where FAHP method is not used for

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assigning the weighting factor to each property. In such case, each property is assumed to

carry the same weighting factor and the results are displayed in Appendix 6.5. From the

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obtained results, it shows that there is an abrupt change in the ranking of molecules for both

acyclic and monocyclic solvents. For acyclic solvents, solvent A6 and solvent A8 which

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ranked the 6th and 8th place have become the 2nd and 4th best solution respectively in the case

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where all the property is assumed to carry the same weighting factor. This may be caused by

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the weighting factor assigned to the boiling point is significantly different. When using the

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proposed FAHP method, the relative importance of each property can be known and Tb is carrying a weighting factor of 0.1618. On the other hand, when assuming all the properties

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are having an equal weighting factor, a weighting factor of 0.08333 is assigned to Tb. This may be the reason why solvent A6 and A8 which were having significantly higher Tb values

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were ranked the 2nd and 4th place. For monocyclic solvents, solvent D5 and D9 have dropped

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out of top ten solvents when proper weighting factor is assigned by using FAHP approach. Thus, it shows that the molecular ranking is sensitive to the weighting factor of each property. It is important to evaluate the relative importance of each property to assign a proper

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weighting factor to each property as different weighting factor will generate different optimal solutions. 4. Conclusion In this work, a systematic multi-objective CAMD framework using FAHP weighting approach has been developed for the optimal design of molecules with multiple properties. 35

This proposed methodology quantifies the subjective judgement of a decision maker through a fuzzy scale that considers their degree of confidence when eliciting the relative importance of each property. With the use of this methodology, the process of evaluating the relative importance of product properties can be done more systematically. Hence, a more precise relative weighting factor which reflects the preferences of decision-makers can be assigned to

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each criterion. A case study on solvent design for extracting residual oil from palm pressed fibre is solved to illustrate the proposed methodology. The results obtained show the best

properties as well as safety, environmental and health aspects.

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balance of performance for criteria from different categories such as physicochemical

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The assumption made in FAHP approach is that all the criteria involved are independent of

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each other. However, in practice the relationship among criteria is usually complex, and there

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might be interdependencies. Thus, future work can be conducted by extending the multi-

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objective CAMD methodology to capture such interdependencies among various criteria involved in molecular design. For instance, business or economic aspects may conflict with

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SHE considerations. Even then, it remains crucial to consider the cost factor during the

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molecular design stage to identify the optimal process-product design. Acknowledgements

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The financial support from the Ministry of Higher Education, Malaysia through the LRGS Grant (LRGS/2013/UKM-UNMC/PT/05) is gratefully acknowledged.

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