Evolutionary algorithms on reducing energy consumption in buildings: An approach to provide smart and efficiency choices, considering the rebound effect

Accepted Manuscript Evolutionary algorithms on reducing energy consumption in buildings: An approach to provide smart and efficiency choices, considering the rebound effect Ricardo S. Santos, J.C.O. Matias, Antonio Abreu, Francisco Reis PII: DOI: Reference:

S0360-8352(18)30466-2 https://doi.org/10.1016/j.cie.2018.09.050 CAIE 5435

To appear in:

Computers & Industrial Engineering

Received Date: Revised Date: Accepted Date:

21 March 2018 7 August 2018 26 September 2018

Please cite this article as: Santos, R.S., Matias, J.C.O., Abreu, A., Reis, F., Evolutionary algorithms on reducing energy consumption in buildings: An approach to provide smart and efficiency choices, considering the rebound effect, Computers & Industrial Engineering (2018), doi: https://doi.org/10.1016/j.cie.2018.09.050

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Manuscript Title: Evolutionary algorithms on reducing energy consumption in buildings: An approach to provide smart and efficiency choices, considering the rebound effect Authors: Ricardo S. Santos1 J.C.O. Matias2 Antonio Abreu3 Francisco Reis4

Affiliations/Contacts: 1

University of Aveiro, Portugal Govcopp - University of Aveiro Postal address: Campus Universitário de Santiago, 3810-193 Aveiro, Portugal E-mail: [email protected] 2

Dept. of Economics, Management, Industrial Engineering and Tourism (DEGEIT) University of Aveiro, Portugal C-MasT – University of Beira Interior Govcopp - University of Aveiro Postal address: Campus Universitário de Santiago, 3810-193 Aveiro, Portugal E-mail: [email protected] 3

ISEL- Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa CTS Uninova, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal Postal address: Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal E-mail: [email protected] 4

ISEL- Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Postal address: Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal E-mail: [email protected]

Corresponding Author: Ricardo S. Santos E-mail: [email protected] 1

Abstract This paper presents a model to promote energy efficiency among household appliances, by supporting the consumer decisions through the maximization of his savings, associated to a set of electrical appliances from the market to be acquired. Not always an efficient equipment from the market, is more expensive than a less efficient one, which can lead the consumer to compromise the expected savings on future. Given the several models/brands available on market and its possible combinations, the problem can be defined as a combinatorial problem, whose complexity can compromise the efficiency of using deterministic algorithms. Genetic algorithms (GAs) were therefore included in the model, whose results were compared later with Simplex to verify the quality of the obtained solutions, as well as their performance. In addition, it was performed a statistical analysis of the obtained results, as well as a sensitivity analysis of GAs parameters, to validate their robustness. we conclude that the proposed method can provide several efficient solutions to the problem, as well as sensitize the consumer to their choices made on future, by estimating their corresponding rebound effect. Keywords: Energy efficiency, Genetic algorithms (GAs), Simplex method, Life Cycle Cost Analysis (LCCA), Indirect Rebound Effect

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1. Introduction Energy is an important element of today’s society, with energetic necessities highly correlated with issues like population’s growth, economic development and technology progress (Matias et al., 2011). Despite the recent advances in technology progress, there was an increase on energy demand in the last years, which can compromise the several commitments made, in order to reduce Greenhouse Gas Emissions (GEE) to the atmosphere, since the electrical energy production is still highly dependent on the use of fossil fuels IPCC (2015). In this sense, and according to IEA (2017a), the reduction of energy consumption is a priority to reach sustainability, with buildings accounting for about 30-45 percent of the energy consumed in most countries (Gul et al, 2015). Regarding the residential sector, the share of electrical energy consumption, represents about 13,9 % of the final energy consumed in the world in 2012 (EIA,2012), while in Portugal, this value is about 18 % of final energy consumption (Santos, 2012), representing thus an important area and an opportunity to increase energy efficiency. In the last years, there were made some energy efficiency improvements, regarding electrical household appliances, by establishing some measures, like the European Directive 2010/30/EU, in which, was established the mandatory labeling, by classifying these appliances regarding their consumption, promoting therefore the energy services cost reduction, and their equivalent CO2 emissions (DGEG, 2002 & ADENE, 2017). This is relevant to inform the consumer about important issues, specifically regarding each appliance (energy consumption, noise, capacity in litters (fridge), clothe capacity (washing machine), among others), promoting therefore an adequate use of each appliance, adjusted to the consumer needs (Wong and Krüger, 2017).

In this sense, and given the several options available on the market, it’s difficult to analyze what’s the best solution to adopt regarding the issues referred before, in order to satisfy the individual needs of each consumer (Hoxha and Jusselme ,2017 & Fell, 2017 & Krivošík and Attali, 2014). The problem increases, when we know that each appliance has its own and distinct characteristics, which varies by brand and model to buy, making the cost-benefit ratio very different, and sometimes difficult to analyze given the different equipment life cycles, energy consumption, among other issues (Wong and Krüger, 2017). Given the different options available on the market and regarding each dimension, the number of possible combinations could be substantially bigger with the increase of the number of dimensions considered for the problem (e.g. lighting, clothes dryer machines, electric ovens, etc.), as well as the number of options/dimension available on the market, which can lead to the existence of several tradeoffs between them. Therefore, and considering a decision maker (consumer) who wishes to acquire different types of household appliances, he will have to deal with a problem of combinatorial nature, which can be tackled by using optimization techniques. Additionally, and regarding the choices with household appliances, there could occur a Rebound Effect phenomenon, which can compromise in a long/short term the efficiency expected, regarding each household appliance chosen on the present (e.g. the influence between air conditioner and lighting) by changing it, and therefore change the expected savings. According to IRGC (2013), the Rebound Effect is linked to the consumer behavior, and it’s normally difficult to estimate him, hence the importance on his estimation, and therefore his reduction Gonzalez (2017). One way to do it, could be by improving the consumer behavior (Ouyang et al, 2010), by trying to catch his attention on the present, to the savings that he could earn or lost with his choices in the future in a long/short term. The purpose of this work, is to present a methodology in order to support the decision maker (household consumer) on the acquisition of a set of desired electrical appliances, satisfying therefore his different needs (economics, comfort, among other issues) and providing at the same time, efficient solutions that tries to minimize the energy consumption, and therefore, its implications into the environment and society. Additionally, and recurring to the concept of Rebound Effect, it is also the purpose of the methodology presented on this work, sensitize the consumer for the implications of his options in the future, so he can avoid on present, the (eventual) negative impacts, that can compromise the efficiency achieved before. To validate the presented methodology and to show its applicability, it is presented on this work a case study with a consumer, who wants to acquire a set of household appliances, by predicting a set of available budget scenarios.

1.1 Literature review Several entities, including governments, associations and manufactures, have tried in recent years through measures, to sensitize the population to the problem of energy efficiency in the residential sector IPCC (2015). (Carli et al, 2017) Other studies found on literature, are based on a type of approach which is mainly economical, giving actions that, and for the same initial investment, it allows to achieve the highest energy savings (e.g. Jafari and Valentim, 2017). Following this principle, there are some approaches regarding energy management, like the ones based on control techniques (e.g.

3

Rodrigues et al, 2017), or even, those based in schedule methodologies (e.g. Martinez-Pabon et al, 2018 & Azaza and Wallin, 2017) for instance. However, this type of approaches is considered somehow Diakaki et al, 2010 & Malatji et al, 2013)

č

ė

optimization with multicriteria techniques in order to obtain feasible solutions, by exploring a large number of alternative measures/solutions, which were pre-selected, according to a set of criteria, suitable to the consumer needs (e.g. Pombo et al, 2016, Jafari and Valentin, 2017). Some of these approaches, explore several issues (e.g. benefit-cost analysis, initial investment, CO2 savings, energy savings, among others) of retrofitting measures (e.g. Asadi et al, 2012, Mauro et al, 2015, Heo et al, 2015), as well as measures and technologies combined (e.g. Wang et al, 2014, Tan et al, 2016, Jafari and Valentin, 2017).

However, the use of traditional optimization techniques, usually begins with a single potential solution of the problem, which is iteratively manipulated until finding a final solution, normally unique (Antunes and Climaco, 2016), thus reducing the available feasible options to the DM (household consumer), which is in this case, undesirable. Additionally, some algorithms (like the ones based on gradient methods), have the inconvenient to find (frequently) a local minimum or maxima, having therefore, some limitations on exploitation of the entire feasible region (Antunes and Climaco, 2016). In order to cope with the difficulties presented above, methods based on metaheuristics, have been applied as an efficient tool to provide a set of feasible solutions, such as greedy strategies (e.g. Ogwumike et al, 2016), Particle Swarm Optimization (PSO) (e.g. Ting et al, 2006 & Pedrasa et al, 2010), Simulated Annealing (SA) (e.g. Ferreira and Lemos, 2010) and Genetic Algorithm (GA) (e.g. Agrawal and Rao, 2014, Ko et al, 2015), among others. These methods are characterized by stochastic nature, global search ability, and a large amount of implicit parallelism (Randall et al, 2015, Abreu et al, 2015). The use of evolutionary algorithms (GAs), like Genetic Algorithms (GAs), allows to obtain different and feasible solutions (Goldberg, 1989 & Randall et al, 2015) i.e., different sets of efficient appliances to attend the consumer needs. Although, and regarding metaheuristic methods, the major deficiencies still are too many control parameters and quite sensitive to initial values of these parameters, which frequently, involves a non-negligible increase of the efforts for properly tuning the control parameters (Kaboli, 2017a, Cortés et al, 2018). Therefore, one of the main objectives of this work is to provide efficient solutions to the consumer from the market, concerning Energy and CO2 savings, as well as the initial investment, satisfying at the same time his different needs according to a set of criteria previously stablished. In this sense, and to achieve several efficient solutions, it was used GAs whose quality results, were tested as well as its robustness attending the concerns referred above. Rebound effect was also included as an indicator on this methodology, since that some of the works don’t take into consideration the possibility of Rebound Effect, associated with the choices made on the present, although there have been some studies about this phenomenon, indicating its relevance and impact on the residential sector (e.g. Chitnis and Sorrell (2015), Lin et al (2013), Gonzalez (2017), IRGC (2013), Thomas (2013)). According to Thomas and Azevedo (2013), the Rebound Effect can be divided into Direct and Indirect Effect, referring thus, the difficulty on his estimation (e.g. Bielle et al, 2018 & IRGC, 2013). In this work, it will be studied the Indirect Rebound Effect. On literature, it’s frequent to find several methods to estimate the indirect rebound effect, like those based on Elasticity of substitution (e.g. Frondel, 2004), Computable general equilibrium (e.g. Barker and Foxon, 2006), econometric models (e.g. Barker et al., 2007), studies on energy, productivity and economic growth (e.g. Stern, 2000), input–output analysis 4

(e.g. Sartori and Hestnes, 2007), or more recently based on direct rebound effect and the use of energy input-output coefficients (e.g. Gonzalez, 2017), among others. However, these studies are usually carried out in a different scope of analysis, considering several families, involving cities, regions or even countries, thus assuming at the same time, some premises and neglecting others (González, 2011). According to Gonzalez (2011), it is possible to calculate the monetary savings of energy efficiency improvements and assume that this increase of disposable income is reused into other services that needs energy to be produced. This approach provides several scenarios to allocate new available income, which can be moved towards either to a new consumption or savings, depending on the household consumption patterns, and therefore their behavior. The indirect rebound effect will be therefore estimated by making a change in household consumption patterns, through the change of light energy services during the air conditioning life cycle. For this purpose, it will be used the life cycle cost analysis (LCCA), by considering the changes in consumption patterns, through scenario evaluation. According to Ouyang et al, 2010), the rebound effect can be mitigated, through an improvement on consumer behavior, by trying to catch his attention to the savings that he could earn or lost with his choices in the future in a long/short term, which can be done by estimating the phenomena, and therefore, the losses around efficiency expected. In this sense and given what was referred before, the purpose of this work, is to present a methodology to support the decision maker (consumer), with efficient choices, given the issues previously discussed.

1.2 Paper contribution The discussed related literature, clearly shows two gaps in the context of retrofit strategies for buildings: on one hand, there is an evident lack of support decision approaches, that allows to provide the decision agent (typical household consumer) with efficient solutions (electrical household appliances) from the market, satisfying therefore both consumer needs as well as the environment and economic concerns (e.g. energy savings, investment savings, CO2 savings, initial investment, among others). On the other hand, the same discussed literature, shows the lack of works that uses rebound effect as an indicator to sensitize the household consumer for the efficiency in the future, achieved with solutions (electrical appliances) obtained on the present, from methodologies like the one presented on this paper. To fill the discussed gaps in the literature, this paper develops a decision support approach that identifies an optimal set of electrical appliances, available from the market, regarding each energy service desired by the decision agent. The main goal of this solutions is to promote energy efficiency (e.g., energy consumption savings, CO2 consumption savings, initial investment) and satisfying at the same time the building’s user/occupant needs, given a limited budget to do. To do this, the approached performs a Life Cycle Cost Analysis (LCCA) of each solution, recurring as well as the Rebound Effect, as an indicator to improve/maintain the energy efficiency solution of one dimension (air conditioning) during its life cycle. This solution was chosen on the present from the methodology presented on this work. This allows to provide the decision maker (household consumer) with information about the best choices that he should made in a long term, to prevent in the future, the energy efficiency reduction regarding the options chosen on present.

2. Material & Research Method 2.1 Nomenclature - Number of efficient options allocated to each dimension j - Efficient option i belonging to dimension j of the problem - Value of objective function - Parameter value for each efficient option i belonging to the dimension j - Investment savings, associated with a given option effective i belonging to the dimension j of the problem - Consumption savings associated with a given option i belonging to the dimension j - Costs associated with the consumption of standard option i, belonging to the dimension j - Costs associated with the consumption of efficient option i, belonging to the dimension j - Investment associated with the use of standard option i, belonging to the dimension j - Investment associated with the use of efficient option i, belonging to the dimension j - Total investment associated to each individual/solution

2.2 Problem dimensions and case study The problem presented here, will consider a decision maker (e.g. household consumer), who wants to acquire a set of electrical appliances (energy services) from the market, as described next. The dimension of the problem (j) corresponds to the number of different types of appliances that can be purchased by the consumer, and the number of combinations will 5

depend on the number of available options (i) regarding each dimension, which in turn, corresponds to a high number of possible options for the user (about 22 million of possible combinations in this case). This number could be reduced, if we consider that the consumer cannot make any choice, since he has a limited budget to do, which greatly affects the process of getting feasible solutions. Each available decision xij, corresponds to an option i, regarding a dimension j of the problem (Fig.1), which are, as follows:       

Dishwasher Oven Dryer machine Lighting Refrigerator Air conditioning Washing machine

The consumer has a limited budget to acquire the appliances that he needs, and after a market research, he founds a set of available solutions. Given the trade-off referred above and the diversity of features regarding each solution, respecting to each dimension, the consumer will be confronted with a problem of combinatorial nature, corresponding to a various possible alternative of choice (Fig.1). J Dimension

Lighting

Air Conditioner

Washing machine

Dryer machine

x11

x12

x13

x14

x15

x16

x17

x21

x22

x23

x24

x25

x26

x27

x31

x32

x33

x34

x35

x36

x37

x101

x102

x103

x104

x105

x106

x107

Refrigerator

Oven

Dishwasher

Option

Option i

Xij

ij

Solutions

Fig. 1. Consumer’s decisions space

One way to promote energy efficiency through household’s appliances, is to maximize their utility, by selecting the appliance, suitable to each household and their occupants (Toulouse, 2013). This can be done, by considering some aspects such as the consumer needs (type of electrical appliance to be acquired), the number of household occupants and the available budget. Therefore, the solutions are selected according to a set of criteria in order to improve the use of the selected appliances, to be acquired by the consumer (decision agent). The process is presented on Fig.2.

Optimal Process Consumer initial data:

  

Appliances to be acquired (Problem dimensions) Number of household occupants Available budget

Savings regarding each option i and dimension j:

Adopted Criteria

VR  xij  



 f Pconsij ( xij ) , Pinv.ij ( xij )

Electric Appliances (solutions) chosen by the consumer:

No

GA solver



Market (Electrical appliances)

Solutions acepted by the consumer?

Yes

      

Ligting Air Condicioner Wash Machine Dryer machine Refrigerator Oven Dishwash

Fig. 2. Decision support process

In this work, it was considered a building with four occupants (e.g. family), where each available solution was preselected, according to the following criteria, presented on Section 2.3. In addition to the methodology presented before, the consumer wants to explore the consequences of his choices in the future, by predicting an eventual situation of indirect rebound effect through the study of the influence of his future behavior (from his choices with lighting appliances) into the efficiency achieved regarding the air conditioner that he will choose on the present.

6

The indirect rebound effect will be estimated by using scenario simulations during the air conditioner life cycle (which has been selected by using the methodology presented on previous section), and by making changes around the different light appliances considered on Table I and according to scenarios considered on Table II.

2.3 Adopted criteria Air conditioner According to ADENE (2017), the air conditioners, represents about 2% of energy consumption. In this work, it was considered the following types of air conditioner:    

Wall (mono split) Wall (multi split) Monoblock Portable

In this work, it was considered just the living room as the zone to be heated/cooled by the air conditioner. To define the needs for heating / cooling and therefore the air conditioner capacity, it was considered the following thermal load calculations. According to ASHRAE (2009), the heat balance equation in steady-state (considering non-conditioned) mode, is given through the sum of the following heat losses/gains: Qsolar  Qint  Qcond  Qvent  0

(1)

Where: Qint [W] Qvent [W] Qsolar [W] Qcond [W] -

internal gains (nr. of occupants, electric appliances, etc) air change (forced or natural) solar radiation (windows, etc.) heat losses through the envelope (conduction through the external walls, etc.)

By preforming these calculations, the minimum capacity obtained was 9905,6 BTU, as a minimum capacity requirement for the air conditioner. Washing Machine Since highest machine’s capacities, normally requires higher quantities of water and energy, it’s important to suit his capacity with the consumer needs to avoid a situation of waste of water and electric energy (DGEG, 2002). This can be done, based on the number of household’s occupants (Table I - ANNEX I), resulting in this case, in seven kilograms of load capacity. Dishwasher The choice of the type of appliance can be done by adjusting his capacity, according to the occupant’s needs. In this case, the capacity to be considered, was defined by choosing the value through Table II - ANNEX I, where only dishwasher machines with 12 cutlery of load capacity were considered. Oven The criteria used to choose the suitable oven, was the useful volume, available for cooking and according to the number of occupants (Table III – ANNEX I). Dryer machine For these appliances, the previous selection was made by considering two types of dryer machines:  Dryer machines by exhaust  Dryer machines by condensation Another considered criteria, was the load capacity. Through Table I – ANNEX I, and according to the number of occupants considered before, it was considered 7 kilograms of load capacity.

7

Lighting The technologies and the criteria, used for the present case, are shown on Table IV (ANNEX I) where it was taken into consideration the quantity of investments needed by the standard technology, to be equal to each efficient one, with more available life cycle. Refrigerator The capacity of the refrigerators, available on the market, was established according to the data presented on Table V ANNEX I, where, and based on the number of occupants in the case study, it was chosen the refrigerator Combined type. Other criteria used in this work, was the classification "number of stars", given the influence in the electrical consumption, since it is related with the maximum time of food frozen (1 month in this case) and with the number of occupants. Thus, and for the present case, it was selected refrigerators with two stars (Table V - ANNEX I).

2.4 . Problem formulation & GAs individual framework Based on the diagram of Fig.1, we can define the decision variables of the problem:

Where the objective is to optimize the savings for the consumer, by making a several efficient choices:

subject to

Rk ( xij ) : k  1..8   xij  0,1   i  1, 20  j  1..7 

(4)

According to the results, obtained from Santos et al (2013), it was considered the following objective function:

which leads to:

Where and are variable parameters, regarding the correspondent savings obtained both in consumption and investment respectively and for a given solution i, regarding to a dimension j. These parameters were obtained by previously making a lifecycle assessment regarding each selected appliance. Since each appliance has not the same impact level on the total investment, it was created a weight , applied to each dimension in order to improve the search in GA for better solutions. The weight is given by:

This weight is based on each investment, and regarding each option, compared to the total investment associated to each individual/solution. Since just only option i, can be selected from each dimension j, the correspondent constraints are: 20

R1 ( xi1 ) :  xi1  1  xi1  ,  i  1..20  xi1  0,1 

(8)

i 1

11

R2 ( xi 2 ) :  xi 2  1  xi 2  ,  i  1..11  xi 2  0,1 

(9)

i 1

8

10

Rk ( xij ) :  xij  1  k  3..7  xij  ,  i  1..10 , j  3..7  xij  0,1  (10) i 1

The constraint associated with the total investment made (budget), can be defined as follows: R8 ( xij ) : I total  xij    xi1.I efi1   xi 2 .I efi 2   xij .I efij I total  20

11

i 1

i 1

7

10

j 3 i 1

 xij  0,1 

(10)

The GAs individual framework is presented on Fig. 3: x11 x21

Lighting

x201 x12 x22

x102 x13 x23

Air Conditionning

x103 x14 x24

Clothes Dryer Machine

x104 x15 x25

Clothes Washing Machine

x105 x16 x26

Refrigerator

x106 x17 x27

x107

Dishwasher

Oven

Fig.3.GA’s Individual framework

The adopted codification of GAs was binary, mainly in terms of the additional number of constraints. For GAs implementation, it was considered the following parameters:         

Population size: 350 individuals Selection method: Roulette Crossover method: 2 points Crossover rate: 0.7 Mutation method: 1 point Mutation rate: 0.06 Convergence: 0.001 Maximum number of generations: not defined Nº of runs/budget constraint scenario: 30

The mutation rate, as well as the population size, was achieved by preforming sensitivity analysis for both parameters (separately) as it will be presented and better described on Section 3. The crossover rate was set to 0.7, from to the work of Santos and Reis (2013) on solving a similar problem with GAs.

2.5 . Indirect rebound effect and its estimation Energy efficiency technologies are implemented, mainly to provide occupants with more comfortable household lifestyle, and to reduce at the same time the energy consumption. However, and throughout the useful life cycle of a chosen household appliance (e.g. air conditioner), the efficiency on energy conversion into their final service will change, either through changes associated with consumer behavior (e.g. choice of efficient lamps), or either by other structural changes (e.g. number of occupants). Therefore, the effective energy saved, will be different from the one initially expected, thereby occurring a phenomenon called Rebound Effect, which can be estimated by:

Re bound Effect (%) 

Expected Savings  Actual Savings 100 Expected Savings

(12)

One of the types of Rebound Effect is the indirect rebound effect. According to IRGC (2013), these phenomena results from the additional income, freed up by saving energy costs, which are used for other energy service or even by increasing consumption with the same energy service. In this case it will be studied the impact from the consumer behavior (through is choices), by assuming that he chooses different light appliances (Table I), during the life cycle of the air conditioner considered on this work (10 years). Therefore, the internal loads regarding the air conditioner, will change also with the final energy consumption. According to Guertin et al (2003), the indirect rebound effect, regarding space cooling energy services, can reach 34-38 %. However, these values can be very different, depending on the country among other factors (González et al, 2011 & IRGC, 2013). In this work, the indirect rebound effect, was estimated by using Life-Cycle Cost Analysis (LCCA), by focusing the analyze on the interaction between two dimensions of the problem (Air Conditioner and Lighting) presented before, and mainly during the usage phase, since that the main goal is to analyze the possible impacts on the overall consumption, regarding the consumer choices (because of his behavior) on future. 9

To do that, it was conducted a set of possible scenarios predicting the consequences of consumer actions (Table II), by estimating the savings (both for investment and electrical consumption), considering the acquisition in the future of different lighting technologies, available on the market and performed in different time periods. Table I – SET OF CONSIDERED OPTIONS EEL1 class.

60,0 60,0 20,1 80,1

Eq.Nr. Same E [lux] 5 4 5 4

24,2 57,8

5 8

A A

Opt.

Technology

Life cycle [h]

P [W]

Eff.Flux [lm/W]

Std A B C

CFL CFL Halogen Reg. Fluorescent Halogen Led

8200 6000 2000 15000

11,0 13,0 35,0 10,0

5000 25000

29,0 7,0

D E

A A A A

On Table II, it’s presented the scenarios, considered for this work, by assuming an air conditioner life cycle of 10 years. Table II – SET OF CONSIDERED SCENARIOS Year/ Scenario

1..4

1

Option Std - CFL

2

Option Std - CFL

Option C – Option A Option E Halogen – CFL – Halogen Option D – Fluorescent

3

Option Std - CFL

Option F – LED

5..6

7..9

10

According to ASHRAE (2009), the internal loads from light-emitting, can be calculated using the following expression: qel .  3, 41.W .Ful .Fsa

(13)

Where: qel = heat gain [Btu/h] W = total light power [W] Ful = lighting use factor Fsa = lighting special allowance factor The total light wattage is obtained from the ratings of all lamps installed, where in this case the lamps is varied according to the following scenarios, presented on Table II. For the remaining variables, it was considered the following values: Ful  0, 78 1, 2 if regular fluorescent 1,10 if CFL  Fsa   1, 0 if ha log en  1,17 if led

(14)

Therefore, and considering an illuminance level (Em) of 300 lux for the living room, it was obtained the following values presented on Table III, regarding the heating loss calculations per lamp, and for the same value of Em (approx.). Table III – HEATING LOSS CALCULATIONS PER LAMP

Opt.

P [W]

Ful

Fsa

qele [W]

Std. A B C D E

11,0 13,0 35,0 10,0 29,0 7,0

0,78 0,78 0,78 0,78 0,78 0,78

1,10 1,10 1,00 1,20 1,00 1,17

32,18 38,04 93,09 31,92 77,13 21,78

Nr.of lamps (same ilumin ance) 5 4 5 4 5 8

qele [W] Equiv.

Air Cond. [BTU/h]

160,92 152,14 465,47 127,67 385,67 174,27

10055,0 10025,0 11252,0 9905,6 10953,0 10116,0

2.6 . Material 1

EEL- Energy efficiency labeling

10

Additionally to the data referred before (Annex I), it was considered data regarding the annual electricity consumption as well as initial investment regarding each selected household electrical appliance and relative to each dimension of the problem (household category) presented above. This data was used to develop a Life-Cycle Cost Analysis (LCCA), regarding each appliance (Annex II). By considering the criteria referred above, it was also considered data through electrical appliances manufacturers (Annex II).

3. Simulation & Results For the model implementation, it was considered the case study presented on Section 2 and used the Risk Solver Platform software, combined with Excel VBA spreadsheet for the implementation of GAs. For Simplex implementation, it was used GAMS software. For the case study, it was considered 30 runs/budget scenario constraint, to validate the robustness of the proposed method. Both programs were executed on a personal computer with 2.70 GHz, Intel i7 processor and 4 GB of RAM memory. This comparison, between GAs and GAMS, was performed to assess GAs solutions in terms of quality, by comparing this with those obtained from GAMS. GAMS uses a solver based on Simplex method to solve the same problem. By preforming the following simulations, it was obtained the results presented on this section, concerning the use of the following parameters:       

Average nº runs/budget value: 12 Selection method: Roulette Crossover method: 2 points Mutation method: 1 point Crossover rate: 0,70 Mutation rate: 0.06 Population size: 350 individuals

Based on Santos and Reis (2013), it was achieved a parameter value for the crossover rate, of 0,70. Although, the best correspondent values of mutation rate and population size, were obtained by making a sensitivity analysis for the case study considered above. Therefore, the mutation rate value was selected to be 0.06 (6%) and population size was selected to be 350 individuals. The average number of generations/run/budget constraint scenario was 157. Regarding the average value of CPU time/run/budget constraint scenario, it was achieved 7,1 s for GAs and 12,3 s for Simplex.

3.1 Quality assessment of obtained results by using Genetic Algorithms (GAs) The following results, presented on this section, are regarding the best solution found, and concerning to each value of the available budget. In case of the investment, made by the consumer, it was considered a budget constraint scenario that varies from 1800 to 3000 euros. Using the formulation proposed before, the model was simulated for different budget constraint scenarios and using both methods; GAs to obtain a set of feasible solutions and Simplex to provide an assessment of GAs solutions, in terms of quality. The results are shown on Figs.4 and 5, regarding the solutions for the investment to be supported by the family, and for each budget constraint scenario (Fig.4), as well as the respective cost (fitness) function containing therefore the correspondent solution (Fig.5).

Fig.4.Investiment to be supported by the family, at each value of the budget

Fig.5.Final value of the objective function for each scenario / budget

The results presented on Figs.4 and 5, allows to show the good quality of the obtained solutions from GAs, even by each budget constraint scenario and the respective initial investment or even by the cost function values (GAs and Simplex). 11

Regarding the average value of CPU time/run/budget constraint scenario, it was achieved 7,1 s for GAs and 12,3 s for Simplex. One solution of this problem, shall be used later to give an example of a set of efficient electrical appliances, chosen from the market by the decision maker (household consumer), as well as for the estimation of the correspondent rebound effect. In order to analyze GAs behavior and its consistency, it was performed, on following sections, a statistical and sensitivity analysis to its parameters (population size and mutation rate), as well as an evaluation of its convergence characteristics.

3.2 Statistical analysis & convergence characteristics As it was referred before, GAs is used to solve various types of combinatorial optimization problems by avoiding the local maximums and providing several feasible solutions. The comparison, presented on Subsection 3.1, between the proposed method and other optimization techniques from the literature (e.g. Simplex) proves the quality of the results achieved from GAs. However, since the method is based on metaheuristics and due to its stochastic nature, it was performed a statistical analysis to assess its consistency, as it suggested in some of related works with metaheuristics (e.g. Aghay Kaboli et al, 2017). In this sense, it was performed a statistical analysis with 30 runs/budget constraint scenario on solving the same problem by GAs, whose results were obtained and presented on Table IV. Through the values presented on Table IV, it is noted that the low values of standard deviation of the objective function (Vr) achieved by GAs, validates its robustness for solving the problem, presented in this case study. Table IV – Convergence results, considering 30 runs/budget constraint scenario of Gas (compared with Simplex) Objective function (Vr) Constraint Budget Scenario

Method

Simplex

1800

1900

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

-

-3.6400 3.1300 2.1000 2.3500 2.1200 2.1650 2.1400 2.1200 2.1000 2.2500 2.1700 2.1100 2.1700

Minimum

1.7784 1,8187 1.9177 2.1980 2.0180 2.0284 2.0282 2.0580 1.9381 2.1967 2.0582 1.9177 2.0284

Average

1.7800 2,9000 1.9200 2.2000 2.0200 2.0300 2.0300 2.0600 1.9400 2.2000 2.0600 1.9800 2.0300

Maximum

1.7816 1,9213 1.9223 2.2020 2.0220 2.0316 2.0318 2.0620 1.9419 2.2033 2.0618 1.9824 2.0316

Standard deviation

0.0112 0,0124 0.0123 0.0178 0.0183 0.0112 0.0124 0.0147 0.0149 0.0152 0.0154 0.0157 0.0160

GAs

The highly similar optimal results with worst negligible standard deviation (0.0183), validate the robustness of GAs for solving the problem of the considered case study (for a budget constraint scenario of 2200 euros). Although, and according to Table IV, the biggest range of the objective function (Vr) obtained by GAs for 30 independent runs, is between 2.1967 to 2.2033 (for a budget constraint scenario of 2700 euros), which also shows that GAs converges to almost the same optimal. Although the statistical results of the 30 runs presented before for each budget constraint scenario, shows the high degree of robustness of GAs, Fig.6 shows the convergence characteristics of the objective function during optimization to reconfirm the high performance of GAs for solving these types of problems.

Fig. 6 - Convergence results of the best individual fitness of each generation (budget constraint scenario of 1900 euros and considering 30 runs)

12

The high-speed convergence characteristics can be seen through Fig.6 within early generations/run. All 30 runs in each constraint budget scenario were initialized with different populations. This figure also proves the highly similar convergence characteristic among all the runs because the shaded regions (in the last iterations) are very thin as it can be seen on the same figure.

3.3 Sensitivity analysis As it was referred on the beginning of this section, the performance of the proposed method is affected by the control parameters, therefore the need to tune both parameters (crossover rate, mutation rate and population size) to reach the best results, as it shown on several studies (e.g. Modiri-Delshad et al.(2016) and Aghay Kaboli et al (2016)). As it was referred before, the value of crossover rate, was fixed into 0.70, according to the work of Santos and Reis (2013), and the last two parameters, were obtained by preform a sensitivity analysis. For this purpose, the mutation rate, was varied, from 0 up to 10 % with steps of 1 %. The population size was varied, from 50 up to 700 individuals with steps of 50. The maximum iteration values (number of generations) wasn’t fixed and only the correspondent parameter was changed. The correspondent results are graphically presented on Fig.7.

a)

b)

Fig. 7 - Sensitivity analysis, considering average values in 30 runs/budget constraint scenario of GAs (compared with Simplex) with application of different parameters values of: a) mutation rate b) population

For the same budget constraint scenario considered above, the sensitivity analysis is carried out to find the best control parameter. For the specific values of the parameters, these problem is run for 30 times and the statistical indices such as minimum, average, maximum, and standard deviation values of the optimal results among the trials were recorded. The correspondent results are presented on Table V. Table V – Sensitivity analysis (mutation rate and population size), considering 30 runs/budget constraint scenario of GAs (compared wit h Simplex) Objective function (Vr) Mutation rate (%) Simplex

GAs

0

1

2

3

4

5

6

7

8

9

10

-

3,1300

3.1300

3.1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

Minimum

1,7784

2.2567

2.4862

2,9843

3,1125

3,1225

3,1230

3,1093

3,0981

3,0675

2,8874

Average

1,7800

2.2583

2.4892

2,9870

3,1156

3,1250

3,1258

3,1123

3,1012

3,0721

2,8900

Maximum

1,7816

2.2599

2.4922

2,9897

3,1187

3,1275

3,1286

3,1153

3,1043

3,0767

2,8926

Standard deviation

0,0009

0.0007

0.0012

0,0009

0,0010

0,0008

0,0009

0,0010

0,0010

0,0015

0,0009

50

100

150

200

250

300

350

400

450

500

550

600

650

700

-

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

3,1300

Minimum

2,6976

2,7980

2,9834

3,1227

3,1092

3,0987

3,1217

3,1093

3,0975

3,0936

3,0431

3,0017

2,8468

2,2324

Average

2,7000

2,8000

2,9870

3,1258

3,1123

3,1012

3,1258

3,1123

3,1012

3,0982

3,0458

3,0041

2,8500

2,2350

Maximum

2,7024

2,8020

2,9906

3,1289

3,1154

3,1037

3,1299

3,1153

3,1049

3,1028

3,0485

3,0065

2,8532

2,2376

Standard deviation

0,0009

0,0007

0,0012

0,0010

0,0010

0,0008

0,0013

0,0010

0,0012

0,0015

0,0009

0,0008

0,0011

0,0012

Population size (individuals) Simplex

GAs

13

The results presented on Table V, as well as the ones from Fig.7, allows to show that GAs reaches the better optimal by selecting a mutation rate value between 0,04 (4%) and 0,08 (8%), and a population size value between 200 e 500 individuals. Therefore, we’ve decided to select the average values of both parameters, which in this case was 0.06 (6%) for the mutation rate, and 350 individuals for the population size.

3.4 An example of an obtained solution On Table VI, it is presented an example of a feasible solution obtained by GAs (it was considered a budget constraint scenario of 2600 Euros). It is also presented the savings in terms of CO2 emissions, regarding the choice of the efficient solution, compared with the standard (inefficient) one (approximated values). Table VI – Example of an efficient solution obtained from this approach Stand. Solution Dimension

Total Invest. (€)

Effic. sol. Total Invest

CO

Invest. Saving (€)

Consum. Saving (€)

Savings (kg)

2

Life cycle [hours/years]

Power [W]

Brand

Model

(€)

Lighting

15,89

10,55

5,34

58,44

28,5

8000 hours

11,0

Philips

Air Conditioning Refrigerator Dishwasher Machine Washing Machine Oven Clothes dryer Total:

368,0 250,0

299,0 529,0

69,0 -279,0

1315,6 704,11

1315,57 8,5

10 years 10 years

930,0 170,0

Electro Indesit

GENIE ESAVER 11W/827 TC N12KRH PORT TAN13FFS

310,0

349,0

-39,0

3,2

6,2

10 years

1050,0

Fagor

1LF-011S

262,0 170,0 349,0 1724,89

294,0 199,0 419,0 2099,55

-32,0 -29,0 -70,00 -374,66

6,85 1,3 11,32 2100,82

94,8 2,6 1,8 1457,97

10 years 10 years 10 years -

1150,0 2100,0 3930,0 9171,0

Zanussi Candy Indesit -

FLN1009 FST100X 1SL79C -

An emission factor was used, as a carbon footprint indicator, to calculate CO2 savings (IEA, 2017b). According to Table VIII, if the consumer, opts for the efficient solution, he can save up to € 1726,16 (€ 2100,82 -374.66), contributing thus, to a reduction of about 1457,97 kg of CO2 for a time horizon of 10 years, according to life cycle considered in this work.

3.5 Consumer education by estimating possible indirect rebound effect As it was mentioned before, the indirect rebound effect, was estimated by using Life-Cycle Cost Analysis (LCCA) by focusing the analyze on the interaction between two dimensions (air conditioner and lighting) of the problem presented before, and mainly during the usage phase, since that the main goal is to provide the consumer with information, regarding the impact of his choices on the future in terms of costs with energy, as well as CO2 emissions. Since both indicators are proportional to the electric consumption, on the following figures (Figs.7, 8 and 9), are graphically presented the projections, regarding the 3 scenarios presented before (Table II). The values are related to the overall electric energy consumption, accumulated with the years.

Fig. 7. Household electric appliances consumption – Scenario 1

Fig.8. Household electric appliances consumption – Scenario 2

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Fig. 9. Household electric appliances consumption – Scenario 3

The numerical results are presented on Tables I, II and III – ANNEX III, respectively. Through the obtained results, it is noted the relevance on the difference between the consumption patterns, mainly through the observation of numerical values, where according to the solution obtained (Option Std-CFL), the decision-agent (consumer) would have better results for the next 10 years, if he chooses Scenario 2, where the rebound effect assumes negative values, suggesting that the energy efficiency could be improved with the new choice, at the same time that the chosen lamp has more life cycle, and therefore, this is the scenario with the best electrical energy consumption (accumulated). Although this could not satisfy the consumer, so through this method, he can choose the 2 nd best Scenario, or even run again the model presented before to get a previous solution, where he can obtain new projections and therefore choose the best scenario.

4. Conclusions In this work, it was presented an approach to provide efficient solutions (electrical household appliances) from the market to the Decision Maker (DM) (e.g. a typical household consumer), satisfying therefore both DM needs (which were pre-selected according to a set of specific criteria regarding each type of energy service (electrical appliance), as well as the environment (CO2 savings) and economic rationality (initial investment and energy consumption savings). In this work, it was also intended to test this approach with GAs, in order to assess is efficiency (computation time), as well as its effectiveness (quality of solutions achieved) and its behavior in terms of convergence results and robustness to the change of some of its parameters. The assessment of its effectiveness (quality of solutions achieved), was performed by comparing the results from GAs, with the ones from another technique Simplex, which have a deterministic behavior and is also used as one of traditional optimization techniques to solve combinatorial problems. The results for a budget constraint scenario between 1800-3000 euros, allows to show the good quality of the obtained solutions from GAs, even for each budget constraint scenario, given de small difference between GAs and Simplex cost function values. The efficiency of each algorithm was also favorable to GAs, since the results presented on section above, were achieved with less time (in average/budget constraint scenario) than the ones from Simplex Through the statistical analyze of its convergence behavior, GAs has demonstrated some consistency on the final achieved results, given the negligible standard deviation reached, as well as on convergence characteristics, demonstrating high convergence on early iterations. The high robustness of GAs, was also demonstrated, even for mutation rate, or even for the population size, by previously tuning its parameters (mutation rate and population size). Although Simplex has provided the best results for this problem rather than GAs, it is possible to run the model by using GAs, providing therefore diversity (and quality) in the obtained solutions, compared with those obtained from Simplex. GAs, can also provide efficient solutions with less time than Simplex, which is important, since the DM is faced with several available options on the market, associated with several trade off’s, regarding the existence of different criteria. The model is also flexible, in respect to be reduced or expanded into other problem dimensions or energy services that the DM who might need at the time. Therefore, it is an approach, where the DM can have an efficient solution or a set of efficient solutions, that attends to its specifically needs, and at the same, promote energy, investment and CO2 savings and reducing as well, the initial investment associated with that choices. The estimation of Rebound Effect by predicting the consumer behavior through is choices on the future, can be particularly interesting, in order to provide him with some information regarding the impacts of his choices in terms of consumption, allowing him to make the best options in the future. Other dimensions could be explored on further work, such the electronic equipment’s, or even a future application, applied into an industrial context, which could promote energy consumption, investment and CO2 savings, from a set of efficient equipment’s.

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Annex I – Adopted criteria TABLE I - WASHING MACHINE LOAD CAPACITY [ DGEG (2002)]

TABLE II – DISH WASHING MACHINE LOAD CAPACITY [SOURCE: DGEG(2002)] Nº Occupants

Nº Occupants

Load Capacity [kg]

1-2 3-4 5 or more

6 7-8 >8

TABLE III - OVENS VOLUME CAPACITY [SOURCE: DGEG (2002)]

Size

Volume (l)

Small Average Large

12-35 35-65 65

Type Simple Combined “American” type

Nº Stars ** ** **

N.Occupants 1-2 2-6 >6

1 2-3 4 or more

Average Capacity [l] 180/200 225/320 550

<10 10-12 >12

TABLE IV - LIGHT TECHNOLOGIES AND CRITERIA [SOURCE: EDP (2010)]

Features/ criteria Power (W) Light Eficiêncy (lúmen/W) Life Cycle (h)

TABLE V - TYPES OF REFRIGERATORS [SOURCE: DGEG (2002)]

Load Capacity [cutlery]

Incandescent Lamps Clássic Halogén 15-2000 20-2000

Fluorescent Lamps Tubular CFL 15-58 9-23

8-15

15-25

58-93

55-65

1000

2000

12000 a 18000

6000 a 15000

Annex II – Pre-calculations to achieve

and

and data about the available choices on the market

considered in this work TABLE I –LIGHT

TABLE II AND III – AIR CONDITIONING

TABLES IV AND V - D ISH WASHING MACHINE

TABLES VI AND VII – CLOTH WASHING MACHINE

TABLES VIII AND IX - REFRIGERATOR

TABLES X AND XI – OVEN

TABLES XII AND XIII - DRYER MACHINE

Annex III – Household electric appliances consumption – Considered scenarios TABLE I –HOUSEHOLD ELECTRIC APPLIANCES CONSUMPTION – SCENARIO 1

TABLE II –HOUSEHOLD ELECTRIC APPLIANCES CONSUMPTION – SCENARIO 2

TABLE III –HOUSEHOLD ELECTRIC APPLIANCES CONSUMPTION – SCENARIO 3

Paper: Evolutionary algorithms on reducing energy consumption in buildings: An approach to provide smart and efficiency choices, considering the rebound effect

Highlights 

Energy efficiency can be achieved through an optimal choice of household appliances



The approach provides the consumer, with savings on consumption, and investment



Genetic Algorithms provides feasible and different solutions



Estimating Rebound Effect, allows the consumer to make better options in the future



The approach, can be extended to other dimensions, to reduced energy consumption