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Optimization under uncertainty: A perspective of soft computing
Applied Soft Computing 56 (2017) 541–542
Contents lists available at ScienceDirect
Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Editorial
Optimization under uncertainty: A perspective of soft computing
1. Introduction Optimization permeates all endeavors of human activities and exhibits a remarkably high diversity of methopdologies and tools when coping with the complexity of problems. There is no surprise that with the ever-increasing complexity of problems, optimization comes with an inherent facet of uncertainty conveyed in different formal ways. This calls for innovative approaches to develop optimal and interpretable solutions as well as deliver user-centric environments. Soft Computing with its broad ornamentation of technologies of knowledge representation, learning, and evolutionary methods, plays a pivotal role in the formulating and solving optimization tasks. This Special Issue aims to deliver a platform, where researchers coming from academia and industry present the methodologies of coping with uncertainty in optimization through the usage of concepts of Soft Computing, report on the linkages between the methodology and practice of optimization, and elaborate on the state-of-the-art case studies in selected areas of applications, such as transportation networks, logistics and supply chains, portfolio optimization, risk management, robust design, network reliability, software reliability, redundancy optimization, and others. Once the Call For Papers was announced in late July 2015, this Special Issue has attracted tremendous attention. In total, we received 60 manuscripts. After a rigorous review process, 18 papers have been finally accepted for publication. To gain a better insight into the essence of the Special Issue, we offer brief highlights of the contributing papers.
2. Theory Li and Zhu in the paper entitled “Parametric optimal control for uncertain linear quadratic models” introduced a parametric optimal control problem of uncertain linear quadratic model and proposed an approximation method to derive the analytical expressions for optimal control and optimal value. Gao et al. developed the idea of Uncertain Coalitional Game by presenting an expected Shapley value and a ␣-optimistic Shapley value. The proposed uncertain Shapley values were used to solve a profit allocation problem of supply chain alliance. Zheng et al. in the paper entitled “Efficient solution concepts and their application in uncertain multiobjective programming” investigated relationships among efficiency concepts of the multi-objective programming with uncertain vectors. They applied theoretical results to a redundancy allocation http://dx.doi.org/10.1016/j.asoc.2017.04.052 1568-4946/© 2017 Published by Elsevier B.V.
problem with two objectives in reparable parallel-series systems, and discussed how to derive different types of efficient solutions according to the decision-maker’s preferences. The paper entitled “Probability box as a tool to model and control the effect of epistemic uncertainty in multiple dependent competing failure processes” introduced probability box as a tool to describe the effect of epistemic uncertainty on the multiple dependent competing failure process model. To efficiently propagate epistemic uncertainty and construct the probability box, they developed a dimensionreduced SQP method. An optimization model was developed to allocate resources in order to optimally reduce the effect of epistemic uncertainty. Bu et al. focused on the problem of how to improve evolutionary algorithms with future prediction for online dynamic optimization problems with time-linkage. A stochasticranking selection scheme based on the prediction accuracy was designed to improve the existing prediction approach under unreliable prediction. The paper entitled “Degree-constrained minimum spanning tree problem with uncertain edge weights” and authored by Gao and Jia investigated the uncertain expected value degreeconstrained minimum spanning tree (DCMST) model, ␣-DCMST model, and most chance DCMST model with uncertain edge weights.
3. Methodologies and case studies Chang in the paper entitled “A more general reliability allocation method using the hesitant fuzzy linguistic term set and minimal variance OWGA weights” integrated the hesitant fuzzy linguistic term sets and minimal variance OWGA weights to impact flexible allocation of system reliability. Qin employed random fuzzy variables to describe stochastic return on individual security with ambiguous information, defined the absolute deviation of random fuzzy variable, and employed it as a risk measure to formulate mean-absolute deviation portfolio optimization models. Palacios et al. tackled a variant of the job shop scheduling problem with uncertain task duration times being modelled as fuzzy numbers. The goal is to simultaneously minimize the schedule’s fuzzy makespan and maximize its robustness. The paper entitled “Contract designing for a supply chain with uncertain information based on confidence level” considered a contract-design problem for two competing heterogeneous suppliers working with a common retailer. Guo et al. studied a potentially hazardous material substitution problem in a bi-level decision-making model with a non-profit organization and two competitive firms. In the consec-
542
Editorial / Applied Soft Computing 56 (2017) 541–542
utive paper, Wen et al. proposed a minimal expected backorder model and a minimal backorder rate model based on a multiechelon inventory supply system, in which Uncertainty Theory was employed to characterize uncertainty arising from subjective personal cognition. Liu and Liu developed a robust credibilistic optimization method for the project portfolio selection problem, in which uncertain parameters were modelled as interval-valued fuzzy variables with variable parametric possibility distributions. Liu et al. presented a cooperative stochastic differential game model to investigate the optimal coordination strategy of a dynamic supply chain under uncertain conditions, and studied how to coordinate the effort level of node enterprise to maximize supply chain profit. in The paper “Design optimization of resource combination for collaborative logistics network under uncertainty” authored by Xu et al. proposed a general two-stage quantitative framework that enables decision makers to select the optimal network design scheme for collaborative logistics networks functioning under uncertainty. Yu et al. considered the user-defined parameters as uncertain factors to construct a least squares support vector regression ensemble learning paradigm. The paper entitled “Scenario-based multi-period program optimization for capability based planning using evolutionary algorithms” formulated capability based planning as a dynamic multi-objective optimization task and proposed an optimizing simulation methodology that combines evolutionary multi- objective optimization and a RL algorithm to select Pareto optimal capability portfolios across a number of objectives as well as over time. Ni in the paper entitled “Sequential seeding to optimize ınfluence diffusion in a social network” studied the problem of sequentially seeding nodes in a social network such that the complete influence time becomes minimized. They formulated a Markov decision process to describe the problem and embedded a modified greedy search method into an online algorithm to solve the Markov decision process.
As Guest Editors, we would like to express their sincere thanks to Prof. R. Roy, the founding Editor-in-Chief of Applied Soft Computing, for the special opportunity to realize this special issue. We would also like to thank all the referees for their support and professional service, and express the gratitude to all authors of their submissions to this special issue. Without the support of the authors and the referees, it would have been impossible to make this special a reality. We envision that the papers published in this special issue would be of interest to researchers and practitioners, and help identify further research directions. We also hope that the readers can find the material of this Special Issue both interesting and inspiring when exploring the field of optimization under uncertainty. Xiang Li School of Economics and Management, Beijing University of Chemical Technology, Beijing, China Witold Pedrycz Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada Dan Ralescu Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA E-mail addresses: [email protected] (X. Li), [email protected] (W. Pedrycz), [email protected] (D. Ralescu).
Contents lists available at ScienceDirect
Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Editorial
Optimization under uncertainty: A perspective of soft computing
1. Introduction Optimization permeates all endeavors of human activities and exhibits a remarkably high diversity of methopdologies and tools when coping with the complexity of problems. There is no surprise that with the ever-increasing complexity of problems, optimization comes with an inherent facet of uncertainty conveyed in different formal ways. This calls for innovative approaches to develop optimal and interpretable solutions as well as deliver user-centric environments. Soft Computing with its broad ornamentation of technologies of knowledge representation, learning, and evolutionary methods, plays a pivotal role in the formulating and solving optimization tasks. This Special Issue aims to deliver a platform, where researchers coming from academia and industry present the methodologies of coping with uncertainty in optimization through the usage of concepts of Soft Computing, report on the linkages between the methodology and practice of optimization, and elaborate on the state-of-the-art case studies in selected areas of applications, such as transportation networks, logistics and supply chains, portfolio optimization, risk management, robust design, network reliability, software reliability, redundancy optimization, and others. Once the Call For Papers was announced in late July 2015, this Special Issue has attracted tremendous attention. In total, we received 60 manuscripts. After a rigorous review process, 18 papers have been finally accepted for publication. To gain a better insight into the essence of the Special Issue, we offer brief highlights of the contributing papers.
2. Theory Li and Zhu in the paper entitled “Parametric optimal control for uncertain linear quadratic models” introduced a parametric optimal control problem of uncertain linear quadratic model and proposed an approximation method to derive the analytical expressions for optimal control and optimal value. Gao et al. developed the idea of Uncertain Coalitional Game by presenting an expected Shapley value and a ␣-optimistic Shapley value. The proposed uncertain Shapley values were used to solve a profit allocation problem of supply chain alliance. Zheng et al. in the paper entitled “Efficient solution concepts and their application in uncertain multiobjective programming” investigated relationships among efficiency concepts of the multi-objective programming with uncertain vectors. They applied theoretical results to a redundancy allocation http://dx.doi.org/10.1016/j.asoc.2017.04.052 1568-4946/© 2017 Published by Elsevier B.V.
problem with two objectives in reparable parallel-series systems, and discussed how to derive different types of efficient solutions according to the decision-maker’s preferences. The paper entitled “Probability box as a tool to model and control the effect of epistemic uncertainty in multiple dependent competing failure processes” introduced probability box as a tool to describe the effect of epistemic uncertainty on the multiple dependent competing failure process model. To efficiently propagate epistemic uncertainty and construct the probability box, they developed a dimensionreduced SQP method. An optimization model was developed to allocate resources in order to optimally reduce the effect of epistemic uncertainty. Bu et al. focused on the problem of how to improve evolutionary algorithms with future prediction for online dynamic optimization problems with time-linkage. A stochasticranking selection scheme based on the prediction accuracy was designed to improve the existing prediction approach under unreliable prediction. The paper entitled “Degree-constrained minimum spanning tree problem with uncertain edge weights” and authored by Gao and Jia investigated the uncertain expected value degreeconstrained minimum spanning tree (DCMST) model, ␣-DCMST model, and most chance DCMST model with uncertain edge weights.
3. Methodologies and case studies Chang in the paper entitled “A more general reliability allocation method using the hesitant fuzzy linguistic term set and minimal variance OWGA weights” integrated the hesitant fuzzy linguistic term sets and minimal variance OWGA weights to impact flexible allocation of system reliability. Qin employed random fuzzy variables to describe stochastic return on individual security with ambiguous information, defined the absolute deviation of random fuzzy variable, and employed it as a risk measure to formulate mean-absolute deviation portfolio optimization models. Palacios et al. tackled a variant of the job shop scheduling problem with uncertain task duration times being modelled as fuzzy numbers. The goal is to simultaneously minimize the schedule’s fuzzy makespan and maximize its robustness. The paper entitled “Contract designing for a supply chain with uncertain information based on confidence level” considered a contract-design problem for two competing heterogeneous suppliers working with a common retailer. Guo et al. studied a potentially hazardous material substitution problem in a bi-level decision-making model with a non-profit organization and two competitive firms. In the consec-
542
Editorial / Applied Soft Computing 56 (2017) 541–542
utive paper, Wen et al. proposed a minimal expected backorder model and a minimal backorder rate model based on a multiechelon inventory supply system, in which Uncertainty Theory was employed to characterize uncertainty arising from subjective personal cognition. Liu and Liu developed a robust credibilistic optimization method for the project portfolio selection problem, in which uncertain parameters were modelled as interval-valued fuzzy variables with variable parametric possibility distributions. Liu et al. presented a cooperative stochastic differential game model to investigate the optimal coordination strategy of a dynamic supply chain under uncertain conditions, and studied how to coordinate the effort level of node enterprise to maximize supply chain profit. in The paper “Design optimization of resource combination for collaborative logistics network under uncertainty” authored by Xu et al. proposed a general two-stage quantitative framework that enables decision makers to select the optimal network design scheme for collaborative logistics networks functioning under uncertainty. Yu et al. considered the user-defined parameters as uncertain factors to construct a least squares support vector regression ensemble learning paradigm. The paper entitled “Scenario-based multi-period program optimization for capability based planning using evolutionary algorithms” formulated capability based planning as a dynamic multi-objective optimization task and proposed an optimizing simulation methodology that combines evolutionary multi- objective optimization and a RL algorithm to select Pareto optimal capability portfolios across a number of objectives as well as over time. Ni in the paper entitled “Sequential seeding to optimize ınfluence diffusion in a social network” studied the problem of sequentially seeding nodes in a social network such that the complete influence time becomes minimized. They formulated a Markov decision process to describe the problem and embedded a modified greedy search method into an online algorithm to solve the Markov decision process.
As Guest Editors, we would like to express their sincere thanks to Prof. R. Roy, the founding Editor-in-Chief of Applied Soft Computing, for the special opportunity to realize this special issue. We would also like to thank all the referees for their support and professional service, and express the gratitude to all authors of their submissions to this special issue. Without the support of the authors and the referees, it would have been impossible to make this special a reality. We envision that the papers published in this special issue would be of interest to researchers and practitioners, and help identify further research directions. We also hope that the readers can find the material of this Special Issue both interesting and inspiring when exploring the field of optimization under uncertainty. Xiang Li School of Economics and Management, Beijing University of Chemical Technology, Beijing, China Witold Pedrycz Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada Dan Ralescu Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA E-mail addresses: [email protected] (X. Li), [email protected] (W. Pedrycz), [email protected] (D. Ralescu).