A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.

[1]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[2]  L. Cooper.  Location-Allocation Problems , 1963 .

[3]  Guohe Huang,et al.  An inventory-theory-based interval-parameter two-stage stochastic programming model for water resources management , 2011 .

[4]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[5]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[6]  Lily Rachmawati,et al.  Incorporation of imprecise goal vectors into evolutionary multi-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

[7]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[8]  Carlos A. Coello Coello,et al.  Solving constrained optimization problems with a hybrid particle swarm optimization algorithm , 2011 .

[9]  Ian C. Parmee,et al.  Multiobjective Satisfaction within an Interactive Evolutionary Design Environment , 2000, Evolutionary Computation.

[10]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[11]  E. F. Khor,et al.  An Evolutionary Algorithm with Advanced Goal and Priority Specification for Multi-objective Optimization , 2011, J. Artif. Intell. Res..

[12]  T. Hout,et al.  Competing Against Time , 1990 .

[13]  Qingfu Zhang,et al.  Interactive MOEA/D for multi-objective decision making , 2011, GECCO '11.

[14]  Andries P. Engelbrecht,et al.  Computational Intelligence: An Introduction , 2002 .

[15]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[16]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[17]  Lothar Thiele,et al.  A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization , 2009, Evolutionary Computation.

[18]  Bilal Toklu,et al.  Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models , 2009, Comput. Oper. Res..

[19]  Mitsuo Gen,et al.  A genetic algorithm for two-stage transportation problem using priority-based encoding , 2006, OR Spectr..

[20]  Antoni Wibowo,et al.  A flexible three-level logistic network design considering cost and time criteria with a multi-objective evolutionary algorithm , 2013, J. Intell. Manuf..

[21]  J. Branke,et al.  Guidance in evolutionary multi-objective optimization , 2001 .

[22]  Mitsuo Gen,et al.  Network Models and Optimization: Multiobjective Genetic Algorithm Approach , 2008 .

[23]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[24]  Helio J. C. Barbosa,et al.  An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization , 2011 .

[25]  Ian C. Parmee,et al.  Introducing prototype interactive evolutionary systems for ill-defined, multi-objective design environments , 2001 .

[26]  Antoni Wibowo,et al.  An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs , 2013, Appl. Soft Comput..

[27]  W. Yang,et al.  Coordinating supply chain response-time: a bi-level programming approach , 2007 .

[28]  Bernhard Sendhoff,et al.  Incorporation Of Fuzzy Preferences Into Evolutionary Multiobjective Optimization , 2002, GECCO.

[29]  Ian C. Parmee,et al.  Preferences and their application in evolutionary multiobjective optimization , 2002, IEEE Trans. Evol. Comput..

[30]  Kiyoshi Tanaka,et al.  Local Dominance Including Control of Dominance Area of Solutions in MOEAs , 2007, 2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making.

[31]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[32]  Ian C. Parmee,et al.  Agent-based support within an interactive evolutionary design system , 2002, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[33]  Tae-Eog Lee,et al.  A three-level supply chain network design model with risk-pooling and lead times , 2010 .

[34]  Eun-Soo Kim,et al.  Preference-Based Solution Selection Algorithm for Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[35]  Qingwei Chen,et al.  A multi-objective optimization evolutionary algorithm incorporating preference information based on fuzzy logic , 2010, Comput. Optim. Appl..

[36]  F. L. Hitchcock.  The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[37]  Marc Goetschalckx,et al.  Strategic production-distribution models: A critical review with emphasis on global supply chain models , 1997 .

[38]  Lothar Thiele,et al.  SPAM: Set Preference Algorithm for Multiobjective Optimization , 2008, PPSN.

[39]  Antoni Wibowo,et al.  Effective local evolutionary searches distributed on an island model solving bi-objective optimization problems , 2012, Applied Intelligence.