Multiobjective combinatorial optimization: some approaches

There have been many developments in multiple criteria decision-making (MCDM) during the last 50 years. Researchers from different areas have also recognized the multiple-criteria nature of problems in their application areas and tried to address these issues. Unfortunately, there has not always been sufficient information flow between the researchers in the MCDM area and the researchers applying MCDM to their problems. More recently, multiobjective combinatorial optimization (MOCO) and multiobjective metaheuristic areas have been enjoying substantial developments. These problems are hard to solve. Many researchers addressed the problem of finding all nondominated solutions. This is a difficult task for MOCO problems. This difficulty limits many of the studies to concentrate on bicriteria problems. In this paper, I review some MCDM approaches that aim to find only the preferred solutions of the decision maker (DM). I argue that this is especially important for MOCO problems. I discuss several of our approaches that incorporate DM's preferences into the solution process of MOCO problems and argue that there is a need for more work to be done in this area. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Carlos A. Coello Coello,et al.  Handling preferences in evolutionary multiobjective optimization: a survey , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[2]  Pekka Korhonen,et al.  A pareto race , 1988 .

[3]  X. Gandibleux,et al.  Approximative solution methods for multiobjective combinatorial optimization , 2004 .

[4]  Stanley Zionts,et al.  An improved method for solving multiple criteria problems involving discrete alternatives , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Murat Köksalan,et al.  An Evolutionary Metaheuristic for Approximating Preference-Nondominated Solutions , 2007, INFORMS J. Comput..

[6]  M. Köksalan,et al.  Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems , 2009 .

[7]  Murat Köksalan,et al.  A Favorable Weight-Based Evolutionary Algorithm for Multiple Criteria Problems , 2010, IEEE Transactions on Evolutionary Computation.

[8]  Murat Köksalan,et al.  Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions , 1995 .

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

[10]  Pekka Korhonen,et al.  A Visual Interactive Method for Solving the Multiple-Criteria Problem , 1986 .

[11]  Stanley Zionts,et al.  A multiple criteria method for choosing among discrete alternatives , 1981 .

[12]  Murat Köksalan,et al.  An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization , 2003, Manag. Sci..

[13]  M Köksalan,et al.  An interactive approach for multiobjective decision making , 2006, J. Oper. Res. Soc..

[14]  Murat Köksalan,et al.  Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making , 2009, Oper. Res..

[15]  S. Zionts,et al.  Solving the Discrete Multiple Criteria Problem using Convex Cones , 1984 .

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

[17]  S. Zionts,et al.  An Interactive Programming Method for Solving the Multiple Criteria Problem , 1976 .

[18]  Lily Rachmawati,et al.  Preference Incorporation in Multi-objective Evolutionary Algorithms: A Survey , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[19]  R. Benayoun,et al.  Linear programming with multiple objective functions: Step method (stem) , 1971, Math. Program..

[20]  M. Köksalan.  A heuristic approach to bicriteria scheduling , 1999 .

[21]  Xavier Gandibleux,et al.  Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications , 2003 .

[22]  Arthur M. Geoffrion,et al.  An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department , 1972 .