Identifying preferred solutions in multiobjective combinatorial optimization problems

We develop an evolutionary algorithm for multiobjective combinatorial optimization problems. The algorithm aims at converging the preferred solutions of a decision-maker. We test the performance of the algorithm on the multiobjective knapsack and multiobjective spanning tree problems. We generate the true nondominated solutions using an exact algorithm and compare the results with those of the evolutionary algorithm. We observe that the evolutionary algorithm works well in approximating the solutions in the preferred regions

Çok amaçlı bileşi optimizasyonu problemlerinde tercih edilen bölgeye yakınsama.

Finding the true nondominated points is typically hard for Multi-objective Combinatorial Optimization (MOCO) problems. Furthermore, it is not practical to generate all of them since the number of nondominated points may grow exponentially as the problem size increases. In this thesis, we develop an exact algorithm to find all nondominated points in a specified region. We combine this exact algorithm with a heuristic algorithm that approximates the possible locations of the nondominated points. Interacting with a decision maker (DM), the heuristic algorithm first approximately identifies the region that is of interest to the DM. Then, the exact algorithm is employed to generate all true nondominated points in this region. We conduct experiments on Multi-objective Assignment Problems (MOAP), Multi-objective Knapsack Problems (MOKP) and Multi-objective Shortest Path (MOSP) Problems; and the algorithms work well. Finding the worst possible value for each criterion among the set of efficient solutions has important uses in multi-criteria problems since the proper scaling of each criterion is required by many approaches. Such points are called nadir points. v It is not straightforward to find the nadir points, especially for large problems with more than two criteria. We develop an exact algorithm to find the nadir values for multi-objective integer programming problems. We also find bounds with performance guarantees. We demonstrate that our algorithms work well in our experiments on MOAP, MOKP and MOSP problems. Assuming that the DM's preferences are consistent with a quasiconcave value function, we develop an interactive exact algorithm to solve MIP problems. Based on the convex cones derived from pairwise comparisons of the DM, we generate constraints to prevent points in the implied inferior regions. We guarantee finding the most preferred point and our computational experiments on MOAP, MOKP and MOSP problems show that a reasonable number of pairwise comparisons are required.Ph.D. - Doctoral Progra

Çok amaçlı bileşi optimizasyonu problemleri için yaklaşımlar.

In this thesis, we develop two exact algorithms and a heuristic procedure for Multiobjective Combinatorial Optimization Problems (MOCO). Our exact algorithms guarantee to generate all nondominated solutions of any MOCO problem. We test the performance of the algorithms on randomly generated problems including the Multiobjective Knapsack Problem, Multi-objective Shortest Path Problem and Multi-objective Spanning Tree Problem. Although we showed the algorithms work much better than the previous ones, we also proposed a fast heuristic method to approximate efficient frontier since it will also be applicable for real-sized problems. Our heuristic approach is based on fitting a surface to approximate the efficient frontier. We experiment our heuristic on randomly generated problems to test how well the heuristic procedure approximates the efficient frontier. Our results showed the heuristic method works well.M.S. - Master of Scienc

Approximating the Nondominated Frontiers of Multi-Objective Combinatorial Optimization Problems

Finding, all nondominated vectors for multi-objective combinatorial optimization (MOCO) problems is computationally very hard in general. We approximate the nondominated Frontiers of MOCO problems by fitting smooth hypersurfaces. For a given problem, we lit the hypersurface using a single nondominated reference vector. We experiment with different types of MOCO problems and demonstrate that in all cases the fitted hypersurfaces approximate all nondominated vectors well. We discuss that such an approximation is useful to find the neighborhood of preferred regions of the nondominated vectors with very little computational effort. Further computational effort can then be spent in the identified region to find the actual nondominated vectors the decision maker will prefer. (C) 2009 Wiley Periodical, Inc. Naval Research Logistics 56: 191-198, 200