Multi-objective branch and bound. Application to the bi-objective spanning tree problem

In this work, we give a formal framework to design multiobjective branch-and-bound procedures, and we provide a generalization of the lower bounding concept, able to more tightly bound the Pareto front of a sub-problem. We tested our approach on the bi-objective spanning tree problem. It significantly improves the existing results for the problem.

[1]  M. Ehrgott,et al.  Connectedness of efficient solutions in multiple criteria combinatorial optimization , 1997 .

[2]  H. G. Daellenbach,et al.  Note on Multiple Objective Dynamic Programming , 1980 .

[3]  Matthias Ehrgott,et al.  Bound sets for biobjective combinatorial optimization problems , 2007, Comput. Oper. Res..

[4]  H. W. Corley,et al.  Efficient spanning trees , 1985 .

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

[6]  Ramaswamy Chandrasekaran,et al.  Minimal ratio spanning trees , 1977, Networks.

[7]  David B. Shmoys,et al.  A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem , 1996, IPCO.

[8]  J. M. Rivera,et al.  A combined approach to solve binary multicriteria problems , 1982 .

[9]  Paolo Serafini,et al.  Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems , 1987 .

[10]  George Mavrotas,et al.  A branch and bound algorithm for mixed zero-one multiple objective linear programming , 1998, Eur. J. Oper. Res..

[11]  Mikael Lind,et al.  On bicriterion minimal spanning trees: An approximation , 1996, Comput. Oper. Res..

[12]  R. Soland,et al.  An interactive branch-and-bound algorithm for multiple criteria optimization , 1986 .

[13]  Tomasz Radzik,et al.  Solving the Biobjective Minimum Spanning Tree problem using a k-best algorithm , 2003 .

[14]  Jacques Teghem,et al.  Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem , 1998, J. Glob. Optim..

[15]  G. Kiziltan,et al.  An Algorithm for Multiobjective Zero-One Linear Programming , 1983 .

[16]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[17]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[18]  Joshua D. Knowles,et al.  A comparison of encodings and algorithms for multiobjective minimum spanning tree problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[19]  S. Alonso,et al.  The problem of the optimal biobjective spanning tree , 1998, Eur. J. Oper. Res..

[20]  Frank Neumann,et al.  Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem , 2004, Eur. J. Oper. Res..

[21]  S. Sarkar,et al.  Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions , 1998 .

[22]  David Corne,et al.  Benchmark Problem Generators and Results for the Multiobjective Degree-Constrained Minimum Spanning , 1997 .

[23]  Horst W. Hamacher,et al.  On spanning tree problems with multiple objectives , 1994, Ann. Oper. Res..

[24]  Mitsuo Gen,et al.  Genetic algorithm approach on multi-criteria minimum spanning tree problem , 1999, Eur. J. Oper. Res..

[25]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[26]  Xavier Gandibleux,et al.  An Annotated Bibliography of Multiobjective Combinatorial Optimization , 2000 .