Network reoptimization procedures for multiobjective network problems

Network models are attractive because of their computational efficiency. Network applications can involve multiple objective analysis. Multiple objective analysis requires generating nondominated solutions in various forms. Two general methods exist to generate new solutions in continuous optimization: changing objective function weights and inserting objective bounds through constraints. In network flow problems, modifying weights is straightforward, allowing use of efficient network codes. Use of bounds on objective attainment levels can provide a more controlled generation of solutions reflecting tradeoffs among objectives. To constrain objective attainment, however, would require a side constrained network code, sacrificing some computational efficiency for greater model flexibility. The authors develop reoptimization procedures for the side constrained problem and use them in conjunction with simplex-based techniques. The present approach provides a useful tool for generating solutions allowing greater decision maker control over objective attainments, allowing multiobjective analysis of large-scale problems. Results are compared with solutions obtained from the computationally more attractive weighting technique. Reoptimization procedures are discussed as a means of more efficiently conducting multiple objective network analyses.