An algorithm for the biobjective integer minimum cost flow problem
Computers and Operations Research
Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem
Journal of Global Optimization
Bound sets for biobjective combinatorial optimization problems
Computers and Operations Research
An algorithm for ranking assignments using reoptimization
Computers and Operations Research
Solving efficiently the 0-1 multi-objective knapsack problem
Computers and Operations Research
The Bicriterion Multimodal Assignment Problem: Introduction, Analysis, and Experimental Results
INFORMS Journal on Computing
A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem
INFORMS Journal on Computing
Computers and Operations Research
Finding all nondominated points of multi-objective integer programs
Journal of Global Optimization
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In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p2 objectives. We apply the method to the assignment problem with three objectives. We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description. Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method.