A new method for optimizing a linear function over the efficient set of a multiobjective integer program

作者：Boland Natashia; Charkhgard Hadi^*; Savel**ergh Martin

来源：European Journal of Operational Research, 2017, 260(3): 904-919.

DOI：10.1016/j.ejor.2016.02.037

• Multiobjective integer programming
• Nondominated points
• Extension of the L-shape search method
• Optimizing over the efficient set
• Nadir point

We present a new algorithm for optimizing a linear function over the set of efficient solutions of a multiobjective integer program (MOIP). The algorithm's success relies on the efficiency of a new algorithm for enumerating the nondominated points of a MOIP, which is the result of employing a novel criterion space decomposition scheme which (1) limits the number of subspaces that are created, and (2) limits the number of sets of disjunctive constraints required to define the single-objective IP that searches a subspace for a nondominated point. An extensive computational study shows that the efficacy of the algorithm. Finally, we show that the algorithm can be easily modified to efficiently compute the nadir point of a multiobjective integer program.

• 出版日期2017-8-1