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A New Exact Algorithm to Optimize a Linear Function Over the Set of Efficient Solutions for Bi-objective Mixed Integer Linear Programming

Alvaro Sierra-Altamiranda (amsierra***at***mail.usf.edu)
Hadi Charkhgard (hcharkhgard***at***usf.edu)

Abstract: We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs. The proposed algorithm is developed based on the Triangle Splitting Method (Boland et al. 2015b) which can find a full representation of the nondominated frontier of any bi-objective mixed integer linear program. The proposed algorithm is easy to implement and converges quickly to an optimal solution. An extensive computational study shows the efficacy of the algorithm. We numerically show that the proposed algorithm can be used to quickly generate a provably high-quality approximate solution because it maintains a lower bound and an upper bound on the optimal value of the linear function at any point in time.

Keywords: bi-objective mixed integer linear programming, criterion space search algorithm, optimization over efficient frontier, triangle splitting method

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Citation:

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Entry Submitted: 10/10/2017
Entry Accepted: 10/10/2017
Entry Last Modified: 10/13/2017

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