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A Criterion Space Search Algorithm for Mixed Integer Linear Maximum Multiplicative Programs: A Multi-objective Optimization Approach

Payman Ghasemi Saghand (payman***at***mail.usf.edu)
Hadi Charkhgard (hcharkhgard***at***usf.edu)

Abstract: We study a class of mixed integer optimization problems with linear constraints and a multi-linear objective function, the so-called mixed integer linear maximum multiplicative programs (MIL-MMPs). Such a problem can be transformed into a Second-order Cone Program (SOCP) and can be solved effectively by a commercial solver such as CPLEX. However, MIL-MMPs can also be viewed as special cases of the problem of optimization over the set of efficient solutions in multi-objective optimization. By using this observation, we develop a criterion space search algorithm for solving any MIL-MMP. An extensive computational study on around 2000 instances illustrates that the proposed algorithm significantly outperforms not only the CPLEX Mixed Integer SOCP solver but also a state-of-the-art algorithm which is capable of solving special cases of MIL-MMPs. Moreover, the computational study illustrates that even if we linearize the objective function and solve the linearized problem by CPLEX, the proposed algorithm still performs significantly better.

Keywords: Mixed integer maximum multiplicative programming, Multi-objective optimization, Optimization over the efficient set, Criterion space search algorithm

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Integer Programming

Citation: author={Payman Ghasemi Saghand and Hadi Charkhgard}, title={A Criterion Space Search Algorithm for Mixed Integer Linear Maximum Multiplicative Programs: A Multi-objective Optimization Approach}, url={https://doi.org/10.13140/RG.2.2.20619.75042}

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Entry Submitted: 01/14/2019
Entry Accepted: 01/14/2019
Entry Last Modified: 01/14/2019

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