A criterion space search algorithm for mixed integer linear maximum multiplicative programs: a multiobjective optimization approach

We study a class of mixed integer optimization problems with linear constraints and a multilinear 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...

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Bibliographic Details
Published in:International transactions in operational research Vol. 29; no. 3; pp. 1659 - 1687
Main Authors: Saghand, Payman Ghasemi, Charkhgard, Hadi
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.05.2022
Subjects:
Algorithms
Criteria
criterion space search algorithm
Mixed integer
mixed integer maximum multiplicative programming
multiobjective optimization
Multiple objective analysis
Operations research
Optimization
optimization over the efficient set
Search algorithms
Solvers
ISSN:0969-6016, 1475-3995
Online Access:Get full text
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Summary:We study a class of mixed integer optimization problems with linear constraints and a multilinear 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 multiobjective optimization. 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 that 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.
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ISSN:0969-6016
1475-3995
DOI:10.1111/itor.12964