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A criterion space search algorithm for mixed integer linear maximum multiplicative programs: a multiobjective optimization approach
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DOI：10.1111/itor.12964.png)
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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.
Keyword:
mixed integer maximum multiplicative programming
multiobjective optimization
optimization over the efficient set
criterion space search algorithm
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