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

Abstract

Abstract 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.