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.

中文翻译：

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混合整数线性最大乘法程序的准则空间搜索算法：一种多目标优化方法

我们研究了一类具有线性约束和多线性目标函数的混合整数优化问题，即所谓的混合整数线性最大乘法程序 (MIL-MMP)。这样的问题可以转化为二阶锥规划（SOCP），并可以通过商业求解器（如 CPLEX）有效解决。然而，MIL-MMP 也可以被视为多目标优化中有效解决方案集优化问题的特例。利用这一观察，我们开发了一种用于解决任何 MIL-MMP 的标准空间搜索算法。对大约 2000 个实例的广泛计算研究表明，所提出的算法不仅明显优于 CPLEX 混合整数 SOCP 求解器，而且还明显优于能够解决 MIL-MMP 特殊情况的最新算法。而且，