Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither objective can be improved without deteriorating another objective. Motivated by the success of matheuristics in the single-objective domain, we propose a linear programming-based matheuristic for tri-objective binary integer programming. To achieve a high-quality approximation of the optimal set of trade-off solutions, a lower bound set is first obtained using the vector linear programming solver Bensolve. Then, feasibility pump-based ideas in combination with path relinking are applied in novel ways so as to obtain a high quality upper bound set. Our matheuristic is compared to a recently-suggested algorithm that is, to the best of our knowledge, the only existing matheuristic method for tri-objective integer programming. In an extensive computational study, we show that our method generates a better approximation of the true Pareto front than the benchmark method on a large set of tri-objective benchmark instances. Since the developed approach starts from a potentially fractional lower bound set, it may also be used as a primal heuristic in the context of linear relaxation-based multi-objective branch-and-bound algorithms.
翻译:许多现实世界的优化问题涉及多重目标。 当同时考虑时,它们会产生一套最佳的折中解决方案,也称为高效解决方案。这些解决方案具有两个目标都无法在不破坏另一个目标的情况下加以改进的属性。由于单一目标领域数学家的成功,我们提议为三目标双向整数编程采用基于线性编程数学的数学。为了实现一套最佳折中解决方案的高质量近似,首先利用矢量线性编程解算器本索尔夫获得一套较低的约束套件。然后,将基于可行性的泵式想法与路径的重新连接结合起来,以创新的方式应用,以便获得高质量的高质量的上限套件。我们的数学家与最近推出的算术相比,根据我们的知识,这是目前唯一的三目标组合制编程性编程的数学学方法。在一项广泛的计算研究中,我们的方法比一套大型三目标基准实例的基准方法更接近真实的Pareto前端方法。而发达的方法是从一个潜在的分数性低端的直线性矩阵中开始的。