Optimizing a linear function over the nondominated set of multiobjective integer programs
Optimizing a linear function over the nondominated set of multiobjective integer programs
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DOI：
10.1111/itor.12627
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发表时间：
2019-01
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影响因子：
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通讯作者：
Banu Lokman
中科院分区：
文献类型：
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作者：
Banu Lokman
在这篇文章中，我们提出了两种算法来优化多目标整数规划的非支配集上的线性函数。该算法迭代产生非劣点，收敛到最优解，减少了可行集。fiRST算法对现有算法提出了改进，该算法在fi和新点的过程中使用分解和搜索过程。不同的是，第二种算法在整个算法中最大化其中一个标准，并通过设置线性函数值的界限来生成新的点。在算法的分解和搜索过程中，伴随着特定于问题的fic机制，以便更科学地探索fi的目标函数空间。这些算法旨在产生满足预定精度水平的解决方案。通过对多目标组合优化问题的实验，证明了算法的有效性。
In this paper, we develop two algorithms to optimize a linear function over the nondominated set of multi-objective integer programs. The algorithms iteratively generate nondominated points and converge to the optimal solution reducing the feasible set. The first algorithm proposes improvements to an existing algorithm employing a decomposition and search procedure in finding a new point. Differently, the second algorithm maximizes one of the criteria throughout the algorithm and generates new points by setting bounds on the linear function value. The decomposition and search procedure in the algorithms is accompanied by problem-specific mechanisms in order to explore the objective function space efficiently. The algorithms are designed to produce solutions that meet a prespecified accuracy level. We conduct experiments on multi-objective combinatorial optimization problems and show that the algorithms work well.