求解二次分配问题的改进单目标和多目标细菌觅食优化
A modified single and multi-objective bacteria foraging optimization for the solution of quadratic assignment problem
摘要：
非多项式困难（NP-困难）问题是具有挑战性的，因为还没有发现多项式时间算法来解决他们在多项式时间。细菌觅食优化（BFO）算法是一种元算法，主要用于解决NP难问题。BFO的灵感来自于细菌觅食的行为，如大肠杆菌（E-coli）。BFO的目的是消除那些具有弱觅食特性的细菌，并将那些具有突破觅食特性的细菌保持在最佳状态。尽管这种算法的强度，大多数问题达到最佳解决方案是时间要求或不可能的。在单目标优化算法中加入变异算子，在多目标优化算法（MOBFO）中加入遗传算法中的变异和交叉算子来更新每一代的解，并采用局部禁忌搜索算法来搜索局部最优解。此外，我们使用了一个快速的非支配排序算法在MOBFO找到最好的非支配解决方案，在每一代。我们通过许多单目标和多目标二次分配问题（QAP）实例评估了所提出算法的性能。实验结果表明，我们的方法优于以往的一些优化算法在收敛和发散的解决方案。
英文摘要：
Non-polynomial hard (NP-hard) problems are challenging because no polynomial-time algorithm has yet been discovered to solve them in polynomial time. The Bacteria Foraging Optimization (BFO) algorithm is one of the metaheuristics algorithms that is mostly used for NP-hard problems. BFO is inspired by the behavior of the bacteria foraging such as Escherichia coli (E-coli). The aim of BFO is to eliminate those bacteria that have weak foraging properties and maintain those bacteria that have breakthrough foraging properties toward the optimum. Despite the strength of this algorithm, most of the problems reaching optimal solutions are time-demanding or impossible. In this paper, we modified single objective BFO by adding a mutation operator and multi-objective BFO (MOBFO) by adding mutation and crossover from genetic algorithm operators to update the solutions in each generation, and local tabu search algorithm to reach the local optimum solution. Additionally, we used a fast nondominated sort algorithm in MOBFO to find the best-nondominated solutions in each generation. We evaluated the performance of the proposed algorithms through a number of single and multi-objective Quadratic Assignment Problem (QAP) instances. The experimental results show that our approaches outperform some previous optimization algorithms in both convergent and divergent solutions.
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