This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a semi-greedy construction procedure followed by a local search procedure. The best solution found over all iterations is returned as the solution of the GRASP. Continuous GRASP (C-GRASP) is an extension of GRASP for continuous optimization in the unit hypercube. A random-key optimizer (RKO) uses a vector of random keys to encode a solution to a combinatorial optimization problem. It uses a decoder to evaluate a solution encoded by the vector of random keys. A random-key GRASP is a C-GRASP where points in the unit hypercube are evaluated employing a decoder. We describe random key GRASP consisting of a problem-independent component and a problem-dependent decoder. As a proof of concept, the random-key GRASP is tested on five NP-hard combinatorial optimization problems: traveling salesman problem, tree of hubs location problem, Steiner triple covering problem, node capacitated graph partitioning problem, and job sequencing and tool switching problem.
翻译:本文提出了一种采用随机密钥优化器(RKO)范式的、与问题无关的GRASP元启发式算法。GRASP(贪婪随机自适应搜索过程)是一种用于组合优化的元启发式方法,它反复执行半贪婪构造过程与局部搜索过程。算法将所有迭代中发现的最优解作为GRASP的最终解输出。连续GRASP(C-GRASP)是GRASP在单位超立方体连续优化问题中的扩展。随机密钥优化器(RKO)使用随机密钥向量对组合优化问题的解进行编码,并通过解码器评估由随机密钥向量编码的解。随机密钥GRASP是一种C-GRASP变体,其通过解码器评估单位超立方体中的点。本文描述的随机密钥GRASP包含与问题无关的通用组件和与问题相关的解码器两部分。作为概念验证,该算法在五个NP难组合优化问题上进行了测试:旅行商问题、枢纽树选址问题、斯坦纳三元覆盖问题、节点容量约束图划分问题以及作业排序与刀具切换问题。