A Methodology to Determine the Subset of Heuristics for Hyperheuristics through Metalearning for Solving Graph Coloring and Capacitated Vehicle Routing Problems

Abstract

In this work, we focus on the problem of selecting low-level heuristics in a hyperheuristic approach with offline learning, for the solution of instances of different problem domains. The objective is to improve the performance of the offline hyperheuristic approach, identifying equivalence classes in a set of instances of different problems and selecting the best performing heuristics in each of them. A methodology is proposed as the first step of a set of instances of all problems, and the generic characteristics of each instance and the performance of the heuristics in each one of them are considered to define the vectors of characteristics and make a grouping of classes. Metalearning with statistical tests is used to select the heuristics for each class. Finally, we used the Naive Bayes to test the set instances with k-fold cross-validation, and we compared all results statistically with the best-known values. In this research, the methodology was tested by applying it to the problems of capacitated vehicle routing (CVRP) and graph coloring (GCP). The experimental results show that the proposed methodology can improve the performance of the offline hyperheuristic approach, correctly identifying the classes of instances and applying the appropriate heuristics in each case. This is based on the statistical comparison of the results obtained with those of the state of the art of each instance.

A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research

“…Hyper-heuristic algorithms generate high-quality solutions by manipulating a series of low-level heuristics (LLH) through high-level heuristics (HLH) [135,184]. These new heuristics are used to solve various NP-hard problems [185]. Hyper-heuristics consist of two levels.…”

“…Leng et al proposed a novel multi-objective hyper-heuristic (MOHH) algorithm to obtain Pareto solutions for the dual-objective cold-chain routing problem considering the environmental impact; three selection strategies were introduced to enhance the performance of the MOHH, and the proposed algorithm was verified to outperform several existing multiobjective evolutionary algorithms [193]. Ortiz-Aguilar et al selected low-level heuristics in the offline learned hyper-heuristic method by way of meta-learning to improve the performance of offline hyper-heuristic algorithms; through verification using the CVRP test, the results show that the proposed method can improve the performance of offline hyper-heuristic algorithms [185]. Kalatzantonakis et al proposed a bandit VNS hyperheuristic algorithm, which was tested on CVRP benchmark instances, and then compared it to the traditional general variable neighborhood search (VNS) metaheuristic, revealing that the computational speed and the quality of solutions were significantly improved [194].…”

Evolutionary Algorithm-Based Iterated Local Search Hyper-Heuristic for Combinatorial Optimization Problems

“…Hence, the impetus for studying hyper-heuristics over heuristics and metaheuristics is to address the problem of generality that hyper-heuristics provide across different forms of optimization problems [12]. Meta-learning for offline learning of heuristic sequences was recently described for solving capacitated vehicle routing and graph coloring problems [13]. The study [14] proposed a novel mechanism to create an effective recombination procedure for sub-trees in a genetic programming hyper-heuristic to solve the job-shop scheduling problem.…”