The Performance of a Metaheuristic Algorithm for Finding a Maximal Weight Clique in the Fill-in-Blank Problem

A programming education is one of the most important fields in Information and Education Technology. Funabiki et al. have developed a Web-based Java Programming Learning Assistant System (JPLAS). JPLAS mainly provides two types of problems, namely the code writing problem and the fill-in-blank problem, to support students' self-studies at various learning levels. Particularly in the fill-in-blank problem (FIBP), the system requires an efficient algorithm to find a maximal clique of the compatibility graph in advance in order to obtain a maximal set of blank elements with unique answers. In this paper, we investigate the performance of a metaheuristic algorithm based on an iterated local search for solving the maximum weight clique problem (MWCP), which is an important generalization of the maximum clique problem, given as an extension of the compatibility graph in the FIBP. Computational results show that our metaheuristic algorithm is capable of finding satisfactory weighted cliques efficiently for well-known benchmark graphs and the performance of our algorithm is comparable to those of state-of-the-art metaheuristics for the MWCP.