Learnable tabu search guided by estimation of distribution for maximum diversity problems

Abstract

This paper presents a learnable tabu search (TS) guided by estimation of distribution algorithm (EDA), called LTS-EDA, for maximum diversity problem. The LTS-EDA introduces knowledge model and can extract knowledge during the search process of TS, and thus it adopts dual or cooperative evolution/search structure, consisting of probabilistic model space in clustered EDA and solution space searched by TS. The clustered EDA, as a learnable constructive method, is used to create a new starting solution, and the simple TS, as an improvement method, attempts to improve the solution created by the clustered EDA in the LTS-EDA. A distinguishing feature of the LTS-EDA is the usage of the clustered EDA with effective linkage learning to guide TS. In the clustered EDA, different clusters (models) focus on different substructures, and the combination of information from different clusters (models) effectively combines substructures. The LTS-EDA is tested on 50 large size benchmark problems with the size ranging from 2,000 to 5,000. Simulation results show that the LTS-EDA is better than the advanced algorithms proposed recently.

A hybrid metaheuristic method for the Maximum Diversity Problem

“…However, experimental results show that TIG and LTS-EDA obtain better or competitive performance than VNS and ITS. Especially, LTS-EDA is able to reach new best solutions [44] for some larger random instances. Thus, these 4 reference algorithms are among the most successful approaches for solving MDP actually available in the literature.…”

“…Moreover, these 4 reference algorithms are tested and compared very recently in [44] under the same time limit on a Pentium R Dual-Core CPU E5400 processor (2.70 GHZ CPU and 2 GB of RAM). According to the Standard Performance Evaluation Cooperation (www.spec.org), this computer is 1.17 time slower than the computer we used for our experiments.…”

“…There are five instances with n = 3000 and m = 1500, and five instances with n = 5000 and m = 2500. These instances were tested in [8,28,36,44]. See http://www.soften.ktu.lt/∼gintaras/max div.html for the sources of the generator and input files to replicate these instances.…”

“…All the instances have 10% density with m = 2500 and n = 1000. These instances were used in [8,28,36,44] to assess the MDP algorithms and are available at http://people.brunel.ac.uk/ ∼mastjjb/jeb/orlib/bqpinfo.html.…”

“…This includes tabu search [1,4,6,10,30,44], iterated tabu search [36], simulated annealing [25], iterated greedy algorithm [28], estimation of distribution algorithms [43], genetic algorithms [13], variable neighborhood search [6,8], scatter search [15,21], path-relinking method [2,3] and memetic search [24]. Another approach that has received considerable attention in the solution of the MDP is greedy randomized adaptive search procedure (GRASP) [2,3,10,16,[40][41][42].…”