A hybrid three-phase approach for the Max-Mean Dispersion Problem

A Hybrid Metaheuristic of Integrating Estimation of Distribution Algorithm with Tabu Search for the Max‐Mean Dispersion Problem

“…In this section, we report experimental comparisons between our EDA-TS algorithm and the best algorithms in the literature on solving different sizes of benchmarks. Table 3 shows results of different algorithms on solving the instances with 500 variables, including a path relinking algorithm (PR) [10], a hybrid heuristic (HH) [11], a tabu search algorithm (TPTS) [13], a hybrid three-phase approach (HTP) [12], a tabu search-based memetic algorithm (TSMA) [9], a variable neighborhood search approach (GVNS) [14], and our EDA-TS algorithm. The results of other algorithms are directly extracted from [9,14].…”

“…Table 3: Computational comparisons between EDA-TS and other state-of-the-art algorithms on instances with 500 variables. Instances PR [10] HH [11] HTP [12] TPTS [13] TSMA [9] GVNS [14] EDA Tables 6 and 7 compare EDA-TS with GVNS for solving instances with 1500 and 2000 variables since GVNS is the only algorithm that reports results on these instances. From these two tables, we find that EDA-TS is able to find better solution values for 38 out of 40 instances.…”

“…Della Croce et al (2014) [11] developed a twophase hybrid heuristic, where the first phase solves a mixed integer programming formulation to obtain an initial set of solutions and the second phase employs a local branch strategy to refine the quality of solutions. An extended version of this algorithm is presented in Della Croce et al (2016) [12], where a path relinking phase is added to further enhance the quality of solutions. Carrasco et al (2015) [13] proposed a dynamic tabu search algorithm, where various short-term and long-term memory structures are integrated to enhance the performance of tabu search.…”

“…To be specific, all the moves are first categorized as tabu and nontabu according to the tabu and aspiration rules. Then, the objective function value of each neighborhood solution caused by the 1-flip move is quickly evaluated according to (11) and (12). Finally, either the nontabu move with the best objective value or a tabu move that satisfies the aspiration rule is chosen to be performed to move to the next solution.…”

Tabu search guided by reinforcement learning for the max-mean dispersion problem

“…In 2014, Croce et al [8] developed a two-stage hybrid heuristic method that combines a mixed integer nonlinear solver and a local branch program. Late in 2016, the same author improved a new version of this algorithm by adding a path phase enhance the quality of the solution [9]. In 2015, Carrasho et al [6] dynamically used an efficient two-savage tabu-search algorithm.…”