A Hybrid Data Mining Metaheuristic for the p-Median Problem

Abstract

Metaheuristics represent an important class of techniques to solve, approximately, hard combinatorial optimization problems for which the use of exact methods is impractical. In this work, we propose a hybrid version of the GRASP metaheuristic, which incorporates a data mining process, to solve the p-median problem. We believe that patterns obtained by a data mining technique, from a set of sub-optimal solutions of a combinatorial optimization problem, can be used to guide metaheuristic procedures in the search for better solutions. Traditional GRASP is an iterative metaheuristic which returns the best solution reached over all iterations. In the hybrid GRASP proposal, after executing a significant number of iterations, the data mining process extracts patterns from an elite set of sub-optimal solutions for the pmedian problem. These patterns present characteristics of near optimal solutions and can be used to guide the following GRASP iterations in the search through the combinatorial solution space. Computational experiments, comparing traditional GRASP and different data mining hybrid proposals for the p-median problem, showed that employing patterns mined from an elite set of sub-optimal solutions made the hybrid GRASP find better results. Besides, the conducted experiments also evidenced that incorporating a data mining technique into a metaheuristic accelerated the process of finding near optimal and optimal solutions.

A hybrid data mining heuristic to solve the point‐feature cartographic label placement problem

“…The CS heuristic of Rabello et al (2014) was chosen to be the base of our proposed hybrid data mining heuristic first because it is the most recent approach to this problem and a state-of-the-art heuristic for the PFCLP, and also due to the challenge of incorporating the data mining technique into a metaheuristic with a different structure, quite distinct from the standard hybrid DM-GRASP and MDM-GRASP processes (Plastino et al, 2011). In the next section, the CS heuristic of Rabello et al (2014) is then revised with details.…”

“…The idea is to collect a set of high-quality solutions of the optimization problem (called the elite set), apply the mining step over this elite set, which extracts a subset of elements (patterns) that frequently occurs in the referred set, and finally use these patterns to guide the search. The DM-GRASP framework has been applied to improve heuristics for different optimization problems (Santos et al, 2008;Plastino et al, 2011Plastino et al, , 2014Barbalho et al, 2013;Guerine et al, 2016;Martins et al, 2018a).…”

“…The mining step (i.e., the mine procedure in line 26) calls the maximal FIM technique each time the elite set becomes stable, similar to the multidata mining (MDM) method described in Plastino et al (2011). An elite set is stable when it remains φ iterations without being updated.…”

“…The third column of Table 1 shows the original configuration of CS reported in Rabello et al (2014). For Table 2, the third column presents usual values for parameters related to data mining hybrid approaches adopted, for example, in Plastino et al (2011) and Guerine et al (2016). Finally, the last columns present the best configuration reached by irace for both CS and MDM-CS, following up the irace output chosen parameters values.…”

“…The DM-GRASP framework has been applied to improve state-of-the-art heuristics for different optimization problems such as the two-path network design problem (Barbalho et al, 2013), p-median problem (Plastino et al, 2011;Martins et al, 2018a), the efficient server replication for reliable multicast problem (Plastino et al, 2014), and the maximum diversity problem (Santos et al, 2008). Besides, based on the hypothesis that mining more than once could explore the gradual evolution of the elite set and extract refined patterns, the concept of multidata mining GRASP (MDM-GRASP) was also investigated (Plastino et al, 2011;Barbalho et al, 2013;Guerine et al, 2016). All these mentioned works follow the same structure: embedding data mining techniques within a GRASP context to solve optimization problems.…”