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.

Flying elephants: a general method for solving non-differentiable problems

“…Xavier (2012) introduces the use of the FE approach to solve the Fermat-Weber problem. The computational experiments with the new approach show a performance similar to the most efficient algorithms for solving problems up to 1,060 cities, the previous largest instance, see Brimberg et al (2000) and Plastino et al (2011). Xavier (2012 and Xavier et al (2014a) present also results for problems never considered in the literature, with up to 85,900 cities, a new superior bound size about 80 times larger.…”

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

“…The CS heuristic of Rabello et al. () 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., ). In the next section, the CS heuristic of Rabello et al.…”

“…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., ), p‐median problem (Plastino et al., ; Martins et al., ), the efficient server replication for reliable multicast problem (Plastino et al., ), and the maximum diversity problem (Santos et al., ). 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., ; Barbalho et al., ; Guerine et al., ). All these mentioned works follow the same structure: embedding data mining techniques within a GRASP context to solve optimization problems.…”

Metaheuristic Approach Based on Neighbourhood Search for Solving P-Median Problem

“…Initially, the variable to hold the optimal solution instigated is initialized with null set. Then the construction phase is implemented which is adopted from [25] and then the neighborhood search approach is employed to the constructed solution. The quality of the so obtained solution is compared to the current optimal solution found and, if necessary, the optimal solution is updated.…”

“…One such hybrid scheme results from the assortment of hypothesis and policies from two or more metaheuristics and another one counterparts to Metaheuristics united with concepts and procedures from other areas accountable for performing exclusive tasks that can progress the original method. The hybridization of GRASP with neighbourhood process initially anticipated, introduced and adopted to the set packing problem [15,16,25].…”