An OR Practitioner's Solution Approach for the Set Covering Problem

Abstract

The set covering problem (SCP) is an NP-complete problem that has many important industrial applications. Since industrial applications are typically large in scale, exact solution algorithms are not feasible for operations research (OR) practitioners to use when called on to solve real-world problems involving SCPs. However, the best performing heuristics for the SCP reported in the literature are not usually straightforward to implement. Additionally, these heuristics usually require the fine-tuning of several parameters. In contrast, simple greedy or even randomized greedy heuristics typically do not give as good results as the more sophisticated heuristics. In this paper, the authors present a compromise; a straightforward to implement, population-based solution approach for the SCP. It uses a randomized greedy approach to generate an initial population and then uses a genetic-based two phase approach to improve the population solutions. This two-phase approach uses transformation equations based on a Teaching-Learning based optimization approach developed by Rao, Savsani and Vakharia (2011, 2012) for continuous nonlinear optimization problems. Empirical results using set covering problems from Beasley's OR-library demonstrate the competitiveness of this approach both in terms of solution quality and execution time. The advantage to this approach is its relative simplicity for the practitioner to implement.

Exploring Further Advantages in an Alternative Formulation for the Set Covering Problem

“…is dataset is widely used to report empirical results in the current literature (see e.g. [9,40,48]).…”

“…However, the most widely applied metaheuristics for solving SCP are SIAs. Some examples are the artificial bee colony (ABC) algorithm [13,40,41], the ant colony optimization (ACO) algorithm [42][43][44], the firefly algorithm (FA) [45,46], the teaching-learning-based optimization (TLBO) algorithm [47,48], the electromagnetism-like (EM-like) algorithm [49,50], the shuffled frog leaping algorithm (SFLA) [51], the fruit fly optimization algorithm (FFOA) [52], the cuckoo search algorithm (CSA) [53,54], the cat swarm optimization (CSO) algorithm [55,56], the jumping particle swarm optimization (JPSO) method [57], the black hole optimization [54,58], and the monkey search algorithm [59].…”

“…us, the best results were usually obtained by SIAs. In this line, we should mention the valuable contributions of Naji-Azimi et al [48,49] and Balaji and Revathi [57] who got optimal or near-optimal solutions for classical SCP benchmarks.…”

“…at means that the algorithm could need to run some iterations before having the right information about the solution component quality. At this point, we propose to include a greedy population initialization step in ACO based on Lu and Vasko [48]. is step corresponds to line 1 of Algorithm 1.…”

Adaptive Black Hole Algorithm for Solving the Set Covering Problem

“…For instance, ant colony optimization [32][33][34][35], simulated annealing [36], tabu search [37], and genetic algorithms [38] have extensively been proposed to tackle the classic set covering problem. In recent years, research has been driven towards solving this problem by using recent bioinspired algorithms, such as teaching-learning based optimization [39] firefly optimization [40], cat swarm optimization [41], shuffled frog leaping [42], artificial bee colony [43], cuckoo search [44], and black hole algorithm [44], among others.…”