Black box scatter search for general classes of binary optimization problems

Abstract

The purpose of this paper is to apply the scatter search methodology to general classes of binary problems. We focus on optimization problems for which the solutions are represented as binary vectors and that may or may not include constraints. Binary problems arise in a variety of settings, including engineering design and statistical mechanics (e.g., the spin glass problem). A distinction is made between two sets of general constraint types that are handled directly by the solver and other constraints that are addressed via penalty functions. In both cases, however, the heuristic treats the objective function evaluation as a black box. We perform computational experiments with four well-known binary optimization problems to study the efficiency (speed) and effectiveness (solution quality) of the proposed method. Comparisons are made against both commercial software and specialized procedures on a set of 376 instances. We chose commercial software that is similar in nature to the proposed procedure, namely, it treats the objective function as a black box and the search is based on evolutionary optimization techniques.

A black-box scatter search for optimization problems with integer variables

“…Computational tests showed that their procedure outperformed the general-purpose optimizers that are not specialized to only tackle permutation problems. Similar results were obtained in (Gortázar, Duarte, Laguna, & Martí, 2010) for problems with binary variables. Some solution methodologies have been designed with the black-box framework in mind, as in the case of random-key genetic algorithms (RKGA).…”

“…It is not expected for blackbox methods to perform better than the state-of-the-art in any particular problem instance; however, the comparison is helpful in assessing the size of the gap between a general and a specialized procedure in each problem class. This work may be viewed as the fourth in a series of general-purpose solvers created for problems with specific types of variables: continuous variables , permutation variables (Campos, Laguna, & Martí, 2005) and binary variables (Gortázar, Duarte, Laguna, & Martí, 2010). Specifically, our interest is to develop a solver for an evaluation black box that takes as input a vector of integers.…”

A review on algorithms for maximum clique problems

“…Three more recent examples of B&B algorithms are provided in Aringhieri, Bruglieri, & Cordone (2009) ;Martí, Gallego, & Duarte (2010) and Sørensen (2004) which can solve problems with up to 150 vertices. On the other hand, there are many heuristics devoted to the MEWCP: Tabu search (Aringhieri & Cordone, 2011;Macambira, 2003), iterated tabu search (Palubeckis, 2007), iterated greedy algorithm (Lozano, Molina, & García-Martínez, 2011), greedy randomized adaptive search procedure (Andrade, de Andrade, Martins, & Plastino, 2005;Silva, De Andrade, Ochi, Martins, & Plastino, 2007), genetic algorithm (Feng, Jiang, Fan, & Fu, 2010), variable neighborhood search (Brimberg, Mladenović, Urošević, & Ngai, 2009), scatter search (Gallego, Duarte, Laguna, & Martí, 2009;Gortázar, Duarte, Laguna, & Martí, 2010), path-relinking method (Andrade, de Andrade, Martins, & Plastino, 2005) and memetic search (Wang, Hao, Glover, & Lü, 2014;Wu & Hao, 2013). Comprehensive surveys and comparisons of the most significant heuristic and metaheuristic methods for the MEWCP before 2011 can be found in Cordone (2011) andPardo (2013).…”

A Scatter Search Heuristic for the Optimal Location, Sizing and Contract Pricing of Distributed Generation in Electric Distribution Systems

“…Developed in the 1970s, recent applications of SS show its effectiveness to solve nonlinear optimization problems [32], and in optimization problems where the evaluation of the objective function implies costly computations (e.g., black-box optimization [33] and simulation optimization [34]). This advantage makes SS a good candidate for the solution of the bilevel optimization problem in models (1)- (20) since every feasible solution of (1)-(7) requires the solution of an optimal dispatch to find the reaction of the DisCo (problems (8)- (20)).…”