Exact computation of the expectation curves of the bit-flip mutation using landscapes theory

Chicano, F., & Alba E. (2011). Exact computation of the expectation curves of the bit-flip mutation using landscapes theory. Proceedings of 13th Annual Genetic and Evolutionary Computation Conference, Dublin, Ireland, July 12-16, 2011. pp. 2027–2034.Bit-flip mutation is a common operation when a genetic algorithm is applied to solve a problem with binary representation. We use in this paper some results of landscapes theory and Krawtchouk polynomials to exactly compute the expected value of the fitness of a mutated solution. We prove that this expectation is a polynomial in p, the probability of flipping a single bit. We analyze these polynomials and propose some applications of the obtained theoretical results.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project) and the Andalusian Government under contract P07-TIC-03044 (DIRICOM project)

Efficient Hill Climber for Multi-Objective Pseudo-Boolean Optimization

Chicano, F., Whitley D., & Tinós R. (2016). Efficient Hill Climber for Multi-Objective Pseudo-Boolean Optimization. 16th European Conference on Evolutionary Computation for Combinatorial Optimization (LNCS 9595), pp. 88-103Local search algorithms and iterated local search algorithms are a basic technique. Local search can be a stand-alone search method, but it can also be hybridized with evolutionary algorithms. Recently, it has been shown that it is possible to identify improving moves in Hamming neighborhoods for k-bounded pseudo-Boolean optimization problems in constant time. This means that local search does not need to enumerate neighborhoods to find improving moves. It also means that evolutionary algorithms do not need to use random mutation as a operator, except perhaps as a way to escape local optima. In this paper, we show how improving moves can be identified in constant time for multiobjective problems that are expressed as k-bounded pseudo-Boolean functions. In particular, multiobjective forms of NK Landscapes and Mk Landscapes are considered.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Fulbright program, Ministerio de Educación (CAS12/00274), Ministerio de Economía y Competitividad (TIN2014-57341-R), Air Force Office of Scientific Research, Air Force Materiel Command, USAF (FA9550-11-1-0088), FAPESP (2015/06462-1) and CNPq

Efficient Hill Climber for Constrained Pseudo-Boolean Optimization Problems

Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For $k$-bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time. These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to the so-called Gray Box Optimization, where part, but not all, of the details of the objective functions are used to better explore the search space. One important limitation of all the previous proposals is that they can only be applied to unconstrained pseudo-Boolean optimization problems. In this work, we address the constrained case for multi-objective $k$-bounded pseudo-Boolean optimization problems. We find that adding constraints to the pseudo-Boolean problem has a linear computational cost in the hill climber.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Dynastic potential crossover operator

An optimal recombination operator provides an optimal solution fulfilling the gene transmission property: the value of any variable in the offspring must be inherited from one of the parents. In the case of binary variables, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. In general, exploring this hyperplane is computationally costly, but if the objective function has a low number of nonlinear interactions among the variables, the exploration can be done in $O(4^{\beta}(n+m)+n^2)$ time, for problems with $n$ decision variables, $m$ subfunctions composing the objective function and where $\beta$ is a constant. In this talk, we present a quasi-optimal recombination operator, called Dynastic Potential Crossover (DPX), that runs in $O(4^{\beta}(n+m)+n^2)$ time in any case and is able to act as an optimal recombination operator for low-epistasis combinatorial problems. We show some experimental results where the operator is integrated in DRILS (an ILS with recombination) and standard EA solving NKQ Landscapes and MAX-SAT.This research is funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2017-88213-R, and the University of Malaga. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Elementary Landscape Decomposition of the Test Suite Minimization Problem

Chicano, F., Ferrer J., & Alba E. (2011). Elementary Landscape Decomposition of the Test Suite Minimization Problem. In Proceedings of Search Based Software Engineering, Szeged, Hungary, September 10-12, 2011. pp. 48–63.Landscape theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of a special kind of landscape called elementary landscape. The decomposition of the objective function of a problem into its elementary components provides additional knowledge on the problem that can be exploited to create new search methods for the problem. We analyze the Test Suite Minimization problem in Regression Testing from the point of view of landscape theory. We find the elementary landscape decomposition of the problem and propose a practical application of such decomposition for the search.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491- C04-01 (the M∗ project) and the Andalusian Government under contract P07- TIC-03044 (DIRICOM project)

Mutantes como apoyo para la valoración de pruebas

En este trabajo proponemos el uso de la técnica de mutation testing, o pruebas basadas en mutación, en asignaturas de pruebas de software para ayudar en la labor de evaluación de las mismas, a la vez que su propio uso ayuda a los alumnos a entender y asimilar la técnica en sí, utilizándola para mejorar sus conjuntos de pruebas. Describimos nuestra experiencia usando mutation testing en una asignatura de pruebas de software. Gracias al uso de una herramienta que automatiza la generación de mutantes y su evaluación, el profesor puede obtener una idea rápida de la calidad de las pruebas que puede servir para guiar/confirmar su evaluación. El alumno, por su parte, puede usarla para obtener una primera evaluación de su trabajo y como guía para mejorar el conjunto de pruebas.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Comparing metaheuristic algorithms for error detection in Java programs

Chicano, F., Ferreira M., & Alba E. (2011). Comparing Metaheuristic Algorithms for Error Detection in Java Programs. In Proceedings of Search Based Software Engineering, Szeged, Hungary, September 10-12, 2011. pp. 82–96.Model checking is a fully automatic technique for checking concurrent software properties in which the states of a concurrent system are explored in an explicit or implicit way. The main drawback of this technique is the high memory consumption, which limits the size of the programs that can be checked. In the last years, some researchers have focused on the application of guided non-complete stochastic techniques to the search of the state space of such concurrent programs. In this paper, we compare five metaheuristic algorithms for this problem. The algorithms are Simulated Annealing, Ant Colony Optimization, Particle Swarm Optimization and two variants of Genetic Algorithm. To the best of our knowledge, it is the first time that Simulated Annealing has been applied to the problem. We use in the comparison a benchmark composed of 17 Java concurrent programs. We also compare the results of these algorithms with the ones of deterministic algorithms.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project) and the Andalusian Government under contract P07-TIC-03044 (DIRICOM project)

Enhancing partition crossover with articulation points analysis

Partition Crossover is a recombination operator for pseudo-Boolean optimization with the ability to explore an exponential number of solutions in linear or square time. It decomposes the objective function as a sum of subfunctions, each one depending on a different set of variables. The decomposition makes it possible to select the best parent for each subfunction independently, and the operator provides the best out of $2^q$ solutions, where $q$ is the number of subfunctions in the decomposition. These subfunctions are defined over the connected components of the recombination graph: a subgraph of the objective function variable interaction graph containing only the differing variables in the two parents. In this paper, we advance further and propose a new way to increase the number of linearly independent subfunctions by analyzing the articulation points of the recombination graph. These points correspond to variables that, once flipped, increase the number of connected components. The presence of a connected component with an articulation point increases the number of explored solutions by a factor of, at least, 4. We evaluate the new operator using Iterated Local Search combined with Partition Crossover to solve NK Landscapes and MAX-SAT.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Funding was provided by the Fulbright program, the Spanish Ministry of Education, Culture and Sport (CAS12/00274), the Spanish Ministry of Economy and Competitiveness and FEDER (TIN2014-57341-R and TIN2017-88213-R), the Air Force Office of Scientific Research, (FA9550-11-1-0088), the Leverhulme Trust (RPG-2015-395), the FAPESP (2015/06462-1) and CNPq (304400/2014-9)

Optimizing One Million Variable NK Landscapes by Hybridizing Deterministic Recombination and Local Search

In gray-box optimization, the search algorithms have access to the variable interaction graph (VIG) of the optimization problem. For Mk Landscapes (and NK Landscapes) we can use the VIG to identify an improving solution in the Hamming neighborhood in constant time. In addition, using the VIG, deterministic Partition Crossover is able to explore an exponential number of solutions in a time that is linear in the size of the problem. Both methods have been used in isolation in previous search algorithms. We present two new gray-box algorithms that combine Partition Crossover with highly efficient local search. The best algorithms are able to locate the global optimum on Adjacent NK Landscape instances with one million variables. The algorithms are compared with a state-of-the-art algorithm for pseudo-Boolean optimization: Gray-Box Parameterless Population Pyramid. The results show that the best algorithm is always one combining Partition Crossover and highly efficient local search. But the results also illustrate that the best optimizer differs on Adjacent and Random NK Landscapes.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech