An annotated bibliography of GRASP – Part I: Algorithms

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the first of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. This paper covers algorithmic aspects of GRASP.     

Elucidating multiprocessors flow shop scheduling with dependent setup times using a twin particle swarm optimization

Particle swarm optimization (PSO) is a novel metaheuristic, which has been applied in a wide variety of production scheduling problems. Two basic characteristics of this algorithm are its efficiency and effectiveness in providing high-quality solutions. In order to improve the traditional PSO, this study proposes the incorporation of a local search heuristic into the basic PSO algorithm. The new, hybrid, metaheuristic is called “twin particle swarm optimization (TPSO)”. The proposed metaheuristic scheme is applied to a flow shop with multiprocessors scheduling problem, which can be considered a real world case regarding the production line. This study, as far as the multiprocessors flow shop production system is concerned, utilizes sequence dependent setup times as constraints. Finally, simulated data confirm the effectiveness and robustness of the proposed algorithm. The data test results indicate that TPSO has potential to replace PSO and become a significant heuristic algorithm for similar problems.     

Clustering search algorithm for the capacitated centered clustering problem

The capacitated centered clustering problem (CCCP) consists in partitioning a set of n points into p disjoint clusters with a known capacity. Each cluster is specified by a centroid. The objective is to minimize the total dissimilarity within each cluster, such that a given capacity limit of the cluster is not exceeded. This paper presents a solution procedure for the CCCP, using the hybrid metaheuristic clustering search (CS), whose main idea is to identify promising areas of the search space by generating solutions through a metaheuristic and clustering them into groups that are then further explored with local search heuristics. Computational results in test problems of the literature show that the CS found a significant number of new best-known solutions in reasonable computational times.     

Agent-based guided local search

The main contribution of the paper is to propose and validate a new hybrid approach for solving combinatorial optimization problems in which guided local search metaheuristic is incorporated into a cooperative multi-agent framework based on the concept of asynchronous teams (A-Teams). Generally, an A-Team assumes that a collection of software agents, each representing a particular problem solving method, cooperate to solve a problem by dynamically evolving a population of solutions. In the suggested implementation each software agent carries out a guided local search. The proposed approach has been extensively validated experimentally on one of the best known combinatorial optimization problem – the vehicle routing problem. The promising results of experiments have confirmed the effectiveness of the suggested approach.     

The discrete Unconscious search and its application to uncapacitated facility location problem

In this paper a discrete variant of Unconscious search (US) for solving uncapacitated facility location problem (UFLP) is proposed. Unconscious search mimics the process of psychoanalytic psychotherapy in which the psychoanalyst tries to access the unconscious of a mental patient to find the root cause his/her problem, which is encapsulated in unconsciousness. Unconscious search is a multi-start metaheuristic which has three main stages, namely construction, construction review and local search. In construction phase a new solution is generated. In construction review the generated solution in construction phase is used to produce more starting points for using in the local search phase. The results of applying US to UFLP shows that this metaheuristic can determine high quality solutions in short processing time comparing to other heuristics.     

A systematic review of search-based testing for non-functional system properties

Search-based software testing is the application of metaheuristic search techniques to generate software tests. The test adequacy criterion is transformed into a fitness function and a set of solutions in the search space are evaluated with respect to the fitness function using a metaheuristic search technique. The application of metaheuristic search techniques for testing is promising due to the fact that exhaustive testing is infeasible considering the size and complexity of software under test. Search-based software testing has been applied across the spectrum of test case design methods; this includes white-box (structural), black-box (functional) and grey-box (combination of structural and functional) testing. In addition, metaheuristic search techniques have also been applied to test non-functional properties. The overall objective of undertaking this systematic review is to examine existing work into non-functional search-based software testing (NFSBST). We are interested in types of non-functional testing targeted using metaheuristic search techniques, different fitness functions used in different types of search-based non-functional testing and challenges in the application of these techniques. The systematic review is based on a comprehensive set of 35 articles obtained after a multi-stage selection process and have been published in the time span 1996–2007. The results of the review show that metaheuristic search techniques have been applied for non-functional testing of execution time, quality of service, security, usability and safety. A variety of metaheuristic search techniques are found to be applicable for non-functional testing including simulated annealing, tabu search, genetic algorithms, ant colony methods, grammatical evolution, genetic programming (and its variants including linear genetic programming) and swarm intelligence methods. The review reports on different fitness functions used to guide the search for each of the categories of execution time, safety, usability, quality of service and security; along with a discussion of possible challenges in the application of metaheuristic search techniques.     

An annotated bibliography of GRASP–Part II: Applications

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic, have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the second of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. In the companion paper, algorithmic aspects of GRASP are surveyed. In this paper, we cover the literature where GRASP is applied to scheduling, routing, logic, partitioning, location, graph theory, assignment, manufacturing, transportation, telecommunications, biology and related fields, automatic drawing, power systems, and VLSI design.     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

Reactive Search strategies using Reinforcement Learning,local search algorithms and Variable Neighborhood Search

Optimization techniques known as metaheuristics have been applied successfully to solve different problems, in which their development is characterized by the appropriate selection of parameters (values) for its execution. Where the adjustment of a parameter is required, this parameter will be tested until viable results are obtained. Normally, such adjustments are made by the developer deploying the metaheuristic. The quality of the results of a test instance [The term instance is used to refer to the assignment of values to the input variables of a problem.] will not be transferred to the instances that were not tested yet and its feedback may require a slow process of “trial and error” where the algorithm has to be adjusted for a specific application. Within this context of metaheuristics the Reactive Search emerged defending the integration of machine learning within heuristic searches for solving complex optimization problems. Based in the integration that the Reactive Search proposes between machine learning and metaheuristics, emerged the idea of putting Reinforcement Learning, more specifically the Q-learning algorithm with a reactive behavior, to select which local search is the most appropriate in a given time of a search, to succeed another local search that can not improve the current solution in the VNS metaheuristic. In this work we propose a reactive implementation using Reinforcement Learning for the self-tuning of the implemented algorithm, applied to the Symmetric Travelling Salesman Problem.     

Competitive Hopfield Network Combined With Estimation of Distribution for Maximum Diversity Problems

This paper presents a discrete competitive Hopfield neural network (HNN) (DCHNN) based on the estimation of distribution algorithm (EDA) for the maximum diversity problem. In order to overcome the local minimum problem of DCHNN, the idea of EDA is combined with DCHNN. Once the network is trapped in local minima, the perturbation based on EDA can generate a new starting point for DCHNN for further search. It is expected that the further search is guided to a promising area by the probability model. Thus, the proposed algorithm can escape from local minima and further search better results. The proposed algorithm is tested on 120 benchmark problems with the size ranging from 100 to 5000. Simulation results show that the proposed algorithm is better than the other improved DCHNN such as multistart DCHNN and DCHNN with random flips and is better than or competitive with metaheuristic algorithms such as tabu-search-based algorithms and greedy randomized adaptive search procedure algorithms.      

Local search versus Path Relinking in metaheuristics: Redesigning Meta-RaPS with application to the multidimensional knapsack problem

Most heuristics for discrete optimization problems consist of two phases: a greedy-based construction phase followed by an improvement (local search) phase. Although the best solutions are usually generated after the improvement phase, there is usually a high computational cost for employing a local search algorithm. This paper seeks another alternative to reduce the computational burden of a local search while keeping solution quality by embedding intelligence in metaheuristics. A modified version of Path Relinking is introduced to replace the local search in the improvement phase of Meta-RaPS (Meta-Heuristic for Randomized Priority Search) which is currently classified as a memoryless metaheuristic. The new algorithm is tested using the 0–1 multidimensional knapsack problem, and it is observed that it could solve even the largest benchmark problems in significantly less time while maintaining solution quality compared to other algorithms in the literature.     

HYBRID METAHEURISTICS FOR THE DESIGN OF COUPLED RESONATOR FILTERS

The design of coupled resonator filters used in many telecommunication applications poses an optimization problem that can be tackled with heuristic methods. In many configurations, simple heuristic methods do not give satisfactory results, and the combination in hybrid metaheuristics of local and global search methods is a better approach. This article analyzes the systematic development of hybrid metaheuristic methods for the design of coupled resonator filters. Engineers normally use the MATLAB computing environment to work on the design of these devices, so the available MATLAB optimization toolboxes are used here as a basis to address those optimization problems. The results obtained are in general satisfactory, and the best results are obtained in the experiments with memetic algorithms in which methods based in populations (Genetic Algorithms and Scatter Search) are combined with local search methods to improve individuals in the population at different parts of the metaheuristic.     

Search‐based software test data generation: a survey

The use of metaheuristic search techniques for the automatic generation of test data has been a burgeoning interest for many researchers in recent years. Previous attempts to automate the test generation process have been limited, having been constrained by the size and complexity of software, and the basic fact that, in general, test data generation is an undecidable problem. Metaheuristic search techniques offer much promise in regard to these problems. Metaheuristic search techniques are high‐level frameworks, which utilize heuristics to seek solutions for combinatorial problems at a reasonable computational cost. To date, metaheuristic search techniques have been applied to automate test data generation for structural and functional testing; the testing of grey‐box properties, for example safety constraints; and also non‐functional properties, such as worst‐case execution time. This paper surveys some of the work undertaken in this field, discussing possible new future directions of research for each of its different individual areas. Copyright © 2004 John Wiley & Sons, Ltd.     

Active-guided evolution strategies for large-scale capacitated vehicle routing problems

We present an adaptation of the active-guided evolution strategies metaheuristic for the capacitated vehicle routing problem. The capacitated vehicle routing problem is a classical problem in operations research in which a set of minimum total cost routes must be determined for a fleet of identical capacitated vehicles in order to service a number of demand or supply points. The applied metaheuristic combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. The computational experiments were carried out on a set of 76 benchmark problems. The results demonstrate that the suggested method is highly competitive, providing the best-known solutions to 70 test instances.     

A multi-objective GRASP for partial classification

Metaheuristic algorithms have been used successfully in a number of data mining contexts and specifically in the production of classification rules. Classification rules describe a class of interest or a subset of this class, and as such may also be used as an aid in prediction. The production and selection of classification rules for a particular class of the database is often referred to as partial classification. Since partial classification rules are often evaluated according to a number of conflicting objectives, the generation of such rules is a task that is well suited to a multi-objective (MO) metaheuristic approach. In this paper we discuss how to adapt well known MO algorithms for the task of partial classification. Additionally, we introduce a new MO algorithm for this task based on a greedy randomized adaptive search procedure (GRASP). GRASP has been applied to a number of problems in combinatorial optimization, but it has very seldom been used in a MO setting, and generally only through repeated optimization of single objective problems, using either linear combinations of the objectives or additional constraints. The approach presented takes advantage of some specific characteristics of the data mining problem being solved, allowing for the very effective construction of a set of solutions that form the starting point for the local search phase of the GRASP. The resulting algorithm is guided solely by the concepts of dominance and Pareto-optimality. We present experimental results for our partial classification GRASP and other MO metaheuristics. These show that such algorithms are generally very well suited to this data mining task and furthermore, the GRASP brings additional efficiency to the search for partial classification rules.     

A scatter search approach for the minimum sum-of-squares clustering problem

A metaheuristic procedure based on the scatter search approach is proposed for the non-hierarchical clustering problem under the criterion of minimum sum-of-squares clustering. This algorithm incorporates procedures based on different strategies, such as local search, GRASP, tabu search or path relinking. The aim is to obtain quality solutions with short computation times. A series of computational experiments has been performed. The proposed algorithm obtains better results than previously reported methods, especially with small numbers of clusters.     

An improvement on the Migrating Birds Optimization with a problem-specific neighboring function for the multi-objective task allocation problem

Allocating tasks to processors is a well-known NP-Hard problem in distributed computing systems. Due to the lack of practicable exact solutions, it has been attracted by the researchers working on heuristic-based suboptimal search algorithms. With the recent inclusion of multiple objectives such as minimizing the cost, maximizing the throughput and maximizing the reliability, the problem gets even more complex and an efficient approximate method becomes more valuable. In this work, I propose a new solution for the multi-objective task allocation problem. My solution consists in designing a problem-specific neighboring function for an existing metaheuristic algorithm that is proven to be successful in quadratic assignment problems. The neighboring function, namely greedy reassignment with maximum release (GR-MR), provides a dynamic mechanism to switch the preference of the search between the exploration and exploitation. The experiments validate both that the quality of the solutions are close to the optimal and the proposed method performs significantly better comparing to three other metaheuristic algorithms. Neighboring functions being the common reusable components of metaheuristic algorithms, GR-MR can also be utilized by other metaheuristic-based solutions in the future.     

Andean Condor Algorithm for cell formation problems

This paper proposes a novel population based optimization algorithm called Andean Condor Algorithm (ACA) for solving cell formation problems. The ACA metaheuristic is inspired by the movement pattern of the Andean Condor when it searches for food. This pattern of movement corresponds to the flight distance traveled by the Andean Condor from its nest to the place where food is found. This distance varies depending on the seasons of the year. The ACA metaheuristic presents a balance of its population through a performance indicator based on the average quality of the population’s fitness. This balance determines the number of Andean Condors that will perform an exploration or intensification movements. ACA metaheuristics have a flexible design. It allows to easily integrate specific heuristics according to the optimization problem to be solved. Two types of computational experiments have been performed. According to the results obtained it has been possible to determine that ACA is an algorithm with an outstanding RPD% in relation to the algorithms BAT, MBO and PSO, robust and with a convergence which tends not to be trapped in the local optimums. Besides, according to the non-parametric multiple comparison, results have been obtained in which the ACA metaheuristic has significant differences in relation to the BAT, MBO and PSO algorithms.

     

Discrete symbiotic organisms search algorithm for travelling salesman problem

A Discrete Symbiotic Organisms Search (DSOS) algorithm for finding a near optimal solution for the Travelling Salesman Problem (TSP) is proposed. The SOS is a metaheuristic search optimization algorithm, inspired by the symbiotic interaction strategies often adopted by organisms in the ecosystem for survival and propagation. This new optimization algorithm has been proven to be very effective and robust in solving numerical optimization and engineering design problems. In this paper, the SOS is improved and extended by using three mutation-based local search operators to reconstruct its population, improve its exploration and exploitation capability, and accelerate the convergence speed. To prove that the proposed solution approach of the DSOS is a promising technique for solving combinatorial problems like the TSPs, a set of benchmarks of symmetric TSP instances selected from the TSPLIB library are used to evaluate its performance against other heuristic algorithms. Numerical results obtained show that the proposed optimization method can achieve results close to the theoretical best known solutions within a reasonable time frame.