Randomized local search,evolutionary algorithms,and the minimum spanning tree problem

Randomized search heuristics, among them randomized local search and evolutionary algorithms, are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization. The analysis of these randomized search heuristics has been started for some well-known problems, and this approach is followed here for the minimum spanning tree problem. After motivating this line of research, it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms.     

Performance analysis of partial-match search algorithms for BD trees

Database systems are becoming increasingly popular for answering queries. Partial-match search queries are an important class of queries in such a system. Several storage structures have been proposed to answer these queries efficiently. The BD tree is an example of such a storage structure. A previous study indicated that the k-d tree performance is better than that of the BD tree for partial-match search queries. A recent paper reported some improved algorithms. However, it is unclear whether the improved algorithms show the BD tree in a favourable light for partial-match search queries. This paper explores the performance of these algorithms and compares their performance to that of the k-d tree. Since the BD tree construction process uses some heuristics to make it a better balanced tree, this paper also evaluates the effect of these heuristics on the partial-match search algorithms. The major conclusions of this study are that the BD tree performance for partial-match search is better than that of the k-d tree when an improved algorithm is used for partial-match search, and only the DZ expression rearrangement heuristic has substantial effect on partial-match search performance.     

Solution counting algorithms for constraint-centered search heuristics

Constraints have played a central role in cp because they capture key substructures of a problem and efficiently exploit them to boost inference. This paper intends to do the same thing for search, proposing constraint-centered heuristics which guide the exploration of the search space toward areas that are likely to contain a high number of solutions. We first propose new search heuristics based on solution counting information at the level of individual constraints. We then describe efficient algorithms to evaluate the number of solutions of two important families of constraints: occurrence counting constraints, such as alldifferent, and sequencing constraints, such as regular. In both cases we take advantage of existing filtering algorithms to speed up the evaluation. Experimental results on benchmark problems show the effectiveness of our approach. An earlier version of this paper appeared as [24].     

Evolutionary algorithms for the satisfiability problem

Several evolutionary algorithms have been proposed for the satisfiability problem. We review the solution representations suggested in literature and choose the most promising one - the bit string representation - for further evaluation. An empirical comparison on commonly used benchmarks is presented for the most successful evolutionary algorithms and for WSAT, a prominent local search algorithm for the satisfiability problem. The key features of successful evolutionary algorithms are identified, thereby providing useful methodological guidelines for designing new heuristics. Our results indicate that evolutionary algorithms are competitive to WSAT.     

Solving the feeder bus network design problem by genetic algorithms and ant colony optimization

This paper proposes the design and analysis of two metaheuristics, genetic algorithms and ant colony optimization, for solving the feeder bus network design problem. A study of how these proposed heuristics perform is carried out on several randomly generated test problems to evaluate their computational efficiency and the quality of solutions obtained by them. The results are also compared to those published in the literature. Computational experiments have shown that both heuristics are comparable to the state-of-the-art algorithms such as simulated annealing and tabu search.     

Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems

The offline 2D bin packing problem (2DBPP) is an NP-hard combinatorial optimization problem in which objects with various width and length sizes are packed into minimized number of 2D bins. Various versions of this well-known industrial engineering problem can be faced frequently. Several heuristics have been proposed for the solution of 2DBPP but it has not been possible to find the exact solutions for large problem instances. Next fit, first fit, best fit, unified tabu search, genetic and memetic algorithms are some of the state-of-the-art methods successfully applied to this important problem. In this study, we propose a set of novel hyper-heuristic algorithms that select/combine the state-of-the-art heuristics and local search techniques for minimizing the number of 2D bins. The proposed algorithms introduce new crossover and mutation operators for the selection of the heuristics. Through the results of exhaustive experiments on a set of offline 2DBPP benchmark problem instances, we conclude that the proposed algorithms are robust with their ability to obtain high percentage of the optimal solutions.     

Exploring very large state spaces using genetic algorithms

We present a novel framework for exploring very large state spaces of concurrent reactive systems. Our framework exploits application-independent heuristics using genetic algorithms to guide a state-space search toward error states. We have implemented this framework in conjunction with VeriSoft, a tool for exploring the state spaces of software applications composed of several concurrent processes executing arbitrary code. We present experimental results obtained with several examples of programs, including a C implementation of a public-key authentication protocol. We discuss heuristics and properties of state spaces that help a genetic search detect deadlocks and assertion violations. For finding errors in very large state spaces, our experiments show that a genetic search using simple heuristics can significantly outperform random and systematic searches.     

Filtered and recovering beam search algorithms for the early/tardy scheduling problem with no idle time

In this paper, we present filtered and recovering beam search algorithms for the single machine earliness/tardiness scheduling problem with no idle time, and compare them with existing neighbourhood search and dispatch rule heuristics. Filtering procedures using both priority evaluation functions and problem-specific properties have been considered.The computational results show that the recovering beam search algorithms outperform their filtered counterparts, while the priority-based filtering procedure proves superior to the rules-based alternative. The best solutions are given by the neighbourhood search algorithm, but this procedure is computationally intensive and can only be applied to small or medium size instances. The recovering beam search heuristic provides results that are close in solution quality and is significantly faster, so it can be used to solve even large problems.     

Applying genetic algorithms to game search trees

 Computer game playing is an important artificial intelligence research field in that the results can usually be applied to other related fields. One of the key computer-game-playing issues is designing effective search algorithms. Traditional search algorithms incur great temporal and spatial complexities when exploring deeply into search trees to find good next moves. Searches are thus usually not deep enough to derive good playing strategies. In this paper, we focus on one-player game search trees, and propose a genetic-algorithm-based approach to enhancing the speed and accuracy of game tree searches. Experiments show that our algorithm can improve solution accuracy and search speed.     

Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: Overview and progress report

Nowadays, a promising way to obtain hybrid metaheuristics concerns the combination of several search algorithms with strong specialization in intensification and/or diversification. The flexible architecture of evolutionary algorithms allows specialized models to be obtained with the aim of providing intensification and/or diversification. The outstanding role that is played by evolutionary algorithms at present justifies the choice of their specialist approaches as suitable ingredients to build hybrid metaheuristics.This paper focuses on hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification. We first give an overview of the existing research on this topic, describing several instances grouped into three categories that were identified after reviewing specialized literature. Then, with the aim of complementing the overview and providing additional results and insights on this line of research, we present an instance that consists of an iterated local search algorithm with an evolutionary perturbation technique. The benefits of the proposal in comparison to other iterated local search algorithms proposed in the literature to deal with binary optimization problems are experimentally shown. The good performance of the reviewed approaches and the suitable results shown by our instance allow an important conclusion to be achieved: the use of evolutionary algorithms specializing in intensification and diversification for building hybrid metaheuristics becomes a prospective line of research for obtaining effective search algorithms.     

Optimal switch location in mobile communication networks using hybrid genetic algorithms

The optimal positioning of switches in a mobile communication network is an important task, which can save costs and improve the performance of the network. In this paper we propose a model for establishing which are the best nodes of the network for allocating the available switches, and several hybrid genetic algorithms to solve the problem. The proposed model is based on the so-called capacitated p-median problem, which have been previously tackled in the literature. This problem can be split in two subproblems: the selection of the best set of switches, and a terminal assignment problem to evaluate each selection of switches. The hybrid genetic algorithms for solving the problem are formed by a conventional genetic algorithm, with a restricted search, and several local search heuristics. In this work we also develop novel heuristics for solving the terminal assignment problem in a fast and accurate way. Finally, we show that our novel approaches, hybridized with the genetic algorithm, outperform existing algorithms in the literature for the p-median problem.     

A comparison of multiobjective depth-first algorithms

Many real world problems involve several, usually conflicting, objectives. Multiobjective analysis deals with these problems locating trade-offs between different optimal solutions. Regarding graph search problems, several algorithms based on best-first and depth-first approaches have been proposed to return the set of all Pareto optimal solutions. This article presents a detailed comparison between two representatives of multiobjective depth-first algorithms, PIDMOA* and MO-DF-BnB. Both of them extend previous single-objective search algorithms with linear-space requirements to the multiobjective case. Experimental analyses on their time performance over tree-shaped search spaces are presented. The results clarify the fitness of both algorithms to parameters like the number or depth of goal nodes.     

Evolutionary algorithms for scheduling m-machine flow shop with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs–m-machines flow shops under lot sizing environment. Lot streaming (Lot sizing) is the process of creating sub lots to move the completed portion of a production sub lots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. Evolutionary algorithms that belong to search heuristics find more applications in recent research. Genetic algorithm (GA) and hybrid genetic algorithm (HEA) also known as hybrid evolutionary algorithm fall under evolutionary heuristics. On this concern this paper proposes two evolutionary algorithms namely, GA and HEA to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set-up time. The following two algorithms are used to evaluate the performance of the proposed GA and HEA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) simulated annealing algorithm (SA) for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

Hybrid genetic algorithms for timetabling

Hybrid genetic algorithms are presented that use optimization heuristics and genetic techniques to outperform all existing programs for the timetabling problem. The timetabling problem is very hard (NP-complete) and a general polynomial time deterministic algorithm is not known. An artificial intelligence approach, in a logic programming environment, may be useful for such a problem. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited for this kind of problem, since there exists an easy way to assess a good timetable but not a well-structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solutions. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the problem knowledge and the heuristics, i.e., from the timetable builder. A fundamental issue and a general problem in the decision process and automated reasoning is how to efficiently obtain logic decisions under disjunctive constraints. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present article illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favorably with the best-known programs to solve decisions problems under logic constraints. Complexity of the new algorithms and results of significant experiments are reported. © 1996 John Wiley & Sons, Inc.     

A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding

Segmentation is a critical task in image processing. Bi-level segmentation involves dividing the whole image into partitions based on a threshold value, whereas multilevel segmentation involves multiple threshold values. A successful segmentation assigns proper threshold values to optimise a criterion such as entropy or between-class variance. High computational cost and inefficiency of an exhaustive search for the optimal thresholds leads to the use of global search heuristics to set the optimal thresholds. An emerging area in global heuristics is swarm-intelligence, which models the collective behaviour of the organisms. In this paper, two successful swarm-intelligence-based global optimisation algorithms, particle swarm optimisation (PSO) and artificial bee colony (ABC), have been employed to find the optimal multilevel thresholds. Kapur's entropy, one of the maximum entropy techniques, and between-class variance have been investigated as fitness functions. Experiments have been performed on test images using various numbers of thresholds. The results were assessed using statistical tools and suggest that Otsu's technique, PSO and ABC show equal performance when the number of thresholds is two, while the ABC algorithm performs better than PSO and Otsu's technique when the number of thresholds is greater than two. Experiments based on Kapur's entropy indicate that the ABC algorithm can be efficiently used in multilevel thresholding. Moreover, segmentation methods are required to have a minimum running time in addition to high performance. Therefore, the CPU times of ABC and PSO have been investigated to check their validity in real-time. The CPU time results show that the algorithms are scalable and that the running times of the algorithms seem to grow at a linear rate as the problem size increases.     

Automated discovery of local search heuristics for satisfiability testing

The development of successful metaheuristic algorithms such as local search for a difficult problem such as satisfiability testing (SAT) is a challenging task. We investigate an evolutionary approach to automating the discovery of new local search heuristics for SAT. We show that several well-known SAT local search algorithms such as Walksat and Novelty are composite heuristics that are derived from novel combinations of a set of building blocks. Based on this observation, we developed CLASS, a genetic programming system that uses a simple composition operator to automatically discover SAT local search heuristics. New heuristics discovered by CLASS are shown to be competitive with the best Walksat variants, including Novelty+. Evolutionary algorithms have previously been applied to directly evolve a solution for a particular SAT instance. We show that the heuristics discovered by CLASS are also competitive with these previous, direct evolutionary approaches for SAT. We also analyze the local search behavior of the learned heuristics using the depth, mobility, and coverage metrics proposed by Schuurmans and Southey.     

Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics

Neural Computing and Applications - The aim of this study was to compare the performance of the well-known genetic algorithms and tabu search heuristics with the financial problem of the partial...     

Fitness landscape analysis and memetic algorithms for the quadratic assignment problem

In this paper, a fitness landscape analysis for several instances of the quadratic assignment problem (QAP) is performed, and the results are used to classify problem instances according to their hardness for local search heuristics and meta-heuristics based on local search. The local properties of the fitness landscape are studied by performing an autocorrelation analysis, while the global structure is investigated by employing a fitness distance correlation analysis. It is shown that epistasis, as expressed by the dominance of the flow and distance matrices of a QAP instance, the landscape ruggedness in terms of the correlation length of a landscape, and the correlation between fitness and distance of local optima in the landscape together are useful for predicting the performance of memetic algorithms-evolutionary algorithms incorporating local search (to a certain extent). Thus, based on these properties, a favorable choice of recombination and/or mutation operators can be found. Experiments comparing three different evolutionary operators for a memetic algorithm are presented.     

Heuristic evaluation functions in artificial intelligence search algorithms

We consider a special case of heuristics, namely numeric heuristic evaluation functions, and their use in artificial intelligence search algorithms. The problems they are applied to fall into three general classes: single-agent path-finding problems, two-player games, and constraint-satisfaction problems. In a single-agent path-finding problem, such as the Fifteen Puzzle or the travelling salesman problem, a single agent searches for a shortest path from an initial state to a goal state. Two-player games, such as chess and checkers, involve an adversarial relationship between two players, each trying to win the game. In a constraint-satisfaction, problem, such as the 8-Queens problem, the task is to find a state that satisfies a set of constraints. All of these problems are computationally intensive, and heuristic evaluation functions are used to reduce the amount of computation required to solve them. In each case we explain the nature of the evaluation functions used, how they are used in search algorithms, and how they can be automatically learned or acquired.