Showing papers in "Journal of Heuristics in 2008"

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

Abstract: The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.

A reactive variable neighborhood tabu search for the heterogeneous fleet vehicle routing problem with time windows

Abstract: This paper presents a solution methodology for the heterogeneous fleet vehicle routing problem with time windows. The objective is to minimize the total distribution costs, or similarly to determine the optimal fleet size and mix that minimizes both the total distance travelled by vehicles and the fixed vehicle costs, such that all problem's constraints are satisfied. The problem is solved using a two-phase solution framework based upon a hybridized Tabu Search, within a new Reactive Variable Neighborhood Search metaheuristic algorithm. Computational experiments on benchmark data sets yield high quality solutions, illustrating the effectiveness of the approach and its applicability to realistic routing problems.

Simple ingredients leading to very efficient heuristics for the maximum clique problem

Abstract: Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules. A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances. It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper).

Approximating the maximum vertex/edge weighted clique using local search

Abstract: This paper extends the recently introduced Phased Local Search (PLS) algorithm to more difficult maximum clique problems and also adapts the algorithm to handle maximum vertex/edge weighted clique instances. PLS is a stochastic reactive dynamic local search algorithm that interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current sub-graph, and plateau search, where vertices of the current sub-graph are swapped with vertices not contained in the current sub-graph. These sub-algorithms differ in firstly their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree, or random selecting within vertex penalties that are dynamically adjusted during the search. Secondly, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. PLS has no problem instance dependent parameters and achieves state-of-the-art performance for maximum clique and maximum vertex/edge weighted clique problems over a large range of the commonly used DIMACS benchmark instances.

Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives

Abstract: In this paper, a new methodology is presented to solve different versions of multi-objective system redundancy allocation problems with prioritized objectives. Multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challenging for many practitioners. On the other hand, methods such as genetic algorithms and tabu search often yield numerous non-dominated Pareto optimal solutions, which makes the selection of one single best solution very difficult. In this research, a tabu search meta-heuristic approach is used to initially find the entire Pareto-optimal front, and then, Monte-Carlo simulation provides a decision maker with a pruned and prioritized set of Pareto-optimal solutions based on user-defined objective function preferences. The purpose of this study is to create a bridge between Pareto optimality and single solution approaches.

A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems

Abstract: We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators are employed to enhance the proposed algorithm's performance in terms of convergence behavior and computational effort as rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs). Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as would be the case when solving expensive MOPs.

Accelerating autonomous learning by using heuristic selection of actions

Abstract: This paper investigates how to make improved action selection for online policy learning in robotic scenarios using reinforcement learning (RL) algorithms. Since finding control policies using any RL algorithm can be very time consuming, we propose to combine RL algorithms with heuristic functions for selecting promising actions during the learning process. With this aim, we investigate the use of heuristics for increasing the rate of convergence of RL algorithms and contribute with a new learning algorithm, Heuristically Accelerated Q-learning (HAQL), which incorporates heuristics for action selection to the Q-Learning algorithm. Experimental results on robot navigation show that the use of even very simple heuristic functions results in significant performance enhancement of the learning rate.

Solving a bi-objective nurse rerostering problem by using a utopic Pareto genetic heuristic

Abstract: Nurse rerostering arises when at least one nurse announces that she will be unable to undertake the tasks previously assigned to her. The problem amounts to building a new roster that satisfies the hard constraints already met by the current one and, as much as possible, fulfils two groups of soft constraints which define the two objectives to be attained. A bi-objective genetic heuristic was designed on the basis of a population of individuals characterised by pairs of chromosomes, whose fitness complies with the Pareto ranking of the respective decoded solution. It includes an elitist policy, as well as a new utopic strategy, introduced for purposes of diversification. The computational experiments produced promising results for the practical application of this approach to real life instances arising from a public hospital in Lisbon.

Combining variable neighborhood search and estimation of distribution algorithms in the protein side chain placement problem

Abstract: The aim of this work is to introduce several proposals for combining two metaheuristics: variable neighborhood search (VNS) and estimation of distribution algorithms (EDAs). Although each of these metaheuristics has been previously hybridized in several ways, this paper constitutes the first attempt to combine both optimization methods. The different ways of combining VNS and EDAs will be classified into three groups. In the first group, we will consider combinations where the philosophy underlying VNS is embedded in EDAs. Considering different neighborhood spaces (points, populations or probability distributions), we will obtain instantiations for the approaches in this group. The second group of algorithms is obtained when probabilistic models (or any other machine learning paradigm) are used in order to exploit the good and bad shakes of the randomly generated solutions in a reduced variable neighborhood search. The last group of algorithms contains the results of alternating VNS and EDAs. An application of the first approach is presented in the protein side chain placement problem. The results obtained show the superiority of the hybrid algorithm in comparison with EDAs and VNS.

Bringing order into the neighborhoods: relaxation guided variable neighborhood search

Abstract: In this article we investigate a new variant of Variable Neighborhood Search (VNS): Relaxation Guided Variable Neighborhood Search. It is based on the general VNS scheme and a new Variable Neighborhood Descent (VND) algorithm. The ordering of the neighborhood structures in this VND is determined dynamically by solving relaxations of them. The objective values of these relaxations are used as indicators for the potential gains of searching the corresponding neighborhoods. We tested this new approach on the well-studied multidimensional knapsack problem. Computational experiments show that our approach is beneficial to the search, improving the obtained results. The concept is, in principle, more generally applicable and seems to be promising for many other combinatorial optimization problems approached by VNS.

Simulated annealing in the presence of noise

Abstract: In many practical optimization problems, evaluation of a solution is subject to noise, e.g., due to stochastic simulations or measuring errors. Therefore, heuristics are needed that are capable of handling such noise. This paper first reviews the state-of-the-art in applying simulated annealing to noisy optimization problems. Then, two new algorithmic variants are proposed: an improved version of stochastic annealing that allows for arbitrary annealing schedules, and a new approach called simulated annealing in noisy environments (SANE). The latter integrates ideas from statistical sequential selection in order to reduce the number of samples required for making an acceptance decision with sufficient statistical confidence. Finally, SANE is shown to significantly outperform other state-of-the-art simulated annealing techniques on a stochastic travelling salesperson problem.

Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

Abstract: We consider the generalized version of the classical Minimum Spanning Tree problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected. We present a Variable Neighborhood Search (VNS) approach which uses three different neighborhood types. Two of them work in complementary ways in order to maximize search effectivity. Both are large in the sense that they contain exponentially many candidate solutions, but efficient polynomial-time algorithms are used to identify best neighbors. For the third neighborhood type we apply Mixed Integer Programming to optimize local parts within candidate solution trees. Tests on Euclidean and random instances with up to 1280 nodes indicate especially on instances with many nodes per cluster significant advantages over previously published metaheuristic approaches.

A large neighborhood search heuristic for the longest common subsequence problem

Abstract: Given a set S={S 1,?,S k } of finite strings, the k-Longest Common Subsequence Problem (k-LCSP) seeks a string L * of maximum length such that L * is a subsequence of each S i for i=1,?,k. This paper presents a large neighborhood search technique that provides quality solutions to large k-LCSP instances. This heuristic runs in linear time in both the length of the sequences and the number of sequences. Some computational results are provided.

Experiments concerning sequential versus simultaneous maximization of objective function and distance

Abstract: Suppose two solution vectors are needed that have good objective function values and are different from each other. The following question has not yet been systematically researched: Should the two vectors be generated sequentially or simultaneously? We provide evidence that for broad ranges of practically achievable distances, sequential generation usually requires less computational effort and produces solutions that are at least as good as produced by simultaneous generation. This is done using experiments based on publicly available instances of the multi-constrained, zero-one knapsack problem, which are corroborated using experiments conducted with the linear assignment problem.

Worst case analysis of Max-Regret, Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman Problems

Abstract: Optimization heuristics are often compared with each other to determine which one performs best by means of worst-case performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the Max-Regret heuristic introduced by Balas and Saltzman (Oper. Res. 39:150---161, 1991) finds the unique worst possible solution for some instances of the s-dimensional (s?3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s=3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the s-dimensional (s?3) assignment problem.

Enhancing set constraint solvers with lexicographic bounds

Abstract: Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as bin-packing, set partitioning, circuit and combinatorial design. In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to the challenging symmetrical set problems often cast as Combinatorial Design Problems (CDPs). While CDPs find a natural formulation in the language of sets, in constraint programming literature, alternative models are often used due to a lack of efficiency of traditional FS solvers. We first identify the main structural components of CDPs that render their modeling suitable to set languages but their solving a technical challenge. Our new prototype solver extends the traditional subset variable domain with lexicographic bounds that better approximate a set domain by satisfying the cardinality restrictions applied to the variable, and allow for active symmetry breaking using ordering constraints. Our contribution includes the formal and practical framework of the new solver implemented on top of a traditional set solver, and an empirical evaluation on benchmark CDPs.

The prize-collecting generalized minimum spanning tree problem

Abstract: We introduce the prize-collecting generalized minimum spanning tree problem. In this problem a network of node clusters needs to be connected via a tree architecture using exactly one node per cluster. Nodes in each cluster compete by offering a payment for selection. This problem is NP-hard, and we describe several heuristic strategies, including local search and a genetic algorithm. Further, we present a simple and computationally efficient branch-and-cut algorithm. Our computational study indicates that our branch-and-cut algorithm finds optimal solutions for networks with up to 200 nodes within two hours of CPU time, while the heuristic search procedures rapidly find near-optimal solutions for all of the test instances.

Crowding with nearest neighbors replacement for multiple species niching and building blocks preservation in binary multimodal functions optimization

Abstract: This paper introduces a novel niching scheme called the q-nearest neighbors replacement (q-NNR) method in the framework of the steady-state GAs (SSGAs) for solving binary multimodal optimization problems. A detailed comparison of the main niching approaches are presented first. The niching paradigm and difference of the selection-recombination genetic algorithms (GAs) and the recombination-replacement SSGAs are discussed. Then the q-NNR is developed by adopting special replacement policies based on the SSGAs; a Boltzmann scheme for dynamically sizing the nearest neighbors set is designed to achieve a speed-up and control the proportion of individuals adapted to different niches. Finally, experiments are carried out on a set of test functions characterized by deception, epistasis, symmetry and multimodality. The results are satisfactory and illustrate the effectivity and efficiency of the proposed niching method.

Simulated annealing algorithm for the robust spanning tree problem

Abstract: This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum spanning tree problem when edge weights are not fixed but take their values from some intervals associated with edges. The problem consists of finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in Kouvelis and Yu (Robust Discrete Optimization and Its Applications, Kluwer Academic, Norwell, 1997), the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem.

Pareto memetic algorithm for multiple objective optimization with an industrial application

Abstract: Multiple objective combinatorial optimization problems are difficult to solve and often, exact algorithms are unable to produce optimal solutions. The development of multiple objective heuristics was inspired by the need to quickly produce acceptable solutions. In this paper, we present a new multiple objective Pareto memetic algorithm called PMSMO. The PMSMO algorithm incorporates an enhanced fine-grained fitness assignment, a double level archiving process and a local search procedure to improve performance. The performance of PMSMO is benchmarked against state-of-the-art algorithms using 0---1 multi-dimensional multiple objective knapsack problem from the literature and an industrial scheduling problem from the aluminum industry.

A permutation-coded evolutionary strategy for multi-objective GSM network planning

Abstract: The base station placement problem, with n potential candidate sites is NP-Hard with 2 n solutions (Mathar and Niessen, Wirel. Netw. 6, 421---428, 2000). When dimensioned on m unknown variable settings (e.g., number of power settings?+?number of tilt settings, etc.) the computational complexity becomes (m+1) n (Raisanen, PhD. thesis, 2006). We introduce a novel approach to reduce the computational complexity by dimensioning sites only once to guarantee traffic hold requirements are satisfied. This approach works by determining the maximum set of service test points candidate sites can handle without exceeding a hard traffic constraint, T MAX . Following this, the ability of two evolutionary strategies (binary and permutation-coded) to search for the minimum set cover are compared. This reverses the commonly followed approach of achieving service coverage first and then dimensioning to meet traffic hold. To test this approach, three realistic GSM network simulation environments are engineered, and a series of tests performed. Results indicate this approach can quickly meet network operator objectives.

Construction of classifier ensembles by means of artificial immune systems

Abstract: This paper presents the application of Artificial Immune Systems to the design of classifier ensembles. Ensembles of classifiers are a very interesting alternative to single classifiers when facing difficult problems. In general, ensembles are able to achieve better performance in terms of learning and generalisation errors. Several papers have shown that the processes of classifier design and combination must be related in order to obtain better ensembles. Artificial Immune Systems are a recent paradigm based on the immune systems of animals. The features of this new paradigm make it very appropriate for the design of systems where many components must cooperate to solve a given task. The design of classifier ensembles can be considered within such a group of systems, as the cooperation of the individual classifiers is able to improve the performance of the overall system. This paper studies the viability of Artificial Immune Systems when dealing with ensemble design. We construct a population of classifiers that is evolved using an Artificial Immune algorithm. From this population of classifiers several different ensembles can be extracted. These ensembles are favourably compared with ensembles obtained using standard methods in 35 real-world classification problems from the UCI Machine Learning Repository.

Learning heuristics for basic block instruction scheduling

Abstract: Instruction scheduling is an important step for improving the performance of object code produced by a compiler. A fundamental problem that arises in instruction scheduling is to find a minimum length schedule for a basic block--a straight-line sequence of code with a single entry point and a single exit point--subject to precedence, latency, and resource constraints. Solving the problem exactly is known to be difficult, and most compilers use a greedy list scheduling algorithm coupled with a heuristic. The heuristic is usually hand-crafted, a potentially time-consuming process. In contrast, we present a study on automatically learning good heuristics using techniques from machine learning. In our study, a recently proposed optimal basic block scheduler was used to generate the machine learning training data. A decision tree learning algorithm was then used to induce a simple heuristic from the training data. The automatically constructed decision tree heuristic was compared against a popular critical-path heuristic on the SPEC 2000 benchmarks. On this benchmark suite, the decision tree heuristic reduced the number of basic blocks that were not optimally scheduled by up to 55% compared to the critical-path heuristic, and gave improved performance guarantees in terms of the worst-case factor from optimality.

Introduction to the special issue on variable neighborhood search

Abstract: Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on systematic changes of structure within a search that may be performed in a deterministic way (Variable Neighborhood Descent, VND) or randomly (reduced VNS). Basic VNS combines random selection of a point in a shaking or perturbation step followed by a deterministic local search from that point. There are several extensions and hybrids of the basic VNS scheme suggested in the literature: if VND is used instead of local search, we have general VNS; the variable neighbourhood decomposition search (VNDS) method extends the basic VNS into a two-level VNS scheme based upon decomposition of the problem; the skewed VNS allows moves to a slightly worse but far solutions, etc. VNS has been successfully applied to a wide range of combinatorial and global optimization problems. In this special issue of Journal of Heuristics we collect several new successful applications of VNS as well as studies of advanced characteristics of VNS. Most of them were presented at the XVIII Mini EURO Conference (MEC), which was held at Tenerife, Spain, in November 2005. On that meeting, 61 VNS contributions by researches from 14 different countries and 4 continents were presented. The papers that make up this special issue on Variable Neighborhood Search illustrate breadth and depth of research in variable neighborhood search since they show some advanced features of the metaheuristic. Michael Polacek, Karl F. Doerner, Richard F. Hartl and Vittorio Maniezzo develop a basic variable neighborhood search algorithm to solve the Capacitated Arc Routing Problem with Intermediate Facilities that outperforms all known heuristics on four benchmark sets. The method uses only one exchange operator, the CROSS-exchange,

Local and variable neighborhood search for the k-cardinality subgraph problem

Abstract: The minimum weighted k-cardinality subgraph problem consists of finding a connected subgraph of a given graph with exactly k edges whose sum of weights is minimum. For this NP-hard combinatorial problem, only constructive types of heuristics have been suggested in the literature. In this paper we propose a new heuristic based on variable neighborhood search metaheuristic rules. This procedure uses a new local search developed by us. Extensive numerical results that include graphs with up to 5,000 vertices are reported. It appears that VNS outperforms all previous methods.

Simple and fast surrogate constraint heuristics for the maximum independent set problem

Abstract: In a recent paper Glover (J. Heuristics 9:175---227, 2003) discussed a variety of surrogate constraint-based heuristics for solving optimization problems in graphs. The key ideas put forth in the paper were illustrated by giving specializations designed for certain covering and coloring problems. In particular, a family of methods designed for the maximum cardinality independent set problem was presented. In this paper we report on the efficiency and effectiveness of these methods based on considerable computational testing carried out on test problems from the literature as well as some new test problems.

A proposal for a hybrid meta-strategy for combinatorial optimization problems

Abstract: In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.

A local linear embedding module for evolutionary computation optimization

Abstract: A Local Linear Embedding (LLE) module enhances the performance of two Evolutionary Computation (EC) algorithms employed as search tools in global optimization problems. The LLE employs the stochastic sampling of the data space inherent in Evolutionary Computation in order to reconstruct an approximate mapping from the data space back into the parameter space. This allows to map the target data vector directly into the parameter space in order to obtain a rough estimate of the global optimum, which is then added to the EC generation. This process is iterated and considerably improves the EC convergence. Thirteen standard test functions and two real-world optimization problems serve to benchmark the performance of the method. In most of our tests, optimization aided by the LLE mapping outperforms standard implementations of a genetic algorithm and a particle swarm optimization. The number and ranges of functions we tested suggest that the proposed algorithm can be considered as a valid alternative to traditional EC tools in more general applications. The performance improvement in the early stage of the convergence also suggests that this hybrid implementation could be successful as an initial global search to select candidates for subsequent local optimization.

A ring-mesh topology design problem for optical transport networks

Abstract: This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.