Showing papers in "Journal of Heuristics in 2011"

Biased random-key genetic algorithms for combinatorial optimization

Abstract: Random-key genetic algorithms were introduced by Bean (ORSA J. Comput. 6:154---160, 1994) for solving sequencing problems in combinatorial optimization. Since then, they have been extended to handle a wide class of combinatorial optimization problems. This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems. Biased random-key genetic algorithms are a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. After introducing the basics of biased random-key genetic algorithms, the paper discusses in some detail implementation issues, illustrating the ease in which sequential and parallel heuristics based on biased random-key genetic algorithms can be developed. A survey of applications that have recently appeared in the literature is also given.

Quantum-inspired evolutionary algorithms: a survey and empirical study

Abstract: Quantum-inspired evolutionary algorithms, one of the three main research areas related to the complex interaction between quantum computing and evolutionary algorithms, are receiving renewed attention. A quantum-inspired evolutionary algorithm is a new evolutionary algorithm for a classical computer rather than for quantum mechanical hardware. This paper provides a unified framework and a comprehensive survey of recent work in this rapidly growing field. After introducing of the main concepts behind quantum-inspired evolutionary algorithms, we present the key ideas related to the multitude of quantum-inspired evolutionary algorithms, sketch the differences between them, survey theoretical developments and applications that range from combinatorial optimizations to numerical optimizations, and compare the advantages and limitations of these various methods. Finally, a small comparative study is conducted to evaluate the performances of different types of quantum-inspired evolutionary algorithms and conclusions are drawn about some of the most promising future research developments in this area.

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

Abstract: This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Local search for the surgery admission planning problem

Abstract: We present a model for the surgery admission planning problem, and a meta-heuristic algorithm for solving it. The problem involves assigning operating rooms and dates to a set of elective surgeries, as well as scheduling the surgeries of each day and room. Simultaneously, a schedule is created for each surgeon to avoid double bookings. The presented algorithm uses simple Relocate and Two-Exchange neighbourhoods, governed by an iterated local search framework. The problem's search space associated with these move operators is analysed for three typical fitness surfaces, representing different compromises between patient waiting time, surgeon overtime, and waiting time for children in the morning on the day of surgery. The analysis shows that for the same problem instances, the different objectives give fitness surfaces with quite different characteristics. We present computational results for a set of benchmarks that are based on the admission planning problem in a chosen Norwegian hospital.

Hybridized evolutionary local search algorithm for the team orienteering problem with time windows

Abstract: The orienteering problem (OP) consists in finding an elementary path over a subset of vertices. Each vertex is associated with a profit that is collected on the visitor’s first visit. The objective is to maximize the collected profit with respect to a limit on the path’s length. The team orienteering problem (TOP) is an extension of the OP where a fixed number m of paths must be determined. This paper presents an effective hybrid metaheuristic to solve both the OP and the TOP with time windows. The method combines the greedy randomized adaptive search procedure (GRASP) with the evolutionary local search (ELS). ELS generates multiple distinct child solutions using a mutation mechanism. Each child solution is further improved by a local search procedure. GRASP provides multiple starting solutions to the ELS. The method is able to improve several best known results on available benchmark instances.

Neighborhood analysis: a case study on curriculum-based course timetabling

Abstract: In this paper, we present an in-depth analysis of neighborhood relations for local search algorithms. Using a curriculum-based course timetabling problem as a case study, we investigate the search capability of four neighborhoods based on three evaluation criteria: percentage of improving neighbors, improvement strength and search steps. This analysis shows clear correlations of the search performance of a neighborhood with these criteria and provides useful insights on the very nature of the neighborhood. This study helps understand why a neighborhood performs better than another one and why and how some neighborhoods can be favorably combined to increase their search power. This study reduces the existing gap between reporting experimental assessments of local search-based algorithms and understanding their behaviors.

Using resource scarceness characteristics to solve the multi-mode resource-constrained project scheduling problem

Abstract: In the past decades, resource parameters have been introduced in project scheduling literature to measure the scarceness of resources of a project instance. In this paper, we incorporate these resource scarceness parameters in the search process to solve the multi-mode resource constrained project scheduling problem, in which multiple execution modes are available for each activity in the project. Therefore, we propose a scatter search algorithm, which is executed with different improvement methods, each tailored to the specific characteristics of different renewable and nonrenewable resource scarceness values. Computational results prove the effectiveness of the improvement methods and reveal that the procedure is among the best performing competitive algorithms in the open literature.

Cooperating local search for the maximum clique problem

Abstract: The advent of desktop multi-core computers has dramatically improved the usability of parallel algorithms which, in the past, have required specialised hardware This paper introduces cooperating local search (CLS), a parallelised hyper-heuristic for the maximum clique problem CLS utilises cooperating low level heuristics which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not in the current clique These low level heuristics differ primarily in their vertex selection techniques and their approach to dealing with plateaus To improve the performance of CLS, guidance information is passed between low level heuristics directing them to particular areas of the search domain In addition, CLS dynamically reconfigures the allocation of low level heuristics to cores, based on information obtained during a trial, to ensure that the mix of low level heuristics is appropriate for the instance being optimised CLS has no problem instance dependent parameters, improves the state-of-the-art performance for the maximum clique problem over all the BHOSLIB benchmark instances and attains unprecedented consistency over the state-of-the-art on the DIMACS benchmark instances

A reactive GRASP with path relinking for capacitated clustering

Abstract: This paper presents a greedy randomized adaptive search procedure (GRASP) coupled with path relinking (PR) to solve the problem of clustering n nodes in a graph into p clusters. The objective is to maximize the sum of the edge weights within each cluster such that the sum of the corresponding node weights does not exceed a fixed capacity. In phase I, both a heaviest weight edge (HWE) algorithm and a constrained minimum cut algorithm are used to select seeds for initializing the p clusters. Feasible solutions are obtained with the help of a self-adjusting restricted candidate list that sequentially guides the assignment of the remaining nodes. At each major GRASP iteration, the list length is randomly set based on a probability density function that is updated dynamically to reflect the solution quality realized in past iterations. In phase II, three neighborhoods, each defined by common edge and node swaps, are explored to attain local optimality. The following exploration strategies are investigated: cyclic neighborhood search, variable neighborhood descent, and randomized variable neighborhood descent (RVND). The best solutions found are stored in an elite pool. In a post-processing step, PR is applied to the pool members to cyclically generate paths between each pair. As new solutions are uncovered, a systematic attempt is made to improve a subset of them with local search. Should a better solution be found, it is saved temporally and placed in the pool after all the pairs are investigated and the bottom member is removed. The procedure ends when no further improvement is possible. Extensive computational testing was done to evaluate the various combinations of construction and local search strategies. For instances with up to 40 nodes and 5 clusters, the reactive GRASP with PR found optimal solutions within a negligible amount of time compared to CPLEX. In general, the HWE algorithm in the construction phase, RVND in the local search phase, and the use of PR provided the best results. The largest instances solved involved 82 nodes and 8 clusters.

A comparative study of crossover in differential evolution

Abstract: In order to understand the role of crossover in differential evolution, theoretical analysis and comparative study of crossover in differential evolution are presented in this paper. Two new crossover methods, namely consecutive binomial crossover and non-consecutive exponential crossover, are designed. The probability distribution and expectation of crossover length for binomial and exponential crossover used in this paper are derived. Various differential evolution algorithms with different crossover methods including mutation-only differential evolution are comprehensively compared at system level instead of parameter level. Based on the theoretical analysis and simulation results, the effect of crossover on the reliability and efficiency of differential evolution algorithms is discussed. Some insights are revealed.

GRASP with path-relinking for the generalized quadratic assignment problem

Abstract: The generalized quadratic assignment problem (GQAP) is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. The GQAP has numerous applications, including facility design, scheduling, and network design. In this paper, we propose several GRASP with path-relinking heuristics for the GQAP using different construction, local search, and path-relinking procedures. We introduce a novel approximate local search scheme, as well as a new variant of path-relinking that deals with infeasibilities. Extensive experiments on a large set of test instances show that the best of the proposed variants is both effective and efficient.

A Bus Driver Scheduling Problem: a new mathematical model and a GRASP approximate solution

Abstract: This paper addresses the problem of determining the best scheduling for Bus Drivers, a $\mathcal{NP}$ -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491---502, 2005).

Optimal enough

Abstract: An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular application, portfolio optimisation. We demonstrate that the randomness of the `optimal' solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample. Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample only to financially meaningless improvements and unpredictable changes (noise) in performance.

A heuristic method for non-homogeneous redundancy optimization of series-parallel multi-state systems

Abstract: This paper develops an efficient heuristic to solve the non-homogeneous redundancy allocation problem for multi-state series-parallel systems. Non identical components can be used in parallel to improve the system availability by providing redundancy in subsystems. Multiple component choices are available for each subsystem. The components are binary and chosen from a list of products available on the market, and are characterized in terms of their cost, performance and availability. The objective is to determine the minimal-cost series-parallel system structure subject to a multi-state availability constraint. System availability is represented by a multi-state availability function, which extends the binary-state availability. This function is defined as the ability to satisfy consumer demand that is represented as a piecewise cumulative load curve. A fast procedure is used, based on universal generating function, to evaluate the multi-state system availability. The proposed heuristic approach is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. The design problem, solved in this study, has been previously analyzed using GA. Numerical results for the test problems from previous research are reported, and larger test problems are randomly generated. These results show that the proposed approach is efficient both in terms of both of solution quality and computational time, as compared to existing approaches.

Local search heuristics for the multidimensional assignment problem

Abstract: The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components.

Memetic algorithm for the antibandwidth maximization problem

Abstract: The antibandwidth maximization problem (AMP) consists of labeling the vertices of a n-vertex graph G with distinct integers from 1 to n such that the minimum difference of labels of adjacent vertices is maximized. This problem can be formulated as a dual problem to the well known bandwidth problem. Exact results have been proved for some standard graphs like paths, cycles, 2 and 3-dimensional meshes, tori, some special trees etc., however, no algorithm has been proposed for the general graphs. In this paper, we propose a memetic algorithm for the antibandwidth maximization problem, wherein we explore various breadth first search generated level structures of a graph--an imperative feature of our algorithm. We design a new heuristic which exploits these level structures to label the vertices of the graph. The algorithm is able to achieve the exact antibandwidth for the standard graphs as mentioned. Moreover, we conjecture the antibandwidth of some 3-dimensional meshes and complement of power graphs, supported by our experimental results.

Adaptive memory in multistart heuristics for multicommodity network design

Abstract: This paper focuses on the use of different memory strategies to improve multistart methods. A network design problem in which the costs are given by discrete stepwise increasing cost functions of the capacities installed in the edges is used to illustrate the contributions of adaptive memory and vocabulary building strategies. Heuristics based on shortest path and maximum flow algorithms are combined with adaptive memory in order to obtain an approximate solution to the problem in the framework of a multistart algorithm. Furthermore, a vocabulary building intensification mechanism supported by the resolution of a linear program is also explored. Numerical experiments have shown that the proposed algorithm obtained the best known solutions for some instances in the literature. These results show the contribution of each memory component and the effectiveness of their combination.

Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem

Abstract: In this paper we develop, study and test new neighborhood structures for the Hop-constrained Minimum Spanning Tree Problem (HMSTP). These neighborhoods are defined by restricted versions of a new dynamic programming formulation for the problem and provide a systematic way of searching neighborhood structures based on node-level exchanges. We have also developed several local search methods that are based on the new neighborhoods. Computational experiments for a set of benchmark instances with up to 80 nodes show that the more elaborate methods produce in a quite fast way, heuristic solutions that are, for all cases, within 2% of the optimum.

Boosting distributed constraint satisfaction

Abstract: Competition and cooperation can boost the performance of a combinatorial search process. Both can be implemented with a portfolio of algorithms which run in parallel, give hints to each other and compete for being the first to finish and deliver the solution. In this paper we present a new generic framework for the application of algorithms for distributed constraint satisfaction that makes use of both cooperation and competition. This framework improves the performance of two different standard algorithms by one order of magnitude. Furthermore, it can reduce the risk of poor performance by up to three orders of magnitude diminishing the heavy-tailed behaviour of complete distributed search. Moreover it greatly reduces the classical idleness flaw usually observed in distributed tree-based searches. We expect our new methods to be similarly beneficial for any tree-based distributed search and describe ways on how to incorporate them. Remarkably, our ideas while applied to a parallel SAT setting were able to beat divide-and-conquers approaches, and win the gold medal of the parallel track of the 2008 SAT-Race.

A tabu search algorithm for the covering design problem

Abstract: A (v, k,t) -covering design is a collection of k-subsets (called blocks) of a v-set V such that every t-subset of V is contained in at least one block. Given v, k and t, the goal of the covering design problem is to find a covering made of a minimum number of blocks. In this paper, we present a new tabu algorithm for tackling this problem. Our algorithm exploits a new implementation designed in order to evaluate efficiently the performance of the neighbors of the current configuration. The new im- plementation is much less space-consuming than the currently used technique, mak- ing it possible to tackle much larger problem instances. It is also significantly faster. Thanks to these improved data structures, our tabu algorithm was able to improve the upper bound of more than 50 problem instances.

Generating highly balanced sudoku problems as hard problems

Abstract: Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in Bailey et al. (Am. Math. Mon. 115:383---404, 2008; J. Agron. Crop Sci. 165:121---130, 1990), Morgan (Latin squares and related experimental designs. Wiley, New York, 2008) and Vaughan (Electron. J. Comb. 16, 2009). On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m?n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables--variables with the same value in all the solutions of an instance--and hardness of GSP.

A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in R d

Abstract: We present a heuristic for the Euclidean Steiner tree problem in R d for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in R d for 2≤d≤5.

Matching based very large-scale neighborhoods for parallel machine scheduling

Abstract: In this paper we study very large-scale neighborhoods for the minimum total weighted completion time problem on parallel machines, which is known to be strongly NP-hard. We develop two different ideas leading to very large-scale neighborhoods in which the best improving neighbor can be determined by calculating a weighted matching. The first neighborhood is introduced in a general fashion using combined operations of a basic neighborhood. Several examples for basic neighborhoods are given. The second approach is based on a partitioning of the job sets on the machines and a reassignment of them. In a computational study we evaluate the possibilities and the limitations of the presented very large-scale neighborhoods.

Boosting video tracking performance by means of Tabu Search in intelligent visual surveillance systems

Abstract: In this paper, we present a fast and efficient technique for the data association problem applied to visual tracking systems. Visual tracking process is formulated as a combinatorial hypotheses search with a heuristic evaluation function taking into account structural and specific information such as distance, shape, color, etc. We introduce a Tabu Search algorithm which performs a search on an indirect space. A novel problem formulation allows us to transform any solution into the real search space, which is needed for fitness calculation, in linear time. This new formulation and the use of auxiliary structures yields a fast transformation from a blob-to-track assignment space to the real shape and position of tracks space (while calculating fitness in an incremental fashion), which is key in order to produce efficient and fast results. Other previous approaches are based on statistical techniques or on evolutionary algorithms. These techniques are quite efficient and robust although they cannot converge as fast as our approach.

Optimal row and column ordering to improve table interpretation using estimation of distribution algorithms

Abstract: A common information representation task in research as well as educational and statistical practice is to comprehensively and intuitively express data in two-dimensional tables. Examples include tables in scientific papers, as well as reports and the popular press. Data is often simple enough for users to reorder. In many other cases though, there are complex data patterns that make finding the best re-arrangement of rows and columns for optimum readability a tough problem. We propose that row and column ordering should be regarded as a combinatorial optimization problem and solved using evolutionary computation techniques. The use of genetic algorithms has already been proposed in the literature. This paper proposes for the first time the use of estimation of distribution algorithms for table ordering. We also propose alternative ways of representing the problem in order to reduce its dimensionality. By learning a selective naive Bayes classifier, we can find out how to jointly combine the parameters of these algorithms to get good table orderings. Experimental examples in this paper are on 2D tables.

A composite algorithm for multiprocessor scheduling

Abstract: A composite algorithm is developed for the classical problem of scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. The algorithm at first obtains a family of initial partial solutions and combines these partial solutions until a feasible solution is generated. Then local search procedures are used for improving the solution. The effectiveness of this approach is evaluated through extensive computational comparisons with recent improvement heuristics for different classes of benchmark instances.

On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices

Abstract: We examine the performance of different subtour-patching heuristics for solving the strongly $\mathcal{NP}$ -hard traveling salesman problem (TSP) on permuted Monge matrices. We prove that a well-known heuristic is asymptotically optimal for the TSP on product matrices and k-root cost matrices. We also show that the heuristic is provably asymptotically optimal for general permuted Monge matrices under some mild conditions. Our theoretical results are strongly supported by the findings of a large-scale experimental study on randomly generated numerical examples, which show that the heuristic is not only asymptotically optimal, but also finds optimal TSP tours with high probability that increases with the problem size. Thus the heuristic represents a practical tool to solve large instances of the problem.

An adaptive multi-start graph partitioning algorithm for structuring cellular networks

Abstract: In mobile network design, the problem of assigning network elements to controllers when defining network structure can be modeled as a graph partitioning problem. In this paper, a comprehensive analysis of a sophisticated graph partitioning algorithm for grouping base stations into packet control units in a mobile network is presented. The proposed algorithm combines multi-level and adaptive multi-start schemes to obtain high quality solutions efficiently. Performance assessment is carried out on a set of problem instances built from measurements in a live network. Overall results confirm that the proposed algorithm finds solutions better than those obtained by the classical multi-level approaches and much faster than classical multi-start approaches. The analysis of the optimization surface shows that the best local minima values follow a Gumbel distribution, which justifies the stagnation of naive multi-start approaches after a few attempts. Likewise, the analysis shows that the best local minima share strong similarities, which is the reason for the superiority of adaptive multi-start approaches. Finally, a sensitivity analysis shows the best internal parameter settings in the algorithm.