Showing papers in "Journal of Heuristics in 2002"

A Taxonomy of Hybrid Metaheuristics

Abstract: Hybrid metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. A wide variety of hybrid approaches have been proposed in the literature. In this paper, a taxonomy of hybrid metaheuristics is presented in an attempt to provide a common terminology and classification mechanisms. The taxonomy, while presented in terms of metaheuristics, is also applicable to most types of heuristics and exact optimization algorithms. As an illustration of the usefulness of the taxonomy an annoted bibliography is given which classifies a large number of hybrid approaches according to the taxonomy.

A Constraint-Based Method for Project Scheduling with Time Windows

Abstract: This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.

Multi Colony Ant Algorithms

Abstract: In multi colony ant algorithms several colonies of ants cooperate in finding good solutions for an optimization problem. At certain time steps the colonies exchange information about good solutions. If the amount of exchanged information is not too large multi colony ant algorithms can be easily parallelized in a natural way by placing the colonies on different processors. In this paper we study the behaviour of multi colony ant algorithms with different kinds of information exchange between the colonies. Moreover we compare the behaviour of different numbers of colonies with a multi start single colony ant algorithm. As test problems we use the Traveling Salesperson problem and the Quadratic Assignment problem.

A Seeded Memetic Algorithm for Large Unit Commitment Problems

Abstract: The paper shows that the use of a memetic algorithm (MA), a genetic algorithm (GA) combined with local search, synergistically combined with Lagrangian relaxation is effective and efficient for solving large unit commitment problems in electric power systems. It is shown that standard implementations of GA or MA are not competitive with the traditional methods of dynamic programming (DP) and Lagrangian relaxation (LR). However, an MA seeded with LR proves to be superior to all alternatives on large problems. Eight problems from the literature and a new large, randomly generated problem are used to compare the performance of the proposed seeded MA with GA, MA, DP and LR. Compared with previously published results, this hybrid approach solves the larger problems better and uses less computational time.

A Hybrid Genetic Algorithm for Assembly Line Balancing

Abstract: This paper presents a hybrid genetic algorithm for the simple assembly line problem, SALBP-1. The chromosome representation of the problem is based on random keys. The assignment of the operations to the workstations is based on a heuristic priority rule in which the priorities of the operations are defined by the chromosomes. A local search is used to improve the solution. The approach is tested on a set of problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the algorithm.

Using Constraint-Based Operators to Solve the Vehicle Routing Problem with Time Windows

Abstract: This paper presents operators searching large neighborhoods in order to solve the vehicle routing problem. They make use of the pruning and propagation techniques of constraint programming which allow an efficient search of such neighborhoods. The advantages of using a large neighborhood are not only the increased probability of finding a better solution at each iteration but also the reduction of the need to invoke specially-designed methods to avoid local minima. These operators are combined in a variable neighborhood descent in order to take advantage of the different neighborhood structures they generate.

Probability Distribution of Solution Time in GRASP: An Experimental Investigation

Abstract: A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a sub-optimal target value fits a two-parameter exponential distribution. Hence, it is possible to approximately achieve linear speed-up by implementing GRASP in parallel.

The Parallel Variable Neighborhood Search for the p -Median Problem

Abstract: The Variable Neighborhood Search (VNS) is a recent metaheuristic that combines series of random and improving local searches based on systematically changed neighborhoods. When a local minimum is reached, a shake procedure performs a random search. This determines a new starting point for running an improving search. The use of interchange moves provides a simple implementation of the VNS algorithm for the p-Median Problem. Several strategies for the parallelization of the VNS are considered and coded in C using OpenMP. They are compared in a shared memory machine with large instances.

Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming

Abstract: In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP) These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms Their performance is compared for 115 problem instances All methods are capable of producing high quality solutions in short time In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100 The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics

Cooperative Parallel Tabu Search for Capacitated Network Design

Abstract: We present a cooperative parallel tabu search method for the fixed charge, capacitated, multicommodity network design problem. Several communication strategies are analyzed and compared. The resulting parallel procedure displays excellent performances in terms of solution quality and solution times. The experiments show that parallel implementations find better solutions than sequential ones. They also show that, when properly designed and implemented, cooperative search outperforms independent search strategies, at least on the class of problems of interest here.

Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows

Abstract: This paper describes the parallelization of a two-phase metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The underlying objective function combines the minimization of the number of vehicles in the first search phase of the metaheuristic with the minimization of the total travel distance in the second search phase. The parallelization of the metaheuristic follows a type 3 parallelization strategy (cf. Crainic and Toulouse (2001). In F. Glover and G. Kochenberger (eds.). State-of-the-Art Handbook in Metaheuristics. Norwell, MA: Kluwer Academic Publishers), i.e. several concurrent searches of the solution space are carried out with a differently configured metaheuristic. The concurrently executed processes cooperate through the exchange of solutions. The parallelized two-phase metaheuristic was subjected to a comparative test on the basis of 358 problems from the literature with sizes varying from 100 to 1000 customers. The derived results seem to justify the proposed parallelization concept.

A Genetic Algorithm with a Compact Solution Encoding for the Container Ship Stowage Problem

Abstract: The purpose of this study is to develop an efficient heuristic for solving the stowage problem. Containers on board a container ship are stacked one on top of the other in columns, and can only be unloaded from the top of the column. A key objective of stowage planning is to minimize the number of container movements. A genetic algorithm technique is used for solving the problem. A compact and efficient encoding of solutions is developed, which reduces significantly the search space. The efficiency of the suggested encoding is demonstrated through an extensive set of simulation runs and its flexibility is demonstrated by successful incorporation of ship stability constraints.

Constraint Programming Based Column Generation for Crew Assignment

Abstract: Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.

Reliability Importance and Invariant Optimal Allocation

Abstract: The reliability importance of a component is a partial derivative of the system reliability with respect to this component reliability. When all components are i.i.d., the reliability importance is called the B-importance. Relationships between reliability allocation and the reliability importance for general coherent systems are explored. The invariant optimal allocation is an allocation related only to the relative ordering rather than the magnitude of the component reliabilities. A strong heuristic method (LK heuristic) is developed to search for an ideal allocation through the application of the reliability importance. The following conclusions are drawn: if there exists an invariant optimal allocation for a system, the optimal allocation is to assign component reliabilities according to the B-importance ordering. Furthermore, the allocation generated by the LK heuristic is the optimal allocation.

Hybrid Genetic Algorithm for DNA Sequencing with Errors

Abstract: In the paper, a new hybrid genetic algorithm solving the DNA sequencing problem with negative and positive errors is presented. The algorithm has as its input a set of oligonucleotides coming from a hybridization experiment. The aim is to reconstruct an original DNA sequence of a known length on the basis of this set. No additional information about the oligonucleotides nor about the errors is assumed. Despite that, the algorithm returns for computationally hard instances surprisingly good results, of a very high similarity to original sequences.

Heuristics for the Phylogeny Problem

Abstract: A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The problem of finding a phylogeny with the minimum number of evolutionary steps (the so-called parsimony criterion) is one of the main problems in comparative biology. In this work, we study different heuristic approaches to the phylogeny problem under the parsimony criterion. New algorithms based on metaheuristics are also proposed. All heuristics are implemented and compared under the same framework, leading to consistent and thorough comparative results. Computational results are reported for benchmark instances from the literature.

On the Hardness of the Quadratic Assignment Problem with Metaheuristics

Abstract: Meta-heuristics are a powerful way to approximately solve hard combinatorial optimization problems. However, for a problem, the quality of results can vary considerably from one instance to another. Understanding such a behaviour is important from a theoretical point of view, but also has practical applications such as for the generation of instances during the evaluation stage of a heuristic. In this paper we propose a new complexity measure for the Quadratic Assignment Problem in the context of metaheuristics based on local search, e.g. simulated annealing. We show how the ruggedness coefficient previously introduced by the authors, in conjunction with the well known concept of dominance, provides important features of the search space explored during a local search algorithm, and gives a rather precise idea of the complexity of an instance for these heuristics. We comment previous experimental studies concerning tabu search methods and genetic algorithms with local search in the light of our complexity measure. New computational results with simulated annealing and taboo search are presented.

A Cellular Genetic Algorithm with Disturbances: Optimisation Using Dynamic Spatial Interactions

Abstract: This paper describes a novel evolutionary algorithm inspired by the nature of spatial interactions in ecological systems. The Cellular Genetic Algorithm with Disturbances (CGAD) can be seen as a hybrid between a fine-grained and a coarse-grained parallel genetic algorithm. The introduction of a “disturbance-colonisation” cycle provides a mechanism for maintaining flexible subpopulation sizes and self-adaptive controls on migration. Experiments conducted, using a range of stationary and non-stationary optimisation problems, show how changes in the structure of the environment can lead to changes in selective pressure, population diversity and subsequently solution quality. The significance of the disturbance events lies in the new “ecological” patterns that arise during the recovery phase.

Soft Constraint Logic Programming and Generalized Shortest Path Problems

Abstract: In this paper we study the relationship between Constraint Programming (CP) and Shortest Path (SP) problems. In particular, we show that classical, multicriteria, partially ordered, and modality-based SP problems can be naturally modeled and solved within the Soft Constraint Logic Programming (SCLP) framework, where logic programming is coupled with soft constraints. In this way we provide this large class of SP problems with a high-level and declarative linguistic support whose semantics takes care of both finding the cost of the shortest path(s) and also of actually finding the path(s). On the other hand, some efficient algorithms for certain classes of SP problems can be exploited to provide some classes of SCLP programs with an efficient way to compute their semantics.

Complete Local Search with Memory

Abstract: Neighborhood search heuristics like local search and its variants are some of the most popular approaches to solve discrete optimization problems of moderate to large size. Apart from tabu search, most of these heuristics are memoryless. In this paper we introduce a new neighborhood search heuristic that makes effective use of memory structures in a way that is different from that in common implementations of tabu search. We report computational experiments with this heuristic on the traveling salesperson problem and the subset sum problem.

Approximation Schemes for Scheduling Jobs with Common Due Date on Parallel Machines to Minimize Total Tardiness

Abstract: The problem of scheduling n nonpreemptive jobs having a common due date d on m, m ≥ 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms lAer and lBer are presented such that (T0 − Ta)/(Ta + d) ≤ e holds for any problem instance and any given e > 0, where Ta is the optimal solution value and T0 is the value of the solution delivered by Ae or Be. Algorithms Ae and Be run in O(n2m/em−1) and O(nm+1/em) time, respectively, if m is a constant. For m e 2, algorithm Ae can be improved to run in O(n3/e) time.

Constraint Propagation in Graph Coloring

Abstract: In this paper we propose a method for integrating constraint propagation algorithms into an optimization procedure for vertex coloring with the goal of finding improved lower bounds. The key point we address is how to get instances of Constraint Satisfaction Problems (CSPs) from a graph coloring problem in order to give rise to new lower bounds outperforming the maximum clique bound. More precisely, the algorithms presented have the common goal of finding CSPs in the graph for which infeasibility can be proven. This is achieved by means of constraint propagation techniques which allow the algorithms to eliminate inconsistencies in the CSPs by updating domains dynamically and rendering such infeasibilities explicit. At the end of this process we use the largest CSP for which it has not been possible to prove infeasibility as an input for an algorithm which enlarges such CSP to get a feasible coloring. We experimented with a set of middle-high density graphs with quite a large difference between the maximum clique and the chromatic number.

Bounds and Heuristics for the Shortest Capacitated Paths Problem

Abstract: Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G. We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value. We then propose two heuristic methods. The first one is based on a greedy approach, while the second one is an adaptation of the tabu search meta-heuristic.

Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

Abstract: The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective.

Parallelizing Tabu Search on a Cluster of Heterogeneous Workstations

Abstract: In this paper, we present the parallelization of tabu search on a network of workstations using PVM. Two parallelization strategies are integrated: functional decomposition strategy and multi-search threads strategy. In addition, domain decomposition strategy is implemented probabilistically. The performance of each strategy is observed and analyzed. The goal of parallelization is to speedup the search in finding better quality solutions. Observations support that both parallelization strategies are beneficial, with functional decomposition producing slightly better results. Experiments were conducted for the VLSI cell placement, an NP-hard problem, and the objective was to achieve the best possible solution in terms of interconnection length, timing performance (circuit speed), and area. The multiobjective nature of this problem is addressed using a fuzzy goal-based cost computation.

Constraint Programming and Operations Research: Comments from an Operations Researcher

Abstract: This paper relates the author's personal experience with constraint programming and gives a personal assessment of the relationships between constraint programming and operations research.

Mathematical Programming Techniques in Constraint Programming: A Short Overview

Abstract: In recent years, the integration of techniques from Artificial Intelligence and Operations Research has shown to improve the solutions of complex and large scale combinatorial optimization problems, in terms of efficiency, scalability and optimality. In this context, Constraint Programming is an emerging discipline situated at the confluence of the two fields that has been recognized as a suitable environment for achieving such an integration. This paper briefly presents the integration directions explored in the literature, and provides some pointers to relevant work in these directions.

Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem

Abstract: During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

Heuristic Approaches for a Scheduling Problem in the Plastic Molding Department of an Audio Company

Abstract: A production scheduling problem for making plastic molds of hi-fi models is considered. The objective is to minimize the total machine makespan in the presence of due dates, variable lot size, multiple machine types, sequence dependent, machine dependent setup times, and inventory limits. Goal programming and load balancing are applied to select the set of machine types and assign mold types to machines, resulting in a set of single-machine scheduling problems. A mixed-integer program (MIP) is formulated for the general problem but could solve only small instances. A single-machine scheduling heuristic is designed to adopt a production sequence from a travelling salesman solution. The start time of every cycle is determined by a simplified MIP. Production cycles are defined to equalize the stockout times of mold types. A post-processing step reduces the number of setups in the last cycle. Results using real-life data are promising. Characteristics giving rise to high machine utilization are discussed.