Path Relinking

The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-ofthe-art procedures on a set of 218 previously reported instances. The comparison favors the Iterated Greedy-Strategic Oscillation with the Path Relinking post-processing, which is able to identify 87 new best objective function values.

Scope and Purpo~--The development of hybrid procedures for optimization focuses on enhancing the strengths and compensating for the weaknesses of two or more complementary approaches. The goal is to intelligently combine the key elements of competing methodologies to create a superior solution procedure. Our paper explores the marriage between tabu search and genetic algorithms in the context of solving difficult optimization problems. Among other ideas, the procedure known as scatter search is revisited to create a unifying environment where tabu search and genetic algorithms can co-exist. Overall, our objective is to demonstrate that it is possible to establish useful connections between methods whose search principles may superficially appear unrelated.

This paper presents a competitive Particle Swarm Optimization algorithm for the Traveling Salesman Problem, where the velocity operator is based upon local search and path-relinking procedures. The paper proposes two versions of the algorithm, each of them utilizing a distinct local search method. The proposed heuristics are compared with other Particle Swarm Optimization algorithms presented previously for the same problem. The results are also compared with three effective algorithms for the TSP. A computational experiment with benchmark instances is reported. The results show that the method proposed in this paper finds high quality solutions and is comparable with the effective approaches presented for the TSP.

Diversity selection is a common task in multiple real-world problems. The maximum diversity problem traditionally consists in selecting a subset of items from a given set, such that a measure of the diversity present in the subset of selected elements is maximized. In literature are reported several variants of this problem, according to the diversity function considered, in this investigation it solves a new problem, called the Max-mean model, which maximizes the average diversity between elements in the subset selected, and in on which the number of elements selected is also a decision variable, we show that finding an optimal solution to this problem is strongly NP-hard. The characteristics of the inter-element distances considered in the new model has applications in the selection of groups of people representative of a population, or in the selection of a group of institutions, etc. In the first part of this research, this new model is proposed, we study some of its properties, and is designed a highly efficient algorithm to solve it, based on a hybridization of metaheuristics with good performance in other similar combinatorial problems, to estimate the efficiency of the proposed method are adapted the best algorithms to solve similar problems, as reported in literature. In the second part of this research extends the optimization problem considered, an additional constraint is added: want also select the best items, the best according to some criterion. In this context, with this additional objective, the optimization problem becomes a classical multiobjective optimization problem. With simple processing techniques this problem can be transformed into the problem uniobjective above, for which we developed a very efficient method. This will solve the general problem of selecting the best and most diverse.

This paper presents a special case of the general shop called partial job shop problem. The partial job shop is a more realistic generalization of the mixed shop problem. The problem is formulated as a mixed integer programming model. A scatter search algorithm combined with tabu search and path relinking is used to tackle this problem with makespan criterion. The computational experiments are performed on some problem instances. The results are compared with a lower bound and the effectiveness of the algorithm is shown.

Synchronous Optical Network (SONET) in North America and Synchronous Digital Hierarchy (SDH) in Europe and Japan are the current transmission and multiplexing standards for high speed signals within the carrier infrastructure. The typical topology of a SONET network is a collection of rings connecting all the customer sites. We deal with a design problem in which each customer has to be assigned to exactly one ring and these rings have to be connected through a single federal ring. A capacity constraint on each ring is also imposed. The problem is to find a feasible assignment of the customers minimizing the total number of rings used. A Tabu Search method is proposed to solve the problem. The key elements are the use of a variable objective function and the strategic use of two neighborhoods. We have also implemented other techniques such as Path Relinking, eXploring Tabu Search and a Scatter Search. Extensive computational experiments have been done using two sets of benchmark instances. The performances of the proposed algorithms have also been compared with those of three multistart algorithms involving greedy methods previously proposed for the problem, and of the CPLEX solver. The computational experiments show the effectiveness of the proposed Tabu Search.

GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: alternative randomized greedy construction schemes, Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss implementation strategies of memory-based intensification and post-optimization techniques using path-relinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.

This paper introduces a new approach called hybrid particle swarm optimization like algorithm (hybrid PSO) with fine tuning operators to solve optimisation problems. This method combines the merits of the parameter-free PSO (pf-PSO) and the extrapolated particle swarm optimization like algorithm (ePSO). In order to accelerate the PSO algorithms to obtain the global optimal solution, three fine tuning operators, namely mutation, cross-over and root mean square variants are introduced. The effectiveness of the fine tuning elements with various PSO algorithms is tested through three benchmark functions along with a few recently developed state-of-the-art methods and the results are compared with those obtained without the fine tuning elements. From several comparative analyses, it is clearly seen that the performance of all the three PSO algorithms (pf-PSO, ePSO, and hybrid PSO) is considerably improved with various fine tuning operators and sometimes more competitive than the recently developed PSO algorithms.

The linear arrangement minimization problem consists of finding a labeling or arrangement of the vertices of a graph that minimizes the sum of the absolute values of the differences between the labels of adjacent vertices. This is a well-known NP-hard problem that presents a challenge to solution methods based on heuristic optimization. Many linear arrangement reduction algorithms have recently been developed and applied to structural engineering, VLSI and software testing. We undertake the development of different heuristic procedures with the goal of uncovering the most effective designs to tackle this difficult but important problem. Specifically, we consider the adaptation of constructive, local search, GRASP and Path Relinking methods for the linear arrangement minimization. We perform computational experiments with previously reported instances to first study the effects of changes in critical search parameters and then to compare the efficiency of our proposal with previous s...

Preface Metaheuristics have often been shown to be effective for difficult combinatorial optimization problems appearing in various industrial, economical, and scientific domains. Prominent examples of metaheuristics are evolutionary algorithms, simulated annealing, tabu search, scatter search, memetic algorithms, variable neighborhood search, iterated local search, greedy randomized adaptive search procedures, estimation of distribution algorithms, and ant colony optimization. Successfully solved problems include scheduling, timetabling, network design, transportation and distribution problems, vehicle routing, the traveling salesperson problem, satisfiability, packing and cutting problems, planning problems, and general mixed integer programming. The EvoCOP event series started in 2001 and has been held annually since then. It was the first specifically dedicated to the application of evolutionary computation and related methods to combinatorial optimization problems. Evolutionary computation involves the study of problem-solving and optimization techniques inspired by principles of natural evolution and genetics. Following the general trend of hybrid metaheuristics and diminishing boundaries between the different classes of metaheuristics, EvoCOP has broadened its scope over the last years and invited submissions on any kind of metaheuristic for combinatorial optimization problems. This volume contains the

We describe a new neighborhood structure for the capacitated minimum spanning tree problem. This neighborhood structure is used by a local search strategy, leading to good trade-offs between solution quality and computation time. We also propose a GRASP with path-relinking heuristic. It uses a randomized version of a savings heuristic in the construction phase and an extension of the above local search strategy, incorporating some short term memory elements of tabu search. Computational results on benchmark problems illustrate the effectiveness of this approach, which is competitive with the best heuristics in the literature in terms of solution quality. The GRASP heuristic using a memory-based local search strategy improved the best known solution for some of the largest benchmark problem.

W e propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP + PR) for the Steiner problem in graphs. In this multistart approach, the greedy randomized construction phase of a GRASP is replaced by the use of several construction heuristics with a weight perturbation strategy that combines intensification and diversification elements, as in a strategic oscillation approach. The improvement phase circularly explores two different local search strategies. The first uses a node-based neighborhood for local search, while the second uses a key-path-based neighborhood. An adaptive path-relinking technique is applied to a set of elite solutions as a post-optimization strategy. Computational results on a broad set of benchmark problems illustrate the effectiveness and the robustness of our heuristic, which is very competitive when compared to other approximate algorithms.

This paper presents a competitive Particle Swarm Optimization algorithm for the Traveling Salesman Problem, where the velocity operator is based upon local search and path-relinking procedures. The paper proposes two versions of the algorithm, each of them utilizing a distinct local search method. The proposed heuristics are compared with other Particle Swarm Optimization algorithms presented previously for the same problem. The results are also compared with three effective algorithms for the TSP. A computational experiment with benchmark instances is reported. The results show that the method proposed in this paper finds high quality solutions and is comparable with the effective approaches presented for the TSP.

The evolutionary approach called Scatter Search, and its generalized form called Path Relinking, have proved unusually effective for solving a diverse array of optimization problems from both classical and real world settings. Scatter Search and Path Relinking differ from other evolutionary procedures, such as genetic algorithms, by providing unifying principles for joining solutions based on generalized path constructions (in both Euclidean and neighborhood spaces) and by utilizing strategic designs where other approaches resort to randomization. Scatter Search and Path Relinking are also intimately related to the Tabu Search metaheuristic, and derive additional advantages by making use of adaptive memory and associated memory-exploiting mechanisms that are capable of being adapted to particular contexts. We describe the features of Scatter Search and Path Relinking that set them apart from other evolutionary approaches, and that offer opportunities for creating increasingly more versatile and effective methods in the future.

We present a population-based approach to the RCPSP. The procedure has two phases. The first phase handles the initial construction of a population of schedules and these are then evolved until high quality solutions are obtained. The evolution of the population is driven by the alternative application of an efficient improving procedure for locally improving the use of resources, and a mechanism for combining schedules that blends scatter search and path relinking characteristics. The objective of the second phase is to explore in depth those vicinities near the high quality schedules. Computational experiments on the standard j120 set, generated using ProGen, show that our algorithm produces higher quality solutions than state-of-the-art heuristics for the RCPSP in an average time of less than five seconds.

In this article we develop a greedy randomized adaptive search procedure (GRASP) for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix, which keeps the nonzero elements in a band that is as close as possible to the main diagonal. The proposed method may be coupled with a Path Relinking strategy to search for improved outcomes.

In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straight-line crossings in a 2-layer graph. The procedure is fast and is particularly appealing when dealing with low-density graphs. When a modest increase in computational time is allowed, the procedure may be coupled with a path relinking strategy to search for improved outcomes. Although the principles of path relinking have appeared in the tabu search literature, this search strategy has not been fully implemented and tested. We perform extensive computational experiments with more than 3,000 graph instances to first study the effect of changes in critical search parameters and then to compare the efficiency of alternative solution procedures. Our results indicate that graph density is a major influential factor on the performance of a solution procedure.

The quadratic assignment problem is a classical combinatorial optimization problem that has garnered much attention due to both its large number of applications and its solution complexity. Originally used to model a location problem in the 1950's, the QAP is computationally very difficult to solve which makes it an ideal candidate for metaheuristic approaches. Path-Relinking (PR) is an evolutionary metaheuristic based on maintaining and exploiting search information by drawing on principles shared in common with tabu search. This paper proposes and implements a design for both a sequential and a parallel path-relinking algorithm tailored for the quadratic assignment problem. We illustrate the potential strength of this solution methodology by developing a very simple PR approach for a classic problem with wide applicability and exploiting the inherent parallelism of the algorithm to reduce total computational time. Results are presented on a set of problems obtained from QAPLIB for both the sequential and parallel versions of the algorithm in order to demonstrate the benefits of the parallelization. Comparisons of longer runs of the parallel algorithm are also given against popular solution approaches from the literature. In spite of the simplicity of the underlying PR method, we obtain results that are competitive with some of the best outcomes in the literature.

The work addressed in this paper is motivated from a real problem proposed to the authors by a bakery company in Northern Spain. The objective is to minimize the total distance travelled for the daily routes over the week. In order to reduce this total distance, some flexibility in the dates of delivery is introduced. A mixed-integer linear model for the problem is formulated. In addition, a two-phase method based in GRASP and path-relinking metaheuristic strategies is proposed. Computational experiments show that the method performs very well, obtaining high-quality solutions in short computational times. Moreover, when it is applied to real-data-based instances, the obtained solutions considerably reduce transportation costs over the planning horizon.

GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This chapter gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies.

Biogeography-based optimization is a novel evolutionary algorithm which mimics the immigration and emigration of species among habitats. In this paper, the biogeography-based optimization is combined with some heuristics to construct an effective hybrid algorithm for solving the fuzzy flexible job-shop scheduling problem. First, path relinking technique is employed as migration operation to generate a new solution. Then, an insertion-based local search heuristic is introduced and embedded in the biogeog-raphy-based optimization to modify the mutation operator. Moreover, an efficient machine assignment rule is also proposed to decode the representation based on the operation sequence. Consequently, the exploration and exploitation abilities of the hybrid algorithm are enhanced and well balanced. Computational results and the comparisons with some existing algorithms are presented to show the effectiveness of the proposed hybrid scheme.

M ost of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances.

With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most commonly used intra-domain Internet routing protocol (IRP). Traffic flow is routed along shortest paths, splitting flow at nodes with several outgoing links on a shortest path to the destination IP address. Link weights are assigned by the network operator. A path length is the sum of the weights of the links in the path. The OSPF weight setting (OSPFWS) problem seeks a set of weights that optimizes network performance. We study the problem of optimizing OSPF weights, given a set of projected demands, with the objective of minimizing network congestion. The weight assignment problem is NP-hard. We present a genetic algorithm (GA) to solve the OSPFWS problem. We compare our results with the best known and commonly used heuristics for OSPF weight setting, as well as with a lower bound of the optimal multi-commodity flow routing, which is a linear programming relaxation of the OSPFWS problem. Computational experiments are made on the AT&T Worldnet backbone with projected demands, and on twelve instances of synthetic networks.

We consider a fixed charge two-stage location problem in which a given number of intermediate transshipment points are to be located between the supply plants and the customer locations. Both plants and transshipment points are capacitated. Scatter search is a population-based heuristic that has been applied to several combinatorial optimization problems. We develop an efficient scatter search-based heuristic approach with hybrid improvements including local search and path-relinking routines. Computational results demonstrate the effectiveness of the heuristic even for realistic problems with larger instances and tighter capacities. ᭧

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.

Particle swarm optimization (PSO) has emerged as an acclaimed approach for solving complex optimization problems. The nature metaphors of flocking birds or schooling fish that originally motivated PSO have made the algorithm easy to describe but have also occluded the view of valuable strategies based on other foundations. From a complementary perspective, scatter search (SS) and path relinking (PR) provide an optimization framework based on the assumption that useful information about the global solution is typically contained in solutions that lie on paths from good solutions to other good solutions. Shared and contrasting principles underlying the PSO and the SS/PR methods provide a fertile basis for combining them. Drawing especially on the adaptive memory and responsive strategy elements of SS and PR, we create a combination to produce a Cyber Swarm Algorithm that proves more effective than the Standard PSO 2007 recently established as a leading form of PSO. Applied to the challenge of finding global minima for continuous nonlinear functions, the Cyber Swarm Algorithm not only is able to obtain better solutions to a well known set of benchmark functions, but also proves more robust under a wide range of experimental conditions.

In a capacitated multi-item dynamic pricing problem one maximizes the profit by choosing a proper production level as well as pricing policy, where the latter depends on a satisfied demand. The objective function involves inventory, production and setup costs, and revenue functions. The products are required to satisfy joined production capacities. We consider a bilinear reduction of the linear mixed integer formulation of the problem and prove that the problem is equivalent to finding a global maximum of the bilinear problem. A heuristic algorithm is proposed, based on the reduction technique. Numerical experiments confirm the efficiency of the proposed technique.

The principles ofthe Greedy Randomized Adaptative Search Procedure (GRASP) metaheuristic are instantiated for the set packing problem. We investigated several construction phases, and evaluated improvements based on advanced strategies. These improvements include a self-tuning procedure (using reactive GRASP), an intensification procedure (using path relinking) and a procedure involving the diversification of the selection (using a learning pro cess). Two sets of various numerical instances were used to perform the computational experiments. The first set contains randomly generated instances, while the second includes instances relating to real problems in railway planning. No metaheuristic has previously been applied to this combinatorial problem. Consequently, we have discussed GRASP's performances both in relation to lower fupper bounds and to the results obtained with Cplex when such results are available. Our analysis, based on the average performances observed, shows the impact of the suggested strategies, and indicates the configuration that produces the best results.

The Maximum Diversity Problem (MDP) consists in identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics between themselves. The identification of such solution is an NP-hard problem. Some heuristics are available to obtain approximate solutions for this problem. In this paper we propose different GRASP heuristics for the MDP, using distinct construction procedures and path-relinking techniques. Performance comparison between related work and the proposed heuristics is provided. Experimental results show that the new GRASP heuristics are quite robust and are able to find high-quality solutions in a feasible computational time.

Multi-objective optimization problems deal with the presence of different conflicting objectives. Given that it is not possible to obtain a single solution by optimizing all the objectives simultaneously, a common way to face these problems is to obtain a set of efficient solutions called the non-dominated frontier. In this paper we address the problem of routing school buses with two objectives: minimize the number of buses, and minimize the longest time a student would have to stay in the bus. The tradeoff in this problem is between service level, which is represented by the maximum route length, and operational cost, which is represented by the number of buses in the solution. We present different constructive solution methods and a tabu search procedure to obtain non-dominated solutions. The procedure is coupled with an intensification phase based on the path relinking methodology; a strategy proposed several years ago, which has been rarely used in actual implementations. Computational experiments with real data in the context of routing school buses in a rural area, establish the effectiveness of our procedure in relation to the approach previously identified to be best.

The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with pathrelinking heuristic for the set k-covering problem, as well as the template of a family of Lagrangean heuristics. The hybrid GRASP Lagrangean heuristic employs the GRASP with path-relinking heuristic using modified costs to obtain approximate solutions for the original problem. Computational experiments carried out on 135 test instances show experimentally that the Lagrangean heuristics performed consistently better than GRASP. By properly tuning the parameters of the GRASP Lagrangean heuristic, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, the GRASP Lagrangean heuristic makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, when other strategies fail to find new improving solutions.

This work investigates two branch and bound algorithms based on different tree representations of the multidimensional assignment problem (MAP). The MAP may be depicted as either an index-based tree in which every level of the tree represents a different value of the first index or as a permutation-based tree that has vertices representing different permutation vectors of a feasible solution. We also look at the benefits of sorting the cost coefficients on each index tree level, performing a local search on either just the initial ...

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges is minimized. This NP-hard problem has applications in network scheduling, automatic graph drawing and information retrieval. We propose a heuristic method based on the Scatter Search (SS) methodology for finding approximate solutions to this optimization problem. This metaheuristic explores solution space by evolving a set of reference points. Our SS method is based on a GRASP constructive algorithm, a local search strategy based on insertion moves and voting-based combination methods. We also introduce a new measure to control the diversity in the search process. Empirical results with 252 previously reported instances indicate that the proposed procedure compares favorably to previous metaheuristics for this problem, such as Simulated Annealing and Evolutionary Path Relinking.

Each day the Internet connects more people, increasing the need for transmitting secure information. One way to protect the data sent over the web is to conceal the relevant information inside a typical image, hiding the data from intruders. This paper proposes a hybrid heuristic, combining a genetic algorithm and the path relinking metaheuristic to efficiently solve this problem. Computational

Evolutionary algorithms are effective search tools for tackling difficult optimization problems. In this paper an algorithm based on living processes where cooperation is the main evolutionary strategy is applied to the Prize Collecting Steiner Tree Problem, an NP-hard combinatorial optimization problem. The Transgenetic Algorithm presented here is hybridized with path-relinking. Computational results of an experiment performed with benchmark instances are reported. The results obtained for the Prize Collecting Steiner Tree Problem with the application of the hybrid Transgenetic Algorithm are compared with the results of three effective approaches presented previously. The computational experiment shows that the proposed approach is very competitive concerning both quality of solution and processing time.

In this paper, we develop a new heuristic procedure for the linear ordering problem (LOP). This NP-hard problem has a signi"cant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input}output tables in economics. In this paper, we concentrate on matrices that arise in the context of this real-world application. The proposed algorithm is based on the tabu search methodology and incorporates strategies for search intensi"cation and diversi"cation. For search intensi"cation, we experiment with path relinking, a strategy proposed several years ago in connection with tabu search, which has been rarely used in actual implementations. Extensive computational experiments with input}output tables show that the proposed procedure outperforms the best heuristics reported in the literature. Furthermore, the experiments also show the merit of achieving a balance between intensi"cation and diversi"cation in the search.

Artificial neural networks (ANN) have been widely used for both classification and prediction. This paper is focused on the prediction problem in which an unknown function is approximated. ANNs can be viewed as models of real systems, built by tuning parameters known as weights. In training the net, the problem is to find the weights that optimize its performance (i.e.

Many real-world optimization problems are dynamic. These problems require from powerful methods to adapt to problem modifications over time. Most applied research on metaheuristics has focused on static (non-changing) optimization problems and these methods lack from adaptation strategies. Particle filters are sequential Monte Carlo estimation methods which can be applied to Bayesian filtering for discrete-time dynamic models that are typically nonlinear and non-Gaussian. In this paper, we propose a general framework to hybridize population-based metaheuristics and particle filters. The aim of this framework is to naturally devise to effective hybrid algorithms to solve dynamic optimization problems by exploiting the benefits of both approaches. Derived algorithms cleverly combine particle filters (PF) and population-based metaheuristic (PBM) methods. As particular examples, two different effective algorithms, named Path Relinking Particle Filter (PRPF) and Scatter Search Particle Filter (SSPF) are respectively derived from the proposed hybridization framework. Finally, efficient applications of these instantiated algorithms to three different dynamic problems are also presented.

M ost of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances.

This paper concerns the urban road network design problem. In urban areas supply has usually been unable to keep pace with increasing demand: the only possibility is often to reorganise the current supply configuration in order to use existing resources efficiently. Thus, in urban areas signal settings and network topology (in particular lane layout) are the two major factors that can be handled by design models. Methods for the combined design of signal settings and topology are proposed in this paper. All the methods proceed in two stages: the first deals with integer variables (topology), while the second deals with continuous variables (signal settings). Some metaheuristics (Hill Climbing, Simulated Annealing, Tabu Search, Genetic Algorithms and Path Relinking) are specified for the topology design stage, and they are used singularly or jointly. The continuous part of the solution, with fixed topology is optimized through an algorithm for asymmetrical deterministic equilibrium assignment. This paper focuses on evaluating performances obtained by all the different algorithms proposed for the topology design stage. The algorithms are compared by applications to real networks, and some conclusions are drawn about their efficiency.

A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path-relinking is a procedure used to intensify the search around good-quality isolated ...

In this work we deal with sandwich graphs G =(V,E) and present the notion of vertices f-controlled by a subset M ⊆ V. We introduce the generalized maxcontrolled set problem (gmcsp), where gaps and positive weights are associated to each vertex of V. In this case, the objective is find a sandwich graph G in order to maximize the sum of the weights associated to all vertices f-controlled by M. We present a 1 2-approximation algorithm for the gmcsp and a new procedure for finding feasible solutions based on a linear relaxation. The best solution is then used as starting point in a local search procedure (Tabu Search with Path Relinking). Finally, we present some computational results and compare the performance of our heuristics with the optimum solution value of some instances of the problem.