HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated mi... more This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A primal-dual approach is achieved by including a scatter search procedure that further exploits the adaptive memory framework. Computational results from applying the methods to a standard set of benchmark problems disclose that the dual RAMP algorithm finds high quality solutions very efficiently and that its primal-dual enhancement is still more effective.
Subpath reversals are common operations in graph-based structures arising in a wide range of appl... more Subpath reversals are common operations in graph-based structures arising in a wide range of applications in combinatorial optimization. We describe the satellite list, a variation on the doubly-linked list that is symmetric, efficient, and can be reversed or reverse subsections in constant time.
The number partitioning problem has proven to be a challenging problem for both exact and heurist... more The number partitioning problem has proven to be a challenging problem for both exact and heuristic solution methods. We present a new modeling and solution approach that consists of recasting the problem as an unconstrained quadratic binary program that can be solved by efficient metaheuristic methods. Our approach readily accommodates both the common two-subset partition case as well as the more general case of multiple subsets. Preliminary computational experience is presented illustrating the attractiveness of the method.
Metaheuristics — general search procedures whose principles allow them to escape the trap of loca... more Metaheuristics — general search procedures whose principles allow them to escape the trap of local optimality using heuristic designs — have been successfully employed to address a variety of important optimization problems over the past few years. Particular gains have been achieved in obtaining high quality solutions to problems that classical exact methods (which guarantee convergence) have found too complex to handle effectively. Typically a metaheuristic method is crafted to suit the particular characteristics of the problem at hand, exploiting to the extent possible the structure available to enable a fruitful and efficient search process. An alternative to this problem specific solution approach is a more general methodology that recasts a given problem into a common modeling format, permitting solutions to be derived by a common, rather than tailor-made, heuristic method. The optimization folklore strongly emphasizes the unproductive consequences of converting problems from ...
We examine a prominent and widely-studied model of the protein folding problem, the two-dimension... more We examine a prominent and widely-studied model of the protein folding problem, the two-dimensional (2D) HP model, by means of a filter-and-fan (F&F) solution approach. Our method is designed to generate compound moves that explore the solution space in a dynamic and adaptive fashion. Computational results for a standard set of benchmark problems show that the F&F algorithm performs more robustly and efficiently than the current leading algorithms, requiring only a single solution trial to obtain best known solutions to all but two of the benchmark problems, in contrast to a hundred or more trials required in the typical case by the best of the alternative methods. On the remaining problems a single trial of our method obtains a solution one unit away from the best known solution.
The well-known K-means clustering algorithm has been employed widely in different application dom... more The well-known K-means clustering algorithm has been employed widely in different application domains ranging from data analytics to logistics applications. However, the K-means algorithm can be affected by factors such as the initial choice of centroids and can readily become trapped in a local optimum. In this paper, we propose an improved K-means clustering algorithm that is augmented by a Tabu Search strategy, and which is better adapted to meet the needs of big data applications. Our design focuses on enhancements to take advantage of parallel processing based on the Spark framework. Computational experiments demonstrate the superiority of our parallel Tabu Search based clustering algorithm over a widely used version of the K-means approach embodied in the parallel Spark MLlib system, comparing the algorithms in terms of scalability, accuracy, and effectiveness.
Ejection chain methods lead the state-of-the-art in local search heuristics for the traveling sal... more Ejection chain methods lead the state-of-the-art in local search heuristics for the traveling salesman problem (TSP). The most effective local search approaches primarily originate from the Stem-and-Cycle ejection chain method and the classical Lin-Kernighan procedure, which can be viewed as an instance of an ejection chain method. This paper describes major components of the most effective ejection chain algorithms that are critical for success in solving large scale TSPs. A performance assessment of foremost algorithms is reported based upon an experimental analysis carried out on a standard set of symmetric and asymmetric TSP benchmark problems.
Years of Internet marketing research have yielded a set of important findings. The purpose of thi... more Years of Internet marketing research have yielded a set of important findings. The purpose of this paper is to review these findings and assess what has been done and what has not been done in the area. In doing so, the authors review existing findings ranging from the types of products on the Internet, the Internet as a marketing channel, the Internet as an advertising and communication medium, the Internet adoption, to the effect of the Internet on traditional markets. Based on the studies reviewed, implications are drawn for further theoretical and empirical investigations.
Relaxation Adaptive Memory Programming (RAMP) is a new metaheuristic methodology recently introdu... more Relaxation Adaptive Memory Programming (RAMP) is a new metaheuristic methodology recently introduced in [4]. The method integrates the concept of Adaptive Memory Programming (AMP), originated in Tabu Search, with mathematical relaxation procedures to produce a unified framework for the design of dual and primal-dual metaheuristics. This paper reviews the fundamentals of the method and discusses major advances that have yielding exceedingly promising results in a variety of applications.
The Job Shop Scheduling Problem (JSSP) is a notorious difficult problem in combinatorial optimiza... more The Job Shop Scheduling Problem (JSSP) is a notorious difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure based on a filter and fan method (F&F). In the algorithm, SBP is used to generate a starting solution as well as to re-optimize the best schedules produced by the F&F method. The F&F is a local search procedure that generates compound moves in a tree search fashion. Computational results carried out on a standard set of 43 benchmark problems shows that the F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best.
The design of effective neighborhood search procedures is a primary issue for the performance of ... more The design of effective neighborhood search procedures is a primary issue for the performance of local search and advanced metaheuristic algorithms. Several recent studies have focused on the development of variable depth neighborhoods that generate sequences of interrelated elementary moves to create more complex compound moves. These methods are chiefly conceived to produce an adaptive search as the number of elementary moves in a compound move may vary from one iteration to another depending on the state of the search. The objective is to achieve this goal with modest computational effort. Although ejection chain methods are currently the most advanced methods in this domain, they usually require more complex implementations. The filter-and-fan (F&F) method appears as an alternative to ejection chain methods allowing for the creation of compound moves based on an effective tree search design. This paper reports the first implementation of the F&F approach to the uncapacitated facility location problem (UFLP). We examine a simple version of the F&F method in this study, and explore two search strategies under this framework. The results obtained on a set of 105 standard benchmark problems from the literature demonstrate that this simple but well-structured approach is highly effective for providing optimal and near-optimal solutions for the UFLP in a very short computation time, and indeed can be advantageously compared with the most advanced metaheuristic procedures in solving these problems.
The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial ... more The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.
We present a Tabu search algorithm for the vehicle routing problem (VRP) under capacity and dista... more We present a Tabu search algorithm for the vehicle routing problem (VRP) under capacity and distance restrictions. The neighborhood search is based on compound moves generated by a node-ejection chain process. During the course of the algorithm, two types of neighborhood structures are used and crossing infeasible solutions is allowed. Then, a parallel version of the algorithm which exploits the moves' characteristics is described. Parallel processing is used to explore the solution space more extensively and to accelerate the search process. Tests are carried out on a SUNSparc workstation and the parallel algorithm uses a network of four of these machines. Numerical tests indicate that the sequential version of the algorithm is highly competitive with the best existing heuristics and that the parallel algorithm outperforms all of these algorithms.
The set covering problem (SCP) is central in a wide variety of practical applications for which f... more The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraints normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective one-pass constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborated normalization rules for surrogate heuristics are also provided.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated mi... more This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A primal-dual approach is achieved by including a scatter search procedure that further exploits the adaptive memory framework. Computational results from applying the methods to a standard set of benchmark problems disclose that the dual RAMP algorithm finds high quality solutions very efficiently and that its primal-dual enhancement is still more effective.
Subpath reversals are common operations in graph-based structures arising in a wide range of appl... more Subpath reversals are common operations in graph-based structures arising in a wide range of applications in combinatorial optimization. We describe the satellite list, a variation on the doubly-linked list that is symmetric, efficient, and can be reversed or reverse subsections in constant time.
The number partitioning problem has proven to be a challenging problem for both exact and heurist... more The number partitioning problem has proven to be a challenging problem for both exact and heuristic solution methods. We present a new modeling and solution approach that consists of recasting the problem as an unconstrained quadratic binary program that can be solved by efficient metaheuristic methods. Our approach readily accommodates both the common two-subset partition case as well as the more general case of multiple subsets. Preliminary computational experience is presented illustrating the attractiveness of the method.
Metaheuristics — general search procedures whose principles allow them to escape the trap of loca... more Metaheuristics — general search procedures whose principles allow them to escape the trap of local optimality using heuristic designs — have been successfully employed to address a variety of important optimization problems over the past few years. Particular gains have been achieved in obtaining high quality solutions to problems that classical exact methods (which guarantee convergence) have found too complex to handle effectively. Typically a metaheuristic method is crafted to suit the particular characteristics of the problem at hand, exploiting to the extent possible the structure available to enable a fruitful and efficient search process. An alternative to this problem specific solution approach is a more general methodology that recasts a given problem into a common modeling format, permitting solutions to be derived by a common, rather than tailor-made, heuristic method. The optimization folklore strongly emphasizes the unproductive consequences of converting problems from ...
We examine a prominent and widely-studied model of the protein folding problem, the two-dimension... more We examine a prominent and widely-studied model of the protein folding problem, the two-dimensional (2D) HP model, by means of a filter-and-fan (F&F) solution approach. Our method is designed to generate compound moves that explore the solution space in a dynamic and adaptive fashion. Computational results for a standard set of benchmark problems show that the F&F algorithm performs more robustly and efficiently than the current leading algorithms, requiring only a single solution trial to obtain best known solutions to all but two of the benchmark problems, in contrast to a hundred or more trials required in the typical case by the best of the alternative methods. On the remaining problems a single trial of our method obtains a solution one unit away from the best known solution.
The well-known K-means clustering algorithm has been employed widely in different application dom... more The well-known K-means clustering algorithm has been employed widely in different application domains ranging from data analytics to logistics applications. However, the K-means algorithm can be affected by factors such as the initial choice of centroids and can readily become trapped in a local optimum. In this paper, we propose an improved K-means clustering algorithm that is augmented by a Tabu Search strategy, and which is better adapted to meet the needs of big data applications. Our design focuses on enhancements to take advantage of parallel processing based on the Spark framework. Computational experiments demonstrate the superiority of our parallel Tabu Search based clustering algorithm over a widely used version of the K-means approach embodied in the parallel Spark MLlib system, comparing the algorithms in terms of scalability, accuracy, and effectiveness.
Ejection chain methods lead the state-of-the-art in local search heuristics for the traveling sal... more Ejection chain methods lead the state-of-the-art in local search heuristics for the traveling salesman problem (TSP). The most effective local search approaches primarily originate from the Stem-and-Cycle ejection chain method and the classical Lin-Kernighan procedure, which can be viewed as an instance of an ejection chain method. This paper describes major components of the most effective ejection chain algorithms that are critical for success in solving large scale TSPs. A performance assessment of foremost algorithms is reported based upon an experimental analysis carried out on a standard set of symmetric and asymmetric TSP benchmark problems.
Years of Internet marketing research have yielded a set of important findings. The purpose of thi... more Years of Internet marketing research have yielded a set of important findings. The purpose of this paper is to review these findings and assess what has been done and what has not been done in the area. In doing so, the authors review existing findings ranging from the types of products on the Internet, the Internet as a marketing channel, the Internet as an advertising and communication medium, the Internet adoption, to the effect of the Internet on traditional markets. Based on the studies reviewed, implications are drawn for further theoretical and empirical investigations.
Relaxation Adaptive Memory Programming (RAMP) is a new metaheuristic methodology recently introdu... more Relaxation Adaptive Memory Programming (RAMP) is a new metaheuristic methodology recently introduced in [4]. The method integrates the concept of Adaptive Memory Programming (AMP), originated in Tabu Search, with mathematical relaxation procedures to produce a unified framework for the design of dual and primal-dual metaheuristics. This paper reviews the fundamentals of the method and discusses major advances that have yielding exceedingly promising results in a variety of applications.
The Job Shop Scheduling Problem (JSSP) is a notorious difficult problem in combinatorial optimiza... more The Job Shop Scheduling Problem (JSSP) is a notorious difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure based on a filter and fan method (F&F). In the algorithm, SBP is used to generate a starting solution as well as to re-optimize the best schedules produced by the F&F method. The F&F is a local search procedure that generates compound moves in a tree search fashion. Computational results carried out on a standard set of 43 benchmark problems shows that the F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best.
The design of effective neighborhood search procedures is a primary issue for the performance of ... more The design of effective neighborhood search procedures is a primary issue for the performance of local search and advanced metaheuristic algorithms. Several recent studies have focused on the development of variable depth neighborhoods that generate sequences of interrelated elementary moves to create more complex compound moves. These methods are chiefly conceived to produce an adaptive search as the number of elementary moves in a compound move may vary from one iteration to another depending on the state of the search. The objective is to achieve this goal with modest computational effort. Although ejection chain methods are currently the most advanced methods in this domain, they usually require more complex implementations. The filter-and-fan (F&F) method appears as an alternative to ejection chain methods allowing for the creation of compound moves based on an effective tree search design. This paper reports the first implementation of the F&F approach to the uncapacitated facility location problem (UFLP). We examine a simple version of the F&F method in this study, and explore two search strategies under this framework. The results obtained on a set of 105 standard benchmark problems from the literature demonstrate that this simple but well-structured approach is highly effective for providing optimal and near-optimal solutions for the UFLP in a very short computation time, and indeed can be advantageously compared with the most advanced metaheuristic procedures in solving these problems.
The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial ... more The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.
We present a Tabu search algorithm for the vehicle routing problem (VRP) under capacity and dista... more We present a Tabu search algorithm for the vehicle routing problem (VRP) under capacity and distance restrictions. The neighborhood search is based on compound moves generated by a node-ejection chain process. During the course of the algorithm, two types of neighborhood structures are used and crossing infeasible solutions is allowed. Then, a parallel version of the algorithm which exploits the moves' characteristics is described. Parallel processing is used to explore the solution space more extensively and to accelerate the search process. Tests are carried out on a SUNSparc workstation and the parallel algorithm uses a network of four of these machines. Numerical tests indicate that the sequential version of the algorithm is highly competitive with the best existing heuristics and that the parallel algorithm outperforms all of these algorithms.
The set covering problem (SCP) is central in a wide variety of practical applications for which f... more The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraints normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective one-pass constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborated normalization rules for surrogate heuristics are also provided.
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