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A selection of useful theoretical tools for the design and analysis of optimization heuristics
 Memetic Computing
, 2009
"... An intensive practical experimentation is certainly required for the purpose of heuristics design and evaluation, however a theoretical approach is also important in this area of research. This paper gives a brief description of a selection of theoretical tools that can be used for designing and ana ..."
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An intensive practical experimentation is certainly required for the purpose of heuristics design and evaluation, however a theoretical approach is also important in this area of research. This paper gives a brief description of a selection of theoretical tools that can be used for designing and analyzing various heuristics. For design and evaluation, we consider several examples of preprocessing procedures and probabilistic instance analysis methods. We also discuss some attempts at the theoretical explanation of successes and failures of certain heuristics. 1
Efficient Local Search Algorithms for Known and New Neighborhoods for the Generalized Traveling Salesman Problem
, 2012
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Greedy Like Algorithms for the Traveling Salesman and Multidimensional Assignment Problems
"... Majority of chapters of this book show usefulness of greedy like algorithms for solving various combinatorial optimization problems. The aim of this chapter is to warn the reader that not always a greedy like approach is a good option and, in certain cases, it is a very bad option being sometimes am ..."
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Cited by 4 (3 self)
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Majority of chapters of this book show usefulness of greedy like algorithms for solving various combinatorial optimization problems. The aim of this chapter is to warn the reader that not always a greedy like approach is a good option and, in certain cases, it is a very bad option being sometimes among the worst possible
A Memetic Algorithm for the Multidimensional Assignment Problem
, 2009
"... The Multidimensional Assignment Problem (MAP or sAP in the case of s dimensions) is an extension of the wellknown assignment problem. The most studied case of MAP is 3AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm ..."
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The Multidimensional Assignment Problem (MAP or sAP in the case of s dimensions) is an extension of the wellknown assignment problem. The most studied case of MAP is 3AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the stateofthe art 3AP memetic algorithm.
An Efficient Hybrid Ant Colony System for the Generalized Traveling Salesman Problem
, 2012
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A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem
"... Memetic Algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm one needs to make a host of decisions; selecting a population size is one of the most important among them. Most algorithms in the literature fix the population size to a cert ..."
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Memetic Algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm one needs to make a host of decisions; selecting a population size is one of the most important among them. Most algorithms in the literature fix the population size to a certain constant value. This reduces the algorithm’s quality since the optimal population size varies for different instances, local search procedures and running times. In this paper we propose an adjustable population size. It is calculated as a function of the running time of the whole algorithm and the average running time of the local search for the given instance. Note that in many applications the running time of a heuristic should be limited and therefore we use this limit as a parameter of the algorithm. The average running time of the local search procedure is obtained during the algorithm’s run. Some coefficients which are independent with respect to the instance or the local search are to be tuned before the algorithm run; we provide a procedure to find these coefficients. The proposed approach was used to develop a memetic algorithm for the Multidimensional Assignment Problem (MAP or sAP in the case of s dimensions) which is an extension of the wellknown assignment problem. MAP is NPhard and has a host of applications. We show that using adjustable population size makes the algorithm flexible to perform well for instances of very different sizes and types and for different running times and local searches. This allows us to select the most efficient local search for every instance type. The results of computational experiments for several instance families and sizes prove that the proposed algorithm performs efficiently for a wide range of the running times and clearly outperforms the stateofthe art 3AP memetic algorithm being given the same time.
Neighborhood Search for the Bounded Diameter Minimum Spaning Tree
"... Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a ..."
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Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a reasonable amount of time. Neighborhood search algorithms are a wide class of algorithms where at each iteration an improved solution is found by searching the “neighborhood ” of the current solution. A critical issue in the design of a neighborhood search algorithm is the choice of the neighborhood structure. Literature reveals that the larger the neighborhood, the better is the quality of the locally optimal solutions and the greater is the accuracy of the final solution obtained. At the same time, the larger the neighborhood search, the longer it takes to search the neighborhood for optimum. For this reason, an efficient search strategy is required to produce an effective heuristic in large neighborhoods. This paper focus on two known neighborhood structures for the BDMST problem. Both types of neighborhoods are large in the sense that they contain exponentially large number of candidate solutions. A novel intelligent neighborhood search technique (INST) is introduced and compared with the previously published local search techniques. Keywords Bounded Diameter Minimum spanning tree, Local search, Heuristics. I.