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40
On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts  Towards Memetic Algorithms
, 1989
"... Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could ..."
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Cited by 186 (10 self)
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Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration." This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., "Polyhedral computations", from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization [124]. It is interesting to compare the number of configurations of realworld problems in combinatorial optimization with those large numbers arising in Cosmol...
Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators
 Artificial Intelligence Review
, 1999
"... This paper is the result of a literature study carried out by the authors. It is a review of the dierent attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Alg ..."
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Cited by 66 (2 self)
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This paper is the result of a literature study carried out by the authors. It is a review of the dierent attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Algorithms with dierent representations such as: binary representation, path representation, adjacency representation, ordinal representation and matrix representation. Likewise, we show the experimental results obtained with dierent standard examples using combination of crossover and mutation operators in relation with path representation. Keywords: Travelling Salesman Problem; Genetic Algorithms; Binary representation; Path representation; Adjacency representation; Ordinal representation; Matrix representation; Hybridation. 1 1 Introduction In nature, there exist many processes which seek a stable state. These processes can be seen as natural optimization processes. Over the last...
Experimental Analysis of Heuristics for the STSP
 Local Search in Combinatorial Optimization
, 2001
"... In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We ..."
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Cited by 53 (1 self)
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In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
"... ..."
HASSOP: Hybrid Ant System For The Sequential Ordering Problem
, 1997
"... We present HASSOP, a new approach to solving sequential ordering problems. HASSOP combines the ant colony algorithm, a populationbased metaheuristic, with a new local optimizer, an extension of a TSP heuristic which directly handles multiple constraints without increasing computational complexity ..."
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Cited by 45 (6 self)
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We present HASSOP, a new approach to solving sequential ordering problems. HASSOP combines the ant colony algorithm, a populationbased metaheuristic, with a new local optimizer, an extension of a TSP heuristic which directly handles multiple constraints without increasing computational complexity. We compare different implementations of HASSOP and present a new data structure that improves system performance. Experimental results on a set of twentythree test problems taken from the TSPLIB show that HASSOP outperforms existing methods both in terms of solution quality and computation time. Moreover, HASSOP improves most of the best known results for the considered problems.
An Ant Colony System Hybridized With A New Local Search For The Sequential Ordering Problem
, 2000
"... We present a new local optimizer called SOP3exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP3exchange with an Ant Col ..."
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Cited by 43 (12 self)
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We present a new local optimizer called SOP3exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP3exchange with an Ant Colony Optimization algorithm is described and we present experimental evidence that the resulting algorithm is more effective than existing methods for the problem. The bestknown results for many of a standard test set of 22 problems are improved using the SOP3exchange with our Ant Colony Optimization algorithm or in combination with the MPO/AI algorithm (Chen and Smith 1996).
The Vehicle Routing Problem with Time Windows  Part II: Genetic Search
, 1996
"... This paper is the second part of a work on the application of new search techniques for the vehicle routing problem with time windows. It describes GENEROUS, the GENEtic ROUting System, which is based on the natural evolution paradigm. Under this paradigm, a population of solutions evolves from one ..."
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Cited by 43 (1 self)
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This paper is the second part of a work on the application of new search techniques for the vehicle routing problem with time windows. It describes GENEROUS, the GENEtic ROUting System, which is based on the natural evolution paradigm. Under this paradigm, a population of solutions evolves from one generation to the next by "mating" parent solutions to form new offspring solutions that exhibit characteristics inherited from their parents. For this vehicle routing application, a specialized methodology is devised for merging two vehicle routing solutions into a single solution that is likely to be feasible with respect to the time window constraints. Computational results on a standard set of test problems are reported, and comparisons are provided with other heuristics.
A View of Local Search in Constraint Programming
 In Proc. of the Principles and Practice of Constraint Programming
, 1996
"... . We propose in this paper a novel way of looking at local search algorithms for combinatorial optimization problems which better suits constraint programming by performing branchandbound search at their core. We concentrate on neighborhood exploration and show how the framework described yields a ..."
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Cited by 39 (2 self)
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. We propose in this paper a novel way of looking at local search algorithms for combinatorial optimization problems which better suits constraint programming by performing branchandbound search at their core. We concentrate on neighborhood exploration and show how the framework described yields a more efficient local search and opens the door to more elaborate neighborhoods. Numerical results are given in the context of the traveling salesman problem with time windows. This work on neighborhood exploration is part of ongoing research to develop constraint programming tabu search algorithms applied to routing problems. Introduction Local search methods in operations research (or) date back to over thirty years ago ([Lin65]). Applied to difficult combinatorial optimization problems, this heuristic approach yields highquality solutions by iteratively considering small modifications (called local moves) of a good solution in the hope of finding a better one. Used within a strategy de...
Memetic Algorithms for the Traveling Salesman Problem
 Complex Systems
, 1997
"... this paper, the tness landscapes of several instances of the traveling salesman problem (TSP) are investigated to illustrate why MAs are wellsuited for nding nearoptimum tours for the TSP. It is shown that recombination{based MAs can exploit the correlation structure of the landscape. A comparis ..."
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Cited by 25 (7 self)
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this paper, the tness landscapes of several instances of the traveling salesman problem (TSP) are investigated to illustrate why MAs are wellsuited for nding nearoptimum tours for the TSP. It is shown that recombination{based MAs can exploit the correlation structure of the landscape. A comparison of several recombination operators { including a new generic recombination operator { reveals that when using the sophisticated Lin{Kernighan local search, the performance dierence of the MAs is small. However, the most important property of eective recombination operators is shown to be respectfulness. In experiments it is shown that our MAs with generic recombination are among the best evolutionary algorithms for the TSP. In particular, optimum solutions could be found up to a problem size of 3795, and for large instances up to 85,900 cities, nearoptimum solutions could be found in a reasonable amount of time