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38
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...
Evolution in time and space  the parallel genetic algorithm
 FOUNDATIONS OF GENETIC ALGORITHMS
, 1991
"... The parallel genetic algorithm (PGA) uses two major modifications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live in a 2D world. Selection of a mate is done by each individual independently in its neighborhood. Secondly, each individual may improve ..."
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Cited by 108 (13 self)
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The parallel genetic algorithm (PGA) uses two major modifications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live in a 2D world. Selection of a mate is done by each individual independently in its neighborhood. Secondly, each individual may improve its fitness during its lifetime by e.g. local hillclimbing. The PGA is totally asynchronous, running with maximal efficiency on MIMD parallel computers. The search strategy of the PGA is based on a small number of active and intelligent individuals, whereas a GA uses a large population of passive individuals. We will investigate the PGA with deceptive problems and the traveling salesman problem. We outline why and when the PGA is succesful. Abstractly, a PGA is a parallel search with information exchange between the individuals. If we represent the optimization problem as a fitness landscape in a certain configuration space, we see, that a PGA tries to jump from two local minima to a third, still better local minima, by using the crossover operator. This jump is (probabilistically) successful, if the fitness landscape has a certain correlation. We show the correlation for the traveling salesman problem by a configuration space analysis. The PGA explores implicitly the above correlation.
Variable neighborhood search: Principles and applications
, 2001
"... Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using an ..."
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Cited by 94 (9 self)
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Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a twolevel VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear
MAXMIN Ant System
 FUTURE GENERATION COMPUTER SYSTEMS
, 2000
"... Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Sa ..."
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Cited by 79 (4 self)
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Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this ares has mainly focused on the development of algorithmic variants which achieve better performance than AS. In this article, we present ¨�©� � –¨��� � Ant System, an Ant Colony Optimization algorithm derived from Ant System. ¨�©� � –¨��� � Ant System differs from Ant System in several important aspects, whose usefulness we demonstrate by means of an experimental study. Additionally, we relate one of the characteristics specific to ¨� ¨ AS — that of using a greedier search than Ant System — to results from the search space analysis of the combinatorial optimization problems attacked in this paper. Our computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that ¨�©� � – ¨��� � Ant System is currently among the best performing algorithms for these problems.
2+p SAT: Relation of typicalcase complexity to the nature of the phase transition. Random Structures and Algorithms
, 1999
"... ABSTRACT: Heuristic methods for solution of problems in the NPcomplete class of decision problems often reach exact solutions, but fail badly at ‘‘phase boundaries,’ ’ across which the decision to be reached changes from almost always having one value to almost always having a different value. We r ..."
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Cited by 50 (2 self)
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ABSTRACT: Heuristic methods for solution of problems in the NPcomplete class of decision problems often reach exact solutions, but fail badly at ‘‘phase boundaries,’ ’ across which the decision to be reached changes from almost always having one value to almost always having a different value. We report an analytic solution and experimental investigations of the phase transition that occurs in the limit of very large problems in KSAT. Studying a model which interpolates KSAT between K�2 and K�3, we find a change from a continuous to a discontinuous phase transition when K, the average number of inputs per clause, exceeds 0.4. The cost of finding solutions also increases dramatically above this changeover. The nature of its ‘‘random firstorder’ ’ phase transition, seen at values of K large enough to make the computational cost of solving typical instances increase exponentially with problem size, suggests a mechanism for the cost increase. There has been
Landscapes, Operators and Heuristic Search
 Annals of Operations Research
, 1997
"... this paper, a simple example will be used to illustrate the fact that the landscape structure changes with the operator; indeed, it often depends even on the way the operators are applied. Recent attention has focused on trying to understand better the nature of these `landscapes'. Recent work by Bo ..."
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Cited by 44 (3 self)
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this paper, a simple example will be used to illustrate the fact that the landscape structure changes with the operator; indeed, it often depends even on the way the operators are applied. Recent attention has focused on trying to understand better the nature of these `landscapes'. Recent work by Boese et al. [2] has shown that instances of the TSP are often characterised by a `big valley' structure in the case of a 2opt exchange operator, and a particular distance metric. In this paper their work is developed by investigating the question of how landscapes change under different search operators in the case of the n=m=P=Cmax
Parallel Genetic Algorithm in Combinatorial Optimization
, 1992
"... Parallel genetic algorithms (PGA) use two major modifications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live in a 2D world. Selection of a mate is done by each individual independently in its neighborhood. Secondly, each individual may improve its ..."
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Cited by 38 (4 self)
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Parallel genetic algorithms (PGA) use two major modifications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live in a 2D world. Selection of a mate is done by each individual independently in its neighborhood. Secondly, each individual may improve its fitness during its lifetime by e.g. local hillclimbing. The PGA is totally asynchronous, running with maximal efficiency on MIMD parallel computers. The search strategy of the PGA is based on a small number of intelligent and active individuals, whereas a GA uses a large population of passive individuals. We will show the power of the PGA with two combinatorial problems  the traveling salesman problem and the m graph partitioning problem. In these examples, the PGA has found solutions of very large problems, which are comparable or even better than any other solution found by other heuristics. A comparison between the PGA search strategy and iterated local hillclimbing is made. KEYWORDS ...
Cost Versus Distance In the Traveling Salesman Problem
, 1995
"... This paper studies the distribution of good solutions for the traveling salesman problem (TSP) on a wellknown 532city instance that has been solved optimally by Padberg and Rinaldi [16]. For each of five local search heuristics, solutions are obtained from 2,500 different random starting points. C ..."
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Cited by 36 (0 self)
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This paper studies the distribution of good solutions for the traveling salesman problem (TSP) on a wellknown 532city instance that has been solved optimally by Padberg and Rinaldi [16]. For each of five local search heuristics, solutions are obtained from 2,500 different random starting points. Comparisons of these solutions show that lowercost solutions have a strong tendency to be both closer to the optimal tour and closer to other good solutions. (Distance between two solutions is defined in terms of the number of edges they have in common.) These results support the conjecture of Boese, Kahng and Muddu [3] that the solution spaces of TSP instances have a "globally convex" or "big valley" character. This observation was used by [3] to motivate a new multistart strategy for global optimization called Adaptive MultiStart (AMS). 1 Introduction Local search is probably the most successful approach to finding heuristic solutions to combinatorial global optimization problems. In gl...
Parallel Distributed Approaches to Combinatorial Optimization  Benchmark Studies on Traveling Salesman Problem
, 1990
"... We present and summarize the results from 50, 100 and 200city TSP benchmarks presented at the 1989 NIPS postconference workshop using neural network, elastic net, genetic algorithm and simulated annealing approaches. These results are also compared with a stateoftheart hybrid approach consist ..."
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Cited by 31 (7 self)
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We present and summarize the results from 50, 100 and 200city TSP benchmarks presented at the 1989 NIPS postconference workshop using neural network, elastic net, genetic algorithm and simulated annealing approaches. These results are also compared with a stateoftheart hybrid approach consisting of greedy solution, simulated annealing, and exhaustive search.