C. Fonlupt, D. Robilliard, Ph. Preux, and E-G. Talbi. Fitness landscape and performance of meta-heuristics. In Proc. Meta-Heuristics'97 (MIC'97), SophiaAntipolis, France, July 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....selection competition operators via S 2 . 5.5 Cooperative Search When a landscape is explored by means of more than one strategy with possibly di erent perspectives and information are exchanged among strategies, we obtain the so called cooperative search. Empirical results (see, for instance, [22]) show that some algorithms (agents) perform better than others on particular kinds of problems, while they are outperformed on other problems. It is conjectured that this depends upon the agent ability to exploit the tness landscape characteristics. Among such properties are: ruggedness, number ....

C. Fonlupt, D. Robilliard, P. Preux, and E.G. Talbi. Fitness landscapes and performance of meta-heuristics. In Stefan Voss, Silvano Martello, Ibrahim Osman, and Catherine Roucairol, editors, Meta-heuristics: advances and trends in local search paradigms for optimization. Kluwer Academic, 1999.

....regions. The ttest agents are those which found the solutions with highest value. Following the genetic algorithms approach, new individuals are generated and the usual operators (mutation, crossover and selection) are applied. 3. 4 Cooperative Search Empirical results (see, for instance, [18]) show that some algorithms (agents) perform better than others on particular kinds of problems, while they are outperformed on other problems. It is conjectured that this depends upon the agent ability to exploit the FL characteristics. Among such properties are: ruggedness, number of local ....

C. Fonlupt, D. Robilliard, P. Preux, and E.G. Talbi. Fitness landscapes and performance of meta-heuristics. In Stefan Voss, Silvano Martello, Ibrahim Osman, and Catherine Roucairol, editors, Meta-heuristics: advances and trends in local search paradigms for optimization. Kluwer Academic, 1999.

....problems (and the TSP is one of them) there is a strong correlation between the cost of a solution and its distance to the optimum: in effect, the best solutions cluster together, i.e. have many similar components. This has been referred to in many different ways: Massif Central phenomenon [23], principle of proximate optimality [31] and replica symmetry [53] If the problem under consideration has this property, it is not unreasonable to hope to find the true optimum using a biased sampling of S . In particular, it is clear that is useful to use intensification to improve the ....

C. Fonlupt, D. Robilliard, P. Preux, and E.-G. Talbi. Fitness landscape and performance of meta-heuristics. In S. Voss, S. Martello, I.H. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 257--268. Kluwer Academic Publishers, Boston, MA, 1999.

....that performs well even for instances that are considered to be hard to solve. We have used two theoretical parameters: the dominance and the ruggedness coefficient, to obtain some features of the landscape of QAP instances, but analyzing landscapes in a more empirical way is also possible [9] [14] 18] Also, others characteristics of landscapes could be considered, for example: are all local optima uniformly dispersed, or concentrated in a small region Gathering knowledge about a landscape could help to refine existing meta heuristics well adapted for a certain types of instance or ....

C. Fonlupt, D. Robilliard, P. Preux, and E-G. Talbi. Fitness landscapes and performance of meta-heuristics. In 2nd International Conference on Metaheuristics, Sophia-Antipolis, France, July 21--24 1997.

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C. Fonlupt, D. Robilliard, Ph. Preux, and E-G. Talbi. Fitness landscape and performance of meta-heuristics. In Proc. Meta-Heuristics'97 (MIC'97), SophiaAntipolis, France, July 1997.

.... BP 719, 62228 Calais Cedex, France Philippe.Preux lil.univ littoral.fr February 2, 1999 Through statistical analysis of experimental results, we have acquired a certain amount of knowledge on the structure of the search space of the TSP involved by the use of 2 change and 3 change operators [FRPT99]. Among other things, local optima are gathered in a tiny region in the case of euclidian 2D TSP instances (a region we call a massif central ) We have used this knowledge to understand the behavior of descent algorithm; we have also been able to better understand genetic algorithms and how ....

C. Fonlupt, D. Robilliard, Ph. Preux, and E-G. Talbi. Fitness landscape and performance of meta-heuristics. In MetaHeuristics --- Advances and Trends in Local Search Paradigms for Optimization, chapter 18, pages 255--266. Kluwer Academic Press, 1999.

....MPV88] KT85] investigates the structure of the 2ETSP with the apparatus of statistical mechanics in order to understand the performance of simulated annealing. Using a completely different approach, we have recently and independently rediscovered some of their results and extended them in [FRPT97] see below) Hertz al. HJRF94] have studied the topology of the k coloring problem in order to explain the behavior of iterated local search algorithms. They propose an algorithm to generate all local optima, and they use a statistical test to analyze their topology. Grounded on ....

....issue to be able to sketch a correct view about landscapes. Our work has shown that from the point of view of the same iterated descent algorithms as was used by Stadler and Schnabl, the uniform distribution of local optima hypothesis is wrong 2 . We summarize here some results presented in [FRPT97] to which the reader is refered for any further detail. The main result which is of use here is that all local optima that are found by those iterated descent algorithms, based on 2 change or city swap, are concentrated in a region of the 1 actually, the authors make the hypothesis of a uniform ....

C. Fonlupt, D. Robilliard, Ph. Preux, and E-G. Talbi. Fitness landscape and performance of meta-heuristics. In Proc. Meta-Heuristics'97 (MIC'97), Sophia-Antipolis, France, July 1997.

....of the sTSP is isotropic thanks to their result on a constant auto correlation along random walks. However, we also have good reasons to think that the sTSP landscape contains a massif central (see Kirkpatrick and Toulouse s work about the presence of a deep valley [16] Boese s [6] and [9]) which means than non average points (including local optima) are not spread at random in the whole landscape but concentrated in even tinier regions that those evoked previously (let us say a part j ffl of the whole search space) In some sense, this region is very specific in the landscape, ....

....one massif central, more than one massif centrals, to rugged landscapes. We also very briefly discuss the case of the simple Job Shop Scheduling Problem landscape. Finally, we draw some conclusions. 2 The Traveling Salesman Problem We have investigated the landscape of the 2 dimensional sTSP [9]. We summarize here the methodology as well as the conclusions of this work. To begin with, we remind that the TSP is an NP hard problem [10, 17] Basically, a set of n points is located in a k dimensional space. One has to find a 2 which is going further than the idea that one operator is ....

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C. Fonlupt, D. Robilliard, Ph. Preux, and EG. Talbi. Fitness landscape and performance of meta-heuristics. In Meta-Heuristics --- Advances and Trends in Local Search Paradigms for Optimization, chapter 18, pages 255--266. Kluwer Academic Press, 1999.

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