Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization

Chicano, Francisco; Alba, Enrique

doi:10.1007/s10732-011-9170-6

Cited by 10 publications

(9 citation statements)

References 27 publications

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“…In [36], the landscape of the problem is proven to consist of three elementary components if the swap neighbourhood is used. The landscape of the 0-1 unconstrained quadratic optimisation is studied in [37], and it is proven that the landscape of this problem can be written as the sum of two elementary components.…”

Section: Introductionmentioning

confidence: 99%

Quadratic assignment problem: a landscape analysis

Tayarani-N.

Prügel-Bennett

2015

Evol. Intel.

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The anatomy of the fitness landscape for the quadratic assignment problem is studied in this paper. We study the properties of both random problems, and realworld problems. Using auto-correlation as a measure for the landscape ruggedness, we study the landscape of the problems and show how this property is related to the problem matrices with which the problems are represented. Our main goal in this paper is to study new properties of the fitness landscape, which have not been studied before, and we believe are more capable of reflecting the problem difficulties. Using local search algorithm which exhaustively explore the plateaus and the local optima, we explore the landscape, store all the local optima we find, and study their properties. The properties we study include the time it takes for a local search algorithm to find local optima, the number of local optima, the probability of reaching the global optimum, the expected cost of the local optima around the global optimum and the basin of attraction of the global and local optima. We study the properties for problems of different sizes, and through extrapolations, we show how the properties change with the system size and why the problem becomes harder as the system size grows. In our study we show how the real-world problems are similar to, or different from the random problems. We also try to show what properties of the problem matrices make the landscape of the real problems be different from or similar to one another.

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Section: Introductionmentioning

confidence: 99%

Quadratic assignment problem: a landscape analysis

Tayarani-N.

Prügel-Bennett

2015

Evol. Intel.

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“…For illustration purposes we show here the values for autocorrelation measures and spectral coefficient of the Unconstrained Quadratic Optimization (UQO). The details can be found in [6]. The autocorrelation coefficient and length is given by the following expressions:…”

Section: Autocorrelationmentioning

confidence: 99%

Problem understanding through landscape theory

Chicano

Luque

Alba

2013

Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation

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In order to understand the structure of a problem we need to measure some features of the problem. Some examples of measures suggested in the past are autocorrelation and fitness-distance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, provides mathematical expressions to efficiently compute statistics on optimization problems. In this paper we discuss how can we use landscape theory in the context of problem understanding and present two software tools that can be used to efficiently compute the mentioned measures.

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“…Chicano and Alba [4] found a negative correlation between and the number of local optima in the 0-1 Unconstrained Quadratic Optimization problem (0-1 UQO), an NP-hard problem [9]. Kinnear [11] also studied the use of the autocorrelation measures as problem difficulty, but the results were inconclusive.…”

Section: Fdc Autocorrelation Length and Local Optimamentioning

confidence: 99%

Exact Computation of the Fitness-Distance Correlation for Pseudoboolean Functions with One Global Optimum

Chicano

Alba

2012

Evolutionary Computation in Combinatorial Optimization

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Abstract. Landscape theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of a special kind of landscapes called elementary landscapes. The decomposition of the objective function of a problem into its elementary components can be exploited to compute summary statistics. We present closed-form expressions for the fitness-distance correlation (FDC) based on the elementary landscape decomposition of the problems defined over binary strings in which the objective function has one global optimum. We present some theoretical results that raise some doubts on using FDC as a measure of problem difficulty.

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Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization

Cited by 10 publications

References 27 publications

Quadratic assignment problem: a landscape analysis

Quadratic assignment problem: a landscape analysis

Problem understanding through landscape theory

Exact Computation of the Fitness-Distance Correlation for Pseudoboolean Functions with One Global Optimum

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