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Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance
 PARALLEL PROBLEM SOLVING FROM NATURE PPSN XII, TAORMINA: ITALY
, 2012
"... Recent developments in fitness landscape analysis include the study of Local Optima Networks (LON) and applications of the Elementary Landscapes theory. This paper represents a first step at combining these two tools to explore their ability to forecast the performance of search algorithms. We base ..."
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Recent developments in fitness landscape analysis include the study of Local Optima Networks (LON) and applications of the Elementary Landscapes theory. This paper represents a first step at combining these two tools to explore their ability to forecast the performance of search algorithms. We base our analysis on the Quadratic Assignment Problem (QAP) and conduct a large statistical study over 600 generated instances of different types. Our results reveal interesting links between the network measures, the autocorrelation measures and the performance of heuristic search algorithms.
Exact computation of the fitnessdistance correlation for pseudoboolean functions with one global optimum
 Evolutionary Computation in Combinatorial Optimization, volume 7245 of Lecture Notes in Computer Science
, 2012
"... 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 b ..."
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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 closedform expressions for the fitnessdistance 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.
Autocorrelation measures for the quadratic assignment problem
 APPLIED MATHEMATICS LETTERS
, 2012
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Quasielementary Landscapes and Superpositions of Elementary Landscapes
"... Abstract. There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called "Elementary Landscapes" and they have a number of spec ..."
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Abstract. There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called "Elementary Landscapes" and they have a number of special mathematical properties. The term "Quasielementary landscapes" is introduced to describe landscapes that are "almost" elementary; in quasielementary landscapes there exists some efficiently computed "correction" that captures those parts of the neighborhood structure that deviate from the normal structure found in elementary landscapes. The "shift" operator, as well as the "3opt" operator for the Traveling Salesman Problem landscapes induce quasielementary landscapes. A local search neighborhood for the Maximal Clique problem is also quasielementary. Finally, we show that landscapes which are a superposition of elementary landscapes can be quasielementary in structure.
Problem Understanding through Landscape Theory
"... ABSTRACT 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 fitnessdistance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, ..."
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ABSTRACT 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 fitnessdistance 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.
Fitness Probability Distribution of BitFlip Mutation
"... Bitflip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary str ..."
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Bitflip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bitflip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closedform expressions for an easy linear problem (Onemax), and an NPhard problem, MAXSAT. We also discuss some implications of the results for runtime analysis. 1