Understanding elementary landscapes

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

Luque

Alba

2013

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.

Section: Introductionmentioning

confidence: 99%

Problem understanding through landscape theory

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

Luque

Alba

2013

“…There exists a special kind of landscapes, called elementary landscapes (EL), which are of particular interest due to their properties [22]. We define and analyze the elementary landscapes in Section 2, but we can advance that they are characterized by the Grover's wave equation:…”

Section: Introductionmentioning

confidence: 99%

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

Evolutionary Computation in Combinatorial Optimization

Alba

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 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.

“…where k = α + β,f /p 3 = w∈C w and p 3 = β/(α + β) [12][13][14]. It should also be noted that some landscapes that are not elementary can nevertheless be expressed as a superposition of a small number of elementary landscapes.…”

Section: Introductionmentioning

confidence: 99%

Quasi-elementary Landscapes and Superpositions of Elementary Landscapes

Whitley

Lecture Notes in Computer Science

2012

Self Cite

Abstract. There exists 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 "Quasi-elementary landscapes" is introduced to describe landscapes that are "almost" elementary; in quasi-elementary 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 "3-opt" operator for the Traveling Salesman Problem landscapes induce quasi-elementary landscapes. A local search neighborhood for the Maximal Clique problem is also quasi-elementary. Finally, we show that landscapes which are a superposition of 2 elementary landscapes are also quasi-elementary in structure.