arXiv subjects

Gabriela Ochoa

Publications and source records attributed to Gabriela Ochoa.

23 records · Page 2Linked to original sources

arXiv2011

Local Optima Networks of the Quadratic Assignment Problem

Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the landscape in which the nodes correspond to the local optima, and the edges account for the notion of adjacency between their basins of attraction. The model was inspired by the notion of 'inherent network' of potential energy surfaces proposed in physical-chemistry. The local optima networks extracted from the so called uniform and real-like QAP instances, show features clearly distinguishing these two types of instances. Apart from a clear confirmation that the search difficulty increases with the problem dimension, the analysis provides new confirming evidence explaining why the real-like instances are easier to solve exactly using heuristic search, while the uniform instances are easier to solve approximately. Although the local optima network model is still under development, we argue that it provides a novel view of combinatorial landscapes, opening up the possibilities for new analytical tools and understanding of problem difficulty in combinatorial optimization.

cs.AI↗

arXiv2011

Local Optima Networks of NK Landscapes with Neutrality

In previous work we have introduced a network-based model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. By using two known neutral variants of the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the non-neutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and non-neutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.

cs.AI↗

arXiv2010

Cheating for Problem Solving: A Genetic Algorithm with Social Interactions

We propose a variation of the standard genetic algorithm that incorporates social interaction between the individuals in the population. Our goal is to understand the evolutionary role of social systems and its possible application as a non-genetic new step in evolutionary algorithms. In biological populations, ie animals, even human beings and microorganisms, social interactions often affect the fitness of individuals. It is conceivable that the perturbation of the fitness via social interactions is an evolutionary strategy to avoid trapping into local optimum, thus avoiding a fast convergence of the population. We model the social interactions according to Game Theory. The population is, therefore, composed by cooperator and defector individuals whose interactions produce payoffs according to well known game models (prisoner's dilemma, chicken game, and others). Our results on Knapsack problems show, for some game models, a significant performance improvement as compared to a standard genetic algorithm.

cs.NE↗

arXiv2008

The Connectivity of NK Landscapes' Basins: A Network Analysis

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph where the vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative small NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties can be related to the search difficulty on the underlying NK landscapes with varying values of K.

cs.NE↗

arXiv2008

A Study of NK Landscapes' Basins and Local Optima Networks

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.

cs.NE↗