Results 1  10
of
13
Firstimprovement vs. Bestimprovement Local Optima Networks of NK Landscapes
"... Abstract. This paper extends a recently proposed model for combinatorial landscapes: Local Optima Networks (LON), to incorporate a firstimprovement (greedyascent) hillclimbing algorithm, instead of a bestimprovement (steepestascent) one, for the definition and extraction of the basins of attract ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
(Show Context)
Abstract. This paper extends a recently proposed model for combinatorial landscapes: Local Optima Networks (LON), to incorporate a firstimprovement (greedyascent) hillclimbing algorithm, instead of a bestimprovement (steepestascent) one, for the definition and extraction of the basins of attraction of the landscape optima. A statistical analysis comparing best and first improvement network models for a set of NK landscapes, is presented and discussed. Our results suggest structural differences between the two models with respect to both the network connectivity, and the nature of the basins of attraction. The impact of these differences in the behavior of search heuristics based on first and best improvement local search is thoroughly discussed. 1
Clustering of Local Optima in Combinatorial Fitness Landscapes
"... Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem instance classes give rise to very different configuration space ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem instance classes give rise to very different configuration spaces. For the socalled reallike class, the optima networks possess a clear modular structure, while the networks belonging to the class of random uniform instances are less well partitionable into clusters. We briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.
Communities of minima in local optima networks of combinatorial spaces
 Physica A: Statistical Mechanics and its Applications, 390(9):1684 – 1694
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
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.
Local optima networks and the performance of iterated local search
, 2012
"... Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possibl ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible weighted transitions between them. A new set of metrics can be derived from this model that capture the distribution and connectivity of the local optima in the underlying configuration space.This paper departs from the descriptive analysis of local optima networks, and actively studies the correlation between network features and the performance of a local search heuristic. The NK family of landscapes and the Iterated Local Search metaheuristic are considered. With a statisticallysound approach based on multiple linear regression, it is shown that some LONs’ features strongly influence and can even partly predict the performance of a heuristic search algorithm. This study validates the expressive power of LONs as a model of combinatorial fitness landscapes.
Local Optima Networks: A New Model of Combinatorial Fitness Landscapes
"... This chapter overviews a recently introduced networkbased model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the pos ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
This chapter overviews a recently introduced networkbased model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basintransition and escapeedges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems.
Tunnelling crossover networks
, 2015
"... Local optima networks are a recent model of fitness landscapes. They compress the landscape by representing local optima as nodes, and search transitions among them as edges. Previous local optima networks considered transitions based on mutation; this study looks instead at transitions based on ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Local optima networks are a recent model of fitness landscapes. They compress the landscape by representing local optima as nodes, and search transitions among them as edges. Previous local optima networks considered transitions based on mutation; this study looks instead at transitions based on deterministic recombination. We define and analyse networks based on the recently proposed partition crossover for kbounded pseudoBoolean functions, using NKq landscapes as a case study. Partition crossover was initially proposed for the travelling salesman problem, where it was found to “tunnel ” between local optima, i.e., jump from local optimum to local optimum. Our network analysis shows that this also happens for NK landscapes: local optima are densely connected via partition crossover. We found marked differences between the adjacent and random interaction NK models. Surprisingly, with the random model, instances have a lower number of local optima on average, but their networks are more sparse and decompose into several clusters. There is also large variability in the size and pattern of connectivity of instances coming from the same landscape parameter values. These network features offer new insight informing why some instances are harder to solve than others.
An Empirical Evaluation of O(1) Steepest Descent for NKLandscapes
 Parallel Problem Solving from Nature  PPSN XII, volume 7491 of Lecture Notes in Computer Science
, 2012
"... Abstract. New methods make it possible to do approximate steepest descent in O(1) time per move for kbounded pseudoBoolean functions using stochastic local search. It is also possible to use the average fitness over the Hamming distance 2 neighborhood as a surrogate fitness function and still ret ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. New methods make it possible to do approximate steepest descent in O(1) time per move for kbounded pseudoBoolean functions using stochastic local search. It is also possible to use the average fitness over the Hamming distance 2 neighborhood as a surrogate fitness function and still retain the O(1) time per move. These are average complexity results. In light of these new results, we examine three factors that can influence both the computational cost and the effectiveness of stochastic local search: 1) Fitness function: f(x) or a surrogate; 2) Local optimum escape method: hard random or soft restarts; 3) Descent strategy: next or steepest. We empirically assess these factors in a study of local search for solving NKlandscape problems.
Local Optima Networks of the Permutation flowshop Problem
"... This article extracts and analyzes local optima networks for the permutation flowshop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this pro ..."
Abstract
 Add to MetaCart
(Show Context)
This article extracts and analyzes local optima networks for the permutation flowshop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this problem is also analyzed. In particular, we study the correlation between local optima network features and the performance of an iterated local search heuristic. Our analysis reveals that network features can explain and predict problem difficulty. The evidence confirms the superiority of the insertion operator for this problem.
The MultiFunnel Structure of TSP Fitness Landscapes: A Visual Exploration
"... Abstract. We use the Local Optima Network model to study the structure of symmetric TSP fitness landscapes. The ‘bigvalley ’ hypothesis holds that for TSP and other combinatorial problems, local optima are not randomly distributed, instead they tend to be clustered around the global optimum. Howev ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We use the Local Optima Network model to study the structure of symmetric TSP fitness landscapes. The ‘bigvalley ’ hypothesis holds that for TSP and other combinatorial problems, local optima are not randomly distributed, instead they tend to be clustered around the global optimum. However, a recent study has observed that, for solutions close in evaluation to the global optimum, this structure breaks down into multiple valleys, forming what has been called ‘multiple funnels’. The multiple funnel concept implies that local optima are organised into clusters, so that a particular local optimum largely belongs to a particular funnel. Our study is the first to extract and visualise local optima networks for TSP and is based on a sampling methodology relying on the Chained LinKernighan algorithm. We confirm the existence of multiple funnels on two selected TSP instances, finding additional funnels in a previously studied instance. Our results suggests that transitions among funnels are possible using operators such as ‘doublebridge’. However, for consistently escaping suboptimal funnels, more robust escaping mechanisms are required. 1