A new adaptive multi-start technique for combinatorial global optimizations

Boese, Kenneth D.; Kahng, Andrew B.; Muddu, S.

doi:10.1016/0167-6377(94)90065-5

Cited by 302 publications

(184 citation statements)

References 15 publications

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“…Understating these features can also inform the design of efficient search algorithms. For example, it has been observed in many combinatorial landscapes that local optima are not randomly distributed, rather they tend to be relatively close to each other (in terms of a plausible metric) and to the known global optimum; clustered in a "central massif" (or "big valley" if we are minimizing) [4,11,18]. Search algorithms exploiting this globally convex structure have been proposed [4,18].…”

Section: Introductionmentioning

confidence: 99%

Local Optima Networks of the Permutation Flow-Shop Problem

Daolio

Vérel

Ochoa

et al. 2014

Lecture Notes in Computer Science

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Abstract. This article extracts and analyzes local optima networks for the permutation flow-shop 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.

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Section: Introductionmentioning

confidence: 99%

Local Optima Networks of the Permutation Flow-Shop Problem

Daolio

Vérel

Ochoa

et al. 2014

Lecture Notes in Computer Science

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“…Features such as the number and distribution of local optima and their basins of attraction are among the most studied. The relationship among local optima for the symmetric Traveling Salesman Problem (TSP) under the standard 2-change neighbourhood was first analysed in [4], where a globally convex structure was discovered. The global optimum was found to be 'central' to all other local optima conforming a 'big-valley' structure.…”

Section: Introductionmentioning

confidence: 99%

The Multi-Funnel Structure of TSP Fitness Landscapes: A Visual Exploration

Ochoa

Veerapen

Whitley

et al. 2016

Lecture Notes in Computer Science

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Abstract. We use the Local Optima Network model to study the structure of symmetric TSP fitness landscapes. The 'big-valley' 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 Lin-Kernighan 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 'double-bridge'. However, for consistently escaping sub-optimal funnels, more robust escaping mechanisms are required.

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“…The similar observations can be found in the results of IKLS and MKLS for all problem sets except for the smallest one. It therefore is considered that the iterated framework is more suitable than the multistart one for the NPP, and it suggests that the search space in the NPP is the big valley structure [32].…”

Section: B Results For Local Search and Iterated Local Searchmentioning

confidence: 99%

“…This assumption implies that many local optima are distributed in a cluster so as to lead toward the global optima in the search space. For such optimization problems in which globally convex or big valley structure has been revealed, e.g., TSP, GPP [32] and UBQP [28], it is quite expected that ILS is more favorable in terms of final solution qualities and running times than MLS. The NPP in this paper also is considered as one of such problems.…”

Section: A Basic Framework For Enhancement Of Local Searchmentioning

confidence: 99%

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

Katayama

Yamashita

Narihisa

2007

2007 IEEE Congress on Evolutionary Computation

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Abstract-We address a problem of finding an optimal node placement that minimizes the amount of traffics by reducing the weighted hop distances in multihop lightwave networks. The problem is called Node Placement Problem (NPP). NPP is known to be NP-hard and one of the most important problems in wavelength division multiplexing (WDM) based networks.In this paper we propose a new local search algorithm for the NPP based on variable depth search, and show its extension to an iterated local search algorithm. To evaluate the performance of the proposed methods, we provided the benchmark instances with known optimal solutions, and performed extensive experiments on the instances. The computational results showed that our iterated local search outperformed multistart local search methods and the best available metaheuristic for the problem.

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A new adaptive multi-start technique for combinatorial global optimizations

Cited by 302 publications

References 15 publications

Local Optima Networks of the Permutation Flow-Shop Problem

Local Optima Networks of the Permutation Flow-Shop Problem

The Multi-Funnel Structure of TSP Fitness Landscapes: A Visual Exploration

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

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