A Probabilistic Analysis of Local Search

Eikelder, ten Hmm Huub; Verhoeven, Mga Marco; Vossen, Twm Thomas; Aarts, Ehl Emile

doi:10.1007/978-1-4613-1361-8_36

Cited by 10 publications

(3 citation statements)

References 8 publications

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“…genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP [4,5,11,12,19,23,31,38,43,47], the random variable time to target solution value is exponentially distributed or fits a two-parameter shifted exponential distribution, i.e., the probability of not having found a given target solution value in t time units is given by P(t) = e −(t−µ)/λ , with λ ∈ R + and µ ∈ R. Hoos and Stützle [22,23] conjecture that this is true for all local search based methods for combinatorial optimization.…”

mentioning

confidence: 99%

TTT plots: a perl program to create time-to-target plots

Aiex

Resende

Ribeiro

2006

Optimization Letters

186

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This paper describes a perl language program to create time-totarget solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution. This is often the case in local search based heuristics for combinatorial optimization, such as simulated annealing, genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP. Such plots are very useful in the comparison of different algorithms or strategies for solving a given problem and have been widely used as a tool for algorithm design and comparison. We first discuss how TTT plots are generated. This is followed by a description of the perl program tttplots.pl.

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mentioning

confidence: 99%

TTT plots: a perl program to create time-to-target plots

Aiex

Resende

Ribeiro

2006

Optimization Letters

186

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“…Some care is needed to ensure that no two iterations start with identical random number generator seeds. These speedups are linear for a number of metaheuristics, including simulated annealing [31,71]; iterated local search algorithms for the traveling salesman problem [33]; tabu search, provided that the search starts from a local optimum [17,94]; and WalkSAT [93] on hard random 3-SAT problems [56]. This observation can be explained if the random variable time to find a solution within some target value is exponentially distributed, as indicated by the following proposition [98]: Proposition 1: Let P ρ (t) be the probability of not having found a given target solution value in t time units with ρ independent processes.…”

Section: Parallel Graspmentioning

confidence: 99%

Greedy Randomized Adaptive Search Procedures

1995

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GRASP is a multi-start metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques and parameter tuning strategies are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss in detail implementation strategies of memory-based intensification and post-optimization techniques using path-relinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.

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“…They also observe that the probability of finding a near-optimal solution is distributed exponentially. Ten Eikelder et al (1995) present some results for the average-case behavior of iterated local search algorithms for the traveling salesman problem. They show that the probability of finding a solution with a small deviation over the global minimum with an iterated local search algorithm is given by a shifted exponential distribution in order to compensate for the time needed to find the first local minimum.…”

Section: Theorem 1 Let Qe(t) Be the Probability Of Not Having Found mentioning

confidence: 99%

Parallel local search

1995

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We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of byper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.

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A Probabilistic Analysis of Local Search

Cited by 10 publications

References 8 publications

TTT plots: a perl program to create time-to-target plots

TTT plots: a perl program to create time-to-target plots

Greedy Randomized Adaptive Search Procedures

Parallel local search

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