scholarly journals Efficient Multi-Start Strategies for Local Search Algorithms

2011 ◽  
Vol 41 ◽  
pp. 407-444 ◽  
Author(s):  
A. György ◽  
L. Kocsis
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Target Function ◽  
Search Algorithms ◽  
Local Optimum ◽  
Local Search Algorithm ◽  
Local Search Algorithms ◽  
Unknown Constant ◽  
Lipschitz Optimization

Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start multiple instances of a local search algorithm, and allocate computational resources (in particular, processing time) to the instances depending on their behavior. Hence, a multi-start strategy has to decide (dynamically) when to allocate additional resources to a particular instance and when to start new instances. In this paper we propose multi-start strategies motivated by works on multi-armed bandit problems and Lipschitz optimization with an unknown constant. The strategies continuously estimate the potential performance of each algorithm instance by supposing a convergence rate of the local search algorithm up to an unknown constant, and in every phase allocate resources to those instances that could converge to the optimum for a particular range of the constant. Asymptotic bounds are given on the performance of the strategies. In particular, we prove that at most a quadratic increase in the number of times the target function is evaluated is needed to achieve the performance of a local search algorithm started from the attraction region of the optimum. Experiments are provided using SPSA (Simultaneous Perturbation Stochastic Approximation) and k-means as local search algorithms, and the results indicate that the proposed strategies work well in practice, and, in all cases studied, need only logarithmically more evaluations of the target function as opposed to the theoretically suggested quadratic increase.

scholarly journals A Variable Neighborhood Walksat-Based Algorithm for MAX-SAT Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Noureddine Bouhmala
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Boolean Formula ◽  
Local Search Algorithms ◽  
Neighborhood Structure ◽  
Np Complete ◽  
Max Sat ◽  
Almost All

The simplicity of the maximum satisfiability problem (MAX-SAT) combined with its applicability in many areas of artificial intelligence and computing science made it one of the fundamental optimization problems. This NP-complete problem refers to the task of finding a variable assignment that satisfies the maximum number of clauses (or the sum of weights of satisfied clauses) in a Boolean formula. The Walksat algorithm is considered to be the main skeleton underlying almost all local search algorithms for MAX-SAT. Most local search algorithms including Walksat rely on the 1-flip neighborhood structure. This paper introduces a variable neighborhood walksat-based algorithm. The neighborhood structure can be combined easily using any local search algorithm. Its effectiveness is compared with existing algorithms using 1-flip neighborhood structure and solvers such as CCLS and Optimax from the eighth MAX-SAT evaluation.

scholarly journals Local search algorithms based on benchmark test functions problem

2020 ◽  
Vol 9 (3) ◽  
pp. 529
Author(s):  
Atheer Bassel ◽  
Hussein M. Haglan ◽  
Akeel Sh. Mahmoud
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Optimization Techniques ◽  
Engineering Optimization ◽  
Local Search Algorithm ◽  
Test Functions ◽  
Local Search Algorithms ◽  
Benchmark Test ◽  
Benchmark Test Functions

<p>Optimization process is normally implemented to solve several objectives in the form of single or multi-objectives modes. Some traditional optimization techniques are computationally burdensome which required exhaustive computational times. Thus, many studies have invented new optimization techniques to address the issues. To realize the effectiveness of the proposed techniques, implementation on several benchmark functions is crucial. In solving benchmark test functions, local search algorithms have been rigorously examined and employed to diverse tasks. This paper highlights different algorithms implemented to solve several problems. The capacity of local search algorithms in the resolution of engineering optimization problem including benchmark test functions is reviewed. The use of local search algorithms, mainly Simulated Annealing (SA) and Great Deluge (GD) according to solve different problems is presented. Improvements and hybridization of the local search and global search algorithms are also reviewed in this paper. Consequently, benchmark test functions are proposed to those involved in local search algorithm.</p>

scholarly journals Socially Motivated Partial Cooperation in Multi-agent Local Search

2018 ◽  
Author(s):  
Tal Ze'evi ◽  
Roie Zivan ◽  
Omer Lev
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Scheduling Problems ◽  
Multi Agent Systems ◽  
Local Search Algorithms ◽  
Partial Cooperation ◽  
Multi Agent ◽  
Socially Motivated

Partial Cooperation is a paradigm and a corresponding model, proposed to represent multi-agent systems in which agents are willing to cooperate to achieve a global goal, as long as some minimal threshold on their personal utility is satisfied. Distributed local search algorithms were proposed in order to solve asymmetric distributed constraint optimization problems (ADCOPs) in which agents are partially cooperative. We contribute by: 1) extending the partial cooperative model to allow it to represent dynamic cooperation intentions, affected by changes in agents’ wealth, in accordance with social studies literature. 2) proposing a novel local search algorithm in which agents receive indications of others’ preferences on their actions and thus, can perform actions that are socially beneficial. Our empirical study reveals the advantage of the proposed algorithm in multiple benchmarks. Specifically, on realistic meeting scheduling problems it overcomes limitations of standard local search algorithms.

scholarly journals Circumspect descent prevails in solving random constraint satisfaction problems

2008 ◽  
Vol 105 (40) ◽  
pp. 15253-15257 ◽  
Author(s):  
Mikko Alava ◽  
John Ardelius ◽  
Erik Aurell ◽  
Petteri Kaski ◽  
Supriya Krishnamurthy ◽  
...  
Keyword(s):  
Local Search ◽  
Linear Time ◽  
Search Algorithm ◽  
Solution Space ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Problem Instance ◽  
Stochastic Local Search ◽  
Local Search Algorithms ◽  
Local Energy Minimum

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios α; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

scholarly journals Local search for parallel optimization algorithms for high diminsional optimization problems

2018 ◽  
Vol 210 ◽  
pp. 04052 ◽  
Author(s):  
Nadia Abd-Alsabour
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Search Algorithms ◽  
Parallel Optimization ◽  
High Dimensional ◽  
Search Process ◽  
Local Search Algorithms

Local search algorithms perform an important role when being employed with optimization algorithms tackling numerous optimization problems since they lead to getting better solutions. However, this is not practical in many applications as they do not contribute to the search process. This was not much studied previously for traditional optimization algorithms or for parallel optimization algorithms. This paper investigates this issue for parallel optimization algorithms when tackling high dimensional subset problems. The acquired results show impressive recommendations.

scholarly journals Local Search with Dynamic-Threshold Configuration Checking and Incremental Neighborhood Updating for Maximum k-plex Problem

2020 ◽  
Vol 34 (03) ◽  
pp. 2343-2350 ◽  
Author(s):  
Peilin Chen ◽  
Hai Wan ◽  
Shaowei Cai ◽  
Jia Li ◽  
Haicheng Chen
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Promising Result ◽  
Dynamic Threshold ◽  
Local Search Algorithm ◽  
Local Search Algorithms ◽  
Worst Case ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Novel Strategy

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamic-threshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V|⋅ΔG) to O(k · Δ‾G). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.

scholarly journals Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1173 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Huan Liu ◽  
Ruiting Li ◽  
Dantong Ouyang ◽  
...  
Keyword(s):  
Local Search ◽  
Ad Hoc ◽  
Search Algorithm ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Local Optimum ◽  
Local Search Algorithm ◽  
Solution Quality ◽  
Minimum Connected Dominating Set ◽  
Hoc Networks

The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks. In this paper, we propose a novel multi-start local search algorithm (MSLS) to tackle the minimum connected dominating set problem. Firstly, we present the fitness mechanism to design the vertex score mechanism so that our algorithm can jump out of the local optimum. Secondly, we use the configuration checking (CC) mechanism to avoid the cycling problem. Then, we propose the vertex flipping mechanism to change the vertex state by combing the CC mechanism with the vertex score mechanism. Finally, we propose a multi-start local search framework based on these mechanisms. We compare the algorithm MSLS with other compared algorithms on extensive instances. The results of experiment show that MSLS is superior to other algorithms in solution quality and time efficiency on most instances.

AN IMPROVED POPULATION BASED OPTIMIZATION SOLUTION METHOD BY COMBINING LOCAL AND GLOBAL SEARCHING

2007 ◽  
Vol 16 (05) ◽  
pp. 907-915
Author(s):  
WEI JIANG ◽  
XIAO-LONG WANG ◽  
XIU-LI PANG
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Problems ◽  
Population Based ◽  
Search Algorithms ◽  
Global Search ◽  
Local Optimum ◽  
Hard Problems ◽  
The Common ◽  
Optimum Solution

Optimization Solution Task is a typical and important task in many applications. Many optimization problems have been proved to be NP-hard problems, which cannot be solved by some predefined mathematic formulae. In this case, computer aided method is very helpful. While some local search algorithms are easily to fall into a local optimum solution. On contrast, the population based methods, such as Genetic Algorithms, Artificial Immune System, Autonomy Oriented Computing, are global search algorithms. However, they are not good at the local search. In this paper, an improved method is proposed by combining the local and global search ability, so as to improve the performance in terms of the convergence speed and the convergence reliability. We construct a generic form to deal with the common objective function space or the objective function with the partial derivative. In addition, we present an n-hold method in population based evolution method. The experiments indicate that our approach can effectively improve the convergence reliability, which is much concerned in some applications with the expensive executing expense.

An Iterated Local Search Algorithm for Fuel Consumption Optimization of Vehicle Routing Problems

2011 ◽  
Vol 148-149 ◽  
pp. 1248-1251
Author(s):  
Xu Dong Wu
Keyword(s):  
Local Search ◽  
Vehicle Routing ◽  
Fuel Consumption ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Iterated Local Search ◽  
Vehicle Routing Problems ◽  
Local Search Algorithm ◽  
Routing Problems ◽  
Combinatorial Optimization Problems

The iterated local search algorithm has been widely used in combinatorial optimization problems. A new fuel consumption objective for the vehicle routing problems was presented in this paper. A fuel consumption modal of the vehicle load is introduced and an improved iterated local search algorithm is used for the problem. An initial solution is generated by the Solomon I1 algorithm, and then the iterated local search algorithm is proposed for the fuel consumption optimization.

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