Efficient Multi-Start Strategies for Local Search Algorithms

01/16/2014
by   András György, et al.
0

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.

READ FULL TEXT
research
01/14/2022

BandMaxSAT: A Local Search MaxSAT Solver with Multi-armed Bandit

We address Partial MaxSAT (PMS) and Weighted PMS (WPMS), two practical g...
research
11/08/2021

An Improved Local Search Algorithm for k-Median

We present a new local-search algorithm for the k-median clustering prob...
research
11/29/2022

Incorporating Multi-armed Bandit with Local Search for MaxSAT

Partial MaxSAT (PMS) and Weighted PMS (WPMS) are two practical generaliz...
research
10/05/2020

Evolving test instances of the Hamiltonian completion problem

Predicting and comparing algorithm performance on graph instances is cha...
research
06/03/2021

Linear regression with partially mismatched data: local search with theoretical guarantees

Linear regression is a fundamental modeling tool in statistics and relat...
research
08/12/2020

A new notion of commutativity for the algorithmic Lovász Local Lemma

The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combina...
research
06/06/2019

Combining Reinforcement Learning and Configuration Checking for Maximum k-plex Problem

The Maximum k-plex Problem is an important combinatorial optimization pr...

Please sign up or login with your details

Forgot password? Click here to reset