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.

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.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Fresa: A Plant Propagation Algorithm for Black-Box Single and Multiple Objective Optimization

2021 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Mathematical Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Population Based ◽  
Black Box ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Multiple Dispatch

Fresa implements a nature inspired plant propagation algorithm for the solution of single and multiple objective optimization problems. The method is population based and evolutionary. Treating the objective function as a black box, the implementation is able to solve problems exhibiting behaviour that is challenging for mathematical programming methods. Fresa is easily adapted to new problems which may benefit from bespoke representations of solutions by taking advantage of the dynamic typing and multiple dispatch capabilities of the Julia language. Further, the support for threads in Julia enables an efficient implementation on multi-core computers.

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.

Global search in single-solution-based metaheuristics

2020 ◽  
Vol 54 (3) ◽  
pp. 275-296 ◽  
Author(s):  
Najmeh Sadat Jaddi ◽  
Salwani Abdullah
Keyword(s):  
Search Space ◽  
Population Based ◽  
Global Optimum ◽  
Global Search ◽  
Hill Climbing ◽  
Search Process ◽  
Local Optimum ◽  
Content Type ◽  
Solution Algorithms ◽  
Single Solution

PurposeMetaheuristic algorithms are classified into two categories namely: single-solution and population-based algorithms. Single-solution algorithms perform local search process by employing a single candidate solution trying to improve this solution in its neighborhood. In contrast, population-based algorithms guide the search process by maintaining multiple solutions located in different points of search space. However, the main drawback of single-solution algorithms is that the global optimum may not reach and it may get stuck in local optimum. On the other hand, population-based algorithms with several starting points that maintain the diversity of the solutions globally in the search space and results are of better exploration during the search process. In this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.Design/methodology/approachIn this method, different starting points in initial step, searching locally in neighborhood of each solution, construct a global search in search space for the single-solution algorithm.FindingsThe proposed method was tested based on three single-solution algorithms involving hill-climbing (HC), simulated annealing (SA) and tabu search (TS) algorithms when they were applied on 25 benchmark test functions. The results of the basic version of these algorithms were then compared with the same algorithms integrated with the global search proposed in this paper. The statistical analysis of the results proves outperforming of the proposed method. Finally, 18 benchmark feature selection problems were used to test the algorithms and were compared with recent methods proposed in the literature.Originality/valueIn this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.

Glowworm Swarm Optimization (GSO) Algorithm for Optimization Problems: A State-of-the-Art Review

2013 ◽  
Vol 421 ◽  
pp. 507-511 ◽  
Author(s):  
Nurezayana Zainal ◽  
Azlan Mohd Zain ◽  
Nor Haizan Mohamed Radzi ◽  
Amirmudin Udin
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Function Optimization ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Multimodal Function Optimization ◽  
Glowworm Swarm Optimization ◽  
Multimodal Function ◽  
Optimum Solution

Glowworm Swarm Optimization (GSO) algorithm is a derivative-free, meta-heuristic algorithm and mimicking the glow behavior of glowworms which can efficiently capture all the maximum multimodal function. Nevertheless, there are several weaknesses to locate the global optimum solution for instance low calculation accuracy, simply falling into the local optimum, convergence rate of success and slow speed to converge. This paper reviews the exposition of a new method of swarm intelligence in solving optimization problems using GSO. Recently the GSO algorithm was used simultaneously to find solutions of multimodal function optimization problem in various fields in today industry such as science, engineering, network and robotic. From the paper review, we could conclude that the basic GSO algorithm, GSO with modification or improvement and GSO with hybridization are considered by previous researchers in order to solve the optimization problem. However, based on the literature review, many researchers applied basic GSO algorithm in their research rather than others.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

2013 ◽  
Vol 415 ◽  
pp. 349-352
Author(s):  
Hong Wei Zhao ◽  
Hong Gang Xia
Keyword(s):  
Differential Evolution ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Local Optimum ◽  
Local Optima ◽  
De Algorithm ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

Differential evolution (DE) is a population-based stochastic function minimizer (or maximizer), whose simple yet powerful and straightforward features make it very attractive for numerical optimization. However, DE is easy to trapped into local optima. In this paper, an improved differential evolution algorithm (IDE) proposed to speed the convergence rate of DE and enhance the global search of DE. The IDE employed a new mutation operation and modified crossover operation. The former can rapidly enhance the convergence of the MDE, and the latter can prevent the MDE from being trapped into the local optimum effectively. Besides, we dynamic adjust the scaling factor (F) and the crossover rate (CR), which is aimed at further improving algorithm performance. Based on several benchmark experiment simulations, the IDE has demonstrated stronger convergence and stability than original differential (DE) algorithm and other algorithms (PSO and JADE) that reported in recent literature.

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.

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