scholarly journals Comparative Analysis of Low Discrepancy Sequence-Based Initialization Approaches Using Population-Based Algorithms for Solving the Global Optimization Problems

2021 ◽  
Vol 11 (16) ◽  
pp. 7591
Author(s):  
Waqas Haider Bangyal ◽  
Kashif Nisar ◽  
Ag. Asri Bin Ag. Ibrahim ◽  
Muhammad Reazul Haque ◽  
Joel J. P. C. Rodrigues ◽  
...  
Keyword(s):  
Random Distribution ◽  
Random Number ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Search Space ◽  
Metaheuristic Algorithms ◽  
Test Problems ◽  
Uniform Random Number ◽  
Low Discrepancy Sequences ◽  
The Family

Metaheuristic algorithms have been widely used to solve diverse kinds of optimization problems. For an optimization problem, population initialization plays a significant role in metaheuristic algorithms. These algorithms can influence the convergence to find an efficient optimal solution. Mainly, for recognizing the importance of diversity, several researchers have worked on the performance for the improvement of metaheuristic algorithms. Population initialization is a vital factor in metaheuristic algorithms such as PSO and DE. Instead of applying the random distribution for the initialization of the population, quasirandom sequences are more useful for the improvement the diversity and convergence factors. This study presents three new low-discrepancy sequences named WELL sequence, Knuth sequence, and Torus sequence to initialize the population in the search space. This paper also gives a comprehensive survey of the various PSO and DE initialization approaches based on the family of quasirandom sequences such as Sobol sequence, Halton sequence, and uniform random distribution. The proposed methods for PSO (TO-PSO, KN-PSO, and WE-PSO) and DE (DE-TO, DE-WE, and DE-KN) have been examined for well-known benchmark test problems and training of the artificial neural network. The finding of our techniques shows promising performance using the family of low-discrepancy sequences over uniform random numbers. For a fair comparison, the approaches using low-discrepancy sequences for PSO and DE are compared with the other family of low-discrepancy sequences and uniform random number and depict the superior results. The experimental results show that the low-discrepancy sequences-based initialization performed exceptionally better than a uniform random number. Moreover, the outcome of our work presents a foresight on how the proposed technique profoundly impacts convergence and diversity. It is anticipated that this low-discrepancy sequence comparative simulation survey would be helpful for studying the metaheuristic algorithm in detail for the researcher.

scholarly journals SOLVING INTEGER PROGRAMMING PROBLEMS BY USING POPULATION-BASED BEETLE ANTENNAE SEARCH ALGORITHM

2021 ◽  
Vol 9 (3-4) ◽  
pp. 89-99
Author(s):  
Ivona Brajević ◽  
Miodrag Brzaković ◽  
Goran Jocić
Keyword(s):  
Integer Programming ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Population Based ◽  
Local Optimum ◽  
Integer Programming Problems ◽  
Metaheuristic Techniques

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems.  This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.  

Comparison of Different Bat Initialization Techniques for Global Optimization Problems

2021 ◽  
Vol 12 (1) ◽  
pp. 157-184
Author(s):  
Wasqas Haider Bangyal ◽  
Jamil Ahmad ◽  
Hafiz Tayyab Rauf
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Search Space ◽  
Research Problem ◽  
Population Based ◽  
Premature Convergence ◽  
Ongoing Research ◽  
Low Discrepancy Sequences ◽  
Stochastic Search Technique

Bat algorithm (BA) is a population-based stochastic search technique that has been widely used to solve the diverse kind of optimization problems. Population initialization is the current ongoing research problem in evolutionary computing algorithms. Appropriate population initialization assists the algorithm to investigate the swarm search space effectively. BA faces premature convergence problem to find actual global optimization value. Low discrepancy sequences are slightly lesser random number than pseudo-random; however, they are more powerful for computational approaches. In this work, new population initialization approach Halton (BA-HA), Sobol (BA-SO), and Torus (BA-TO) are proposed, which helps bats to avoid from the premature convergence. The proposed approaches are examined on standard benchmark functions, and simulation results are compared with standard BA initialized with uniform distribution. The results depict that substantial enhancement can be attained in the performance of standard BA while varying the random numbers sequences to low discrepancy sequences.

Numerical Optimization Using the Heart Algorithm

2018 ◽  
Vol 9 (2) ◽  
pp. 33-37
Author(s):  
Abdolreza Hatamlou
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Heart Function ◽  
Circulatory System ◽  
Optimal Solution ◽  
Search Space ◽  
Human Beings ◽  
Unconstrained Optimization Problems ◽  
And Performance ◽  
The Given

In this article the authors investigate the application of the heart algorithm for solving unconstraint numerical optimization problems. Heart algorithms are a novel optimization algorithm which mimics the heart function and circulatory system procedure in the human beings. It starts with a number of candidate solutions for the given problem and utilizes the contraction and expansion actions to move the candidates in the search space for finding optimal solution. The applicability and performance of the heart algorithm for solving unconstrained optimization problems has been tested using several benchmark functions. Experimental results show its potential and superiority.

Genetic Algorithms with Immigrants Scheme for Dynamic Optimization Problems

2013 ◽  
Vol 333-335 ◽  
pp. 1379-1383
Author(s):  
Yan Wu ◽  
Xiao Xiong Liu
Keyword(s):  
Genetic Algorithms ◽  
Dynamic Optimization ◽  
Optimization Problems ◽  
Main Idea ◽  
Optimal Solution ◽  
Search Space ◽  
Dynamic Environments ◽  
Dynamic Optimization Problems ◽  
New Space ◽  
Over Time

In dynamic environments, it is difficult to track a changing optimal solution over time. Over the years, many approaches have been proposed to solve the problem with genetic algorithms. In this paper a new space-based immigrant scheme for genetic algorithms is proposed to solve dynamic optimization problems. In this scheme, the search space is divided into two subspaces using the elite of the previous generation and the range of variables. Then the immigrants are generated from both the subspaces and inserted into current population. The main idea of the approach is to increase the diversity more evenly and dispersed. Finally an experimental study on dynamic sphere function was carried out to compare the performance of several genetic algorithms. The experimental results show that the proposed algorithm is effective for the function with moving optimum and can adapt the dynamic environments rapidly.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Generate random rectangular maps

2018 ◽  
Author(s):  
I. V. Kozin ◽  
S. E. Batovskiy
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Test Problems ◽  
Complex Shapes ◽  
Applied Optimization ◽  
Open Question ◽  
Complex Algorithm ◽  
Guillotine Cutting

It is known that a large number of applied optimization problems can’t be exactly solved nowadays, because their computational complexity is related to the NP-hard class. In many cases metaheuristics of various types are used to search for approximate solutions, but the choice of the concrete metaheuristic has open question of the quality of the chosen method. There are several possible solutions to this problem, one of which is the verification of metaheuristic algorithms using examples from known test libraries with known records. Another approach to solving the problem of evaluating the quality of algorithms is to compare the "new" algorithm with other algorithms, the work of which has already been investigated. The construction a generator of random problems with a known optimal solution can solve the problem of obtaining "average" estimates of the accuracy for used algorithm in comparison with other methods. The article considers the construction of generators of random non-waste maps of rec-tangular cutting with restrictions on the rectangles of limited sizes. The existence of sets of such cards forms the basis of test problems for checking the quality of approximate algorithms for searching for optimal solution. Rectangular cutting, which is considered in the article, is also the basis for building cuts using more complex shapes. As the simplest method of generating random rectangular non-waste maps, considered a method that uses guillotine cutting. Also, a more complex algorithm for generating a random rectangular cut is given, whose job is to generate a random dot grid and remove some random points from this grid. Much attention is paid to the implementation of the above methods, since the main purpose of the article is to simplify using of generators in practice. All the above algorithms are already used in the software system for testing evolution-aryfragmentary algorithms for various classes of optimization problems on the graphs

scholarly journals Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

2017 ◽  
Vol 25 (3) ◽  
pp. 439-471 ◽  
Author(s):  
Ali Ahrari ◽  
Kalyanmoy Deb ◽  
Mike Preuss
Keyword(s):  
Covariance Matrix ◽  
Optimization Problems ◽  
Search Space ◽  
Optimization Method ◽  
Evolution Strategy ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Niching Methods ◽  
Self Adaptation ◽  
Adaptation Evolution

During the recent decades, many niching methods have been proposed and empirically verified on some available test problems. They often rely on some particular assumptions associated with the distribution, shape, and size of the basins, which can seldom be made in practical optimization problems. This study utilizes several existing concepts and techniques, such as taboo points, normalized Mahalanobis distance, and the Ursem’s hill-valley function in order to develop a new tool for multimodal optimization, which does not make any of these assumptions. In the proposed method, several subpopulations explore the search space in parallel. Offspring of a subpopulation are forced to maintain a sufficient distance to the center of fitter subpopulations and the previously identified basins, which are marked as taboo points. The taboo points repel the subpopulation to prevent convergence to the same basin. A strategy to update the repelling power of the taboo points is proposed to address the challenge of basins of dissimilar size. The local shape of a basin is also approximated by the distribution of the subpopulation members converging to that basin. The proposed niching strategy is incorporated into the covariance matrix self-adaptation evolution strategy (CMSA-ES), a potent global optimization method. The resultant method, called the covariance matrix self-adaptation with repelling subpopulations (RS-CMSA), is assessed and compared to several state-of-the-art niching methods on a standard test suite for multimodal optimization. An organized procedure for parameter setting is followed which assumes a rough estimation of the desired/expected number of minima available. Performance sensitivity to the accuracy of this estimation is also studied by introducing the concept of robust mean peak ratio. Based on the numerical results using the available and the introduced performance measures, RS-CMSA emerges as the most successful method when robustness and efficiency are considered at the same time.

Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm

2012 ◽  
Vol 20 (1) ◽  
pp. 27-62 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Amit Saha
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Space ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Optimization Task ◽  
Pareto Optimal Set ◽  
Single Objective

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.

scholarly journals Solving integer programming problems by using population-based beetle antennae search algorithm

2021 ◽  
Vol 9 (3-4) ◽  
pp. 89-99
Author(s):  
Ivona Brajević ◽  
Miodrag Brzaković ◽  
Goran Jocić
Keyword(s):  
Integer Programming ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Population Based ◽  
Local Optimum ◽  
Integer Programming Problems ◽  
Metaheuristic Techniques

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems. This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.

scholarly journals Designation of Candidate Solutions in Differential Evolution Based on Bandit Algorithm and its Evaluation

2019 ◽  
Vol 23 (4) ◽  
pp. 758-766
Author(s):  
Masaya Sakakibara ◽  
◽  
Akira Notsu ◽  
Seiki Ubukata ◽  
Katsuhiro Honda
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Random Search ◽  
Optimal Solution ◽  
Search Space ◽  
Optimization Method ◽  
Local Solution ◽  
Search Speed ◽  
Mathematical Programming Problems

We propose UCT-Grid Area Search (UCT-GAS), which is an efficient optimization method that roughly estimates specific values in areas, and consider exploration and exploitation in optimization problems. This approach divides the search space and imagines it to be a multi-armed bandit, which enables us to use bandit algorithms to solve mathematical programming problems. Although the search speed is fast than other search algorithm like differential evolution, it might converge to a local solution. In this study, we improve this algorithm by replacing its random search part with differential evolution after several searches. Comparative experiments confirmed the search ability of the optimal solution, and our method benefits by showing that it avoids falling into a local solution and that its search speed is fast.

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