scholarly journals A Cuckoo Search Algorithm for Multimodal Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Erik Cuevas ◽  
Adolfo Reyna-Orta
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Search Space ◽  
Selection Strategy ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Local Optima ◽  
Fitness Value

Interest in multimodal optimization is expanding rapidly, since many practical engineering problems demand the localization of multiple optima within a search space. On the other hand, the cuckoo search (CS) algorithm is a simple and effective global optimization algorithm which can not be directly applied to solve multimodal optimization problems. This paper proposes a new multimodal optimization algorithm called the multimodal cuckoo search (MCS). Under MCS, the original CS is enhanced with multimodal capacities by means of (1) the incorporation of a memory mechanism to efficiently register potential local optima according to their fitness value and the distance to other potential solutions, (2) the modification of the original CS individual selection strategy to accelerate the detection process of new local minima, and (3) the inclusion of a depuration procedure to cyclically eliminate duplicated memory elements. The performance of the proposed approach is compared to several state-of-the-art multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. Experimental results indicate that the proposed strategy is capable of providing better and even a more consistent performance over existing well-known multimodal algorithms for the majority of test problems yet avoiding any serious computational deterioration.

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

scholarly journals Binary Spring Search Algorithm for Solving Various Optimization Problems

2021 ◽  
Vol 11 (3) ◽  
pp. 1286 ◽  
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ali Dehghani ◽  
Om P. Malik ◽  
Ruben Morales-Menendez ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
High Performance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Bat Algorithm ◽  
Search Space ◽  
Binary Particle Swarm Optimization ◽  
Dragonfly Algorithm ◽  
Grasshopper Optimization Algorithm

One of the most powerful tools for solving optimization problems is optimization algorithms (inspired by nature) based on populations. These algorithms provide a solution to a problem by randomly searching in the search space. The design’s central idea is derived from various natural phenomena, the behavior and living conditions of living organisms, laws of physics, etc. A new population-based optimization algorithm called the Binary Spring Search Algorithm (BSSA) is introduced to solve optimization problems. BSSA is an algorithm based on a simulation of the famous Hooke’s law (physics) for the traditional weights and springs system. In this proposal, the population comprises weights that are connected by unique springs. The mathematical modeling of the proposed algorithm is presented to be used to achieve solutions to optimization problems. The results were thoroughly validated in different unimodal and multimodal functions; additionally, the BSSA was compared with high-performance algorithms: binary grasshopper optimization algorithm, binary dragonfly algorithm, binary bat algorithm, binary gravitational search algorithm, binary particle swarm optimization, and binary genetic algorithm. The results show the superiority of the BSSA. The results of the Friedman test corroborate that the BSSA is more competitive.

scholarly journals Near Infrared and Visible Image Registration using Whale Optimization Algorithm

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Image Registration ◽  
Optimization Algorithm ◽  
Near Infrared ◽  
Optimization Problems ◽  
Search Space ◽  
Whale Optimization Algorithm ◽  
Visible Image ◽  
Local Optima ◽  
Multimodal Image Registration ◽  
Whale Optimization

This paper reports the use of a nature-inspired metaheuristic algorithm known as ‘Whale Optimization Algorithm’ (WOA) for multimodal image registration. WOA is based on the hunting behaviour of Humpback whales and provides better exploration and exploitation of the search space with small possibility of trapping in local optima. Though WOA is used in various optimization problems, no detailed study is available for its use in image registration. For this study different sets of NIR and visible images are considered. The registration results are compared with the other state of the art image registration methods. The results show that WOA is a very competitive algorithm for NIR-visible image registration. With the advantages of better exploration of search space and local optima avoidance, the algorithm can be a suitable choice for multimodal image registration.

A Survey of the Cuckoo Search and Its Applications in Real-World Optimization Problems

2017 ◽  
pp. 541-555 ◽  
Author(s):  
Christopher Expósito-Izquierdo ◽  
Airam Expósito-Márquez
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Search Space ◽  
Population Based ◽  
Cuckoo Search Algorithm ◽  
Breeding Strategy ◽  
Egg Laying ◽  
Practical Applications ◽  
Wide Range

The chapter at hand seeks to provide a general survey of the Cuckoo Search Algorithm and its most highlighted variants. The Cuckoo Search Algorithm is a relatively recent nature-inspired population-based meta-heuristic algorithm that is based upon the lifestyle, egg laying, and breeding strategy of some species of cuckoos. In this case, the Lévy flight is used to move the cuckoos within the search space of the optimization problem to solve and obtain a suitable balance between diversification and intensification. As discussed in this chapter, the Cuckoo Search Algorithm has been successfully applied to a wide range of heterogeneous optimization problems found in practical applications over the last few years. Some of the reasons of its relevance are the reduced number of parameters to configure and its ease of implementation.

On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms

2013 ◽  
Vol 21 (3) ◽  
pp. 471-495 ◽  
Author(s):  
Carlos Echegoyen ◽  
Alexander Mendiburu ◽  
Roberto Santana ◽  
Jose A. Lozano
Keyword(s):  
Probabilistic Model ◽  
Hamming Distance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Necessary Condition ◽  
Estimation Of Distribution Algorithms ◽  
Local Optima ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space [Formula: see text].

scholarly journals A hybrid cuckoo–harmony search algorithm for optimal design of water distribution systems

2015 ◽  
Vol 18 (3) ◽  
pp. 544-563 ◽  
Author(s):  
Razi Sheikholeslami ◽  
Aaron C. Zecchin ◽  
Feifei Zheng ◽  
Siamak Talatahari
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Cuckoo Search ◽  
Search Space ◽  
Optimization Method

Meta-heuristic algorithms have been broadly used to deal with a range of water resources optimization problems over the past decades. One issue that exists in the use of these algorithms is the requirement of large computational resources, especially when handling real-world problems. To overcome this challenge, this paper develops a hybrid optimization method, the so-called CSHS, in which a cuckoo search (CS) algorithm is combined with a harmony search (HS) scheme. Within this hybrid framework, the CS is employed to find the promising regions of the search space within the initial explorative stages of the search, followed by a thorough exploitation phase using the combined CS and HS algorithms. The utility of the proposed CSHS is demonstrated using four water distribution system design problems with increased scales and complexity. The obtained results reveal that the CSHS method outperforms the standard CS, as well as the majority of other meta-heuristics that have previously been applied to the case studies investigated, in terms of efficiently seeking optimal solutions. Furthermore, the CSHS has two control parameters that need to be fine-tuned compared to many other algorithms, which is appealing for its practical application as an extensive parameter-calibration process is typically computationally very demanding.

A New Hybrid Binary-Real Coded Cuckoo Search and Tabu Search Algorithm for Solving the Unit-Commitment Problem

2021 ◽  
Vol 10 (2) ◽  
pp. 104-119
Author(s):  
Amel Terki ◽  
Hamid Boubertakh
Keyword(s):  
Tabu Search ◽  
Local Search ◽  
Unit Commitment ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Search Space ◽  
Optimization Techniques ◽  
Optimization Approach ◽  
Unit Commitment Problem ◽  
Local Optima

This paper proposes a new intelligent optimization approach to deal with the unit commitment (UC) problem by finding the optimal on/off states strategy of the units under the system constraints. The proposed method is a hybridization of the cuckoo search (CS) and the tabu search (TS) optimization techniques. The former is distinguished by its efficient global exploration mechanism, namely the levy flights, and the latter is a successful local search method. For this sake, a binary code is used for the status of units in the scheduled time horizon, and a real code is used to determine the generated power by the committed units. The proposed hybrid CS and TS (CS-TS) algorithm is used to solve the UC problem such that the CS guarantees the exploration of the whole search space, while the TS algorithm deals with the local search in order to avoid the premature convergence and prevent from trapping into local optima. The proposed method is applied to the IEEE standard systems of different scales ranging from 10 to 100 units. The results show clearly that the proposed method gives better quality solutions than the existing methods.

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.

scholarly journals Properties of Gray and Binary Representations

2004 ◽  
Vol 12 (1) ◽  
pp. 47-76 ◽  
Author(s):  
Jonathan Rowe ◽  
Darrell Whitley ◽  
Laura Barbulescu ◽  
Jean-Paul Watson
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Gray Code ◽  
Global Optimum ◽  
Gray Codes ◽  
Neighborhood Structure ◽  
Local Optima ◽  
Vertex Set

Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding and present a review of properties related to the use of Gray codes. Gray codes are widely used in conjunction with genetic algorithms and bit-climbing algorithms for parameter optimization problems. We present new convergence proofs for a special class of unimodal functions; the proofs show that a steepest ascent bit climber using any reflected Gray code representation reaches the global optimum in a number of steps that is linear with respect to the encoding size. There are in fact many different Gray codes.Shifting is defined as a mechanism for dynamically switching from one Gray code representation to another in order to escape local optima. Theoretical results that substantially improve our understanding of the Gray codes and the shifting mechanism are presented. New proofs also shed light on the number of unique Gray code neighborhoods accessible via shifting and on how neighborhood structure changes during shifting. We show that shifting can improve the performance of both a local search algorithm as well as one of the best genetic algorithms currently available.

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.

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