Skill Optimization Algorithm: A New Human-Based Metaheuristic Technique

Metaheuristic algorithms are widely used in solving optimization problems. In this paper, a new metaheuristic algorithm called Skill Optimization Algorithm (SOA) is proposed to solve optimization problems. The fundamental inspiration in designing SOA is human efforts to acquire and improve skills. Various stages of SOA are mathematically modeled in two phases, including: (i) exploration, skill acquisition from experts and (ii) exploitation, skill improvement based on practice and individual effort. The efficiency of SOA in optimization applications is analyzed through testing this algorithm on a set of twenty-three standard benchmark functions of a variety of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types. The optimization results show that SOA, by balancing exploration and exploitation, is able to provide good performance and appropriate solutions for optimization problems. In addition, the performance of SOA in optimization is compared with ten metaheuristic algorithms to evaluate the quality of the results obtained by the proposed approach. Analysis and comparison of the obtained simulation results show that the proposed SOA has a superior performance over the considered algorithms and achieves much more competitive results.     

SSABA: Search Step Adjustment Based Algorithm

Finding the suitable solution to optimization problems is a fundamental challenge in various sciences. Optimization algorithms are one of the effective stochastic methods in solving optimization problems. In this paper, a new stochastic optimization algorithm called Search Step Adjustment Based Algorithm (SSABA) is presented to provide quasi-optimal solutions to various optimization problems. In the initial iterations of the algorithm, the step index is set to the highest value for a comprehensive search of the search space. Then, with increasing repetitions in order to focus the search of the algorithm in achieving the optimal solution closer to the global optimal, the step index is reduced to reach the minimum value at the end of the algorithm implementation. SSABA is mathematically modeled and its performance in optimization is evaluated on twenty-three different standard objective functions of unimodal and multimodal types. The results of optimization of unimodal functions show that the proposed algorithm SSABA has high exploitation power and the results of optimization of multimodal functions show the appropriate exploration power of the proposed algorithm. In addition, the performance of the proposed SSABA is compared with the performance of eight well-known algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), and Tunicate Swarm Algorithm (TSA). The simulation results show that the proposed SSABA is better and more competitive than the eight compared algorithms with better performance.     

A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.     

AMBO: All Members-Based Optimizer for Solving Optimization Problems

There are many optimization problems in different branches of science that should be solved using an appropriate methodology. Population-based optimization algorithms are one of the most efficient approaches to solve this type of problems. In this paper, a new optimization algorithm called All Members-Based Optimizer (AMBO) is introduced to solve various optimization problems. The main idea in designing the proposed AMBO algorithm is to use more information from the population members of the algorithm instead of just a few specific members (such as best member and worst member) to update the population matrix. Therefore, in AMBO, any member of the population can play a role in updating the population matrix. The theory of AMBO is described and then mathematically modeled for implementation on optimization problems. The performance of the proposed algorithm is evaluated on a set of twenty-three standard objective functions, which belong to three different categories: unimodal, high-dimensional multimodal, and fixed-dimensional multimodal functions. In order to analyze and compare the optimization results for the mentioned objective functions obtained by AMBO, eight other well-known algorithms have been also implemented. The optimization results demonstrate the ability of AMBO to solve various optimization problems. Also, comparison and analysis of the results show that AMBO is superior and more competitive than the other mentioned algorithms in providing suitable solution.     

A decreasing inertia weight particle swarm optimizer

It has been over ten years since the pioneering work of particle swarm optimization (PSO) espoused by Kennedy and Eberhart. Since then, various modifications, well suited to particular application areas, have been reported widely in the literature. The evolutionary concept of PSO is clear-cut in nature, easy to implement in practice, and computationally efficient in comparison to other evolutionary algorithms. The above-mentioned merits are primarily the motivation of this article to investigate PSO when applied to continuous optimization problems. The performance of conventional PSO on the solution quality and convergence speed deteriorates when the function to be optimized is multimodal or with a large problem size. Toward that end, it is of great practical value to develop a modified particle swarm optimizer suitable for solving high-dimensional, multimodal optimization problems. In the first part of the article, the design of experiments (DOE) has been conducted comprehensively to examine the influences of each parameter in PSO. Based upon the DOE results, a modified PSO algorithm, termed Decreasing-Weight Particle Swarm Optimization (DW-PSO), is addressed. Two performance measures, the success rate and number of function evaluations, are used to evaluate the proposed method. The computational comparisons with the existing PSO algorithms show that DW-PSO exhibits a noticeable advantage, especially when it is performed to solve high-dimensional problems.     

Archery Algorithm: A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge. Therefore, these must be addressed utilizing proper approaches. Based on a random search space, optimization algorithms can find acceptable solutions to problems. Archery Algorithm (AA) is a new stochastic approach for addressing optimization problems that is discussed in this study. The fundamental idea of developing the suggested AA is to imitate the archer's shooting behavior toward the target panel. The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer. The AA is mathematically described, and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions. Furthermore, the proposed algorithm's performance is compared vs. eight approaches, including teaching-learning based optimization, marine predators algorithm, genetic algorithm, grey wolf optimization, particle swarm optimization, whale optimization algorithm, gravitational search algorithm, and tunicate swarm algorithm. According to the simulation findings, the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios, and it can give adequate quasi-optimal solutions to these problems. The analysis and comparison of competing algorithms’ performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.     

Dark Forest Algorithm: A Novel Metaheuristic Algorithm for Global Optimization Problems

Metaheuristic algorithms, as effective methods for solving optimization problems, have recently attracted considerable attention in science and engineering fields. They are popular and have broad applications owing to their high efficiency and low complexity. These algorithms are generally based on the behaviors observed in nature, physical sciences, or humans. This study proposes a novel metaheuristic algorithm called dark forest algorithm (DFA), which can yield improved optimization results for global optimization problems. In DFA, the population is divided into four groups: highest civilization, advanced civilization, normal civilization, and low civilization. Each civilization has a unique way of iteration. To verify DFA’s capability, the performance of DFA on 35 well-known benchmark functions is compared with that of six other metaheuristic algorithms, including artificial bee colony algorithm, firefly algorithm, grey wolf optimizer, harmony search algorithm, grasshopper optimization algorithm, and whale optimization algorithm. The results show that DFA provides solutions with improved efficiency for problems with low dimensions and outperforms most other algorithms when solving high dimensional problems. DFA is applied to five engineering projects to demonstrate its applicability. The results show that the performance of DFA is competitive to that of current well-known metaheuristic algorithms. Finally, potential upgrading routes for DFA are proposed as possible future developments.     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

IRKO: An Improved Runge-Kutta Optimization Algorithm for Global Optimization Problems

Optimization is a key technique for maximizing or minimizing functions and achieving optimal cost, gains, energy, mass, and so on. In order to solve optimization problems, metaheuristic algorithms are essential. Most of these techniques are influenced by collective knowledge and natural foraging. There is no such thing as the best or worst algorithm; instead, there are more effective algorithms for certain problems. Therefore, in this paper, a new improved variant of a recently proposed metaphorless Runge-Kutta Optimization (RKO) algorithm, called Improved Runge-Kutta Optimization (IRKO) algorithm, is suggested for solving optimization problems. The IRKO is formulated using the basic RKO and local escaping operator to enhance the diversification and intensification capability of the basic RKO version. The performance of the proposed IRKO algorithm is validated on 23 standard benchmark functions and three engineering constrained optimization problems. The outcomes of IRKO are compared with seven state-of-the-art algorithms, including the basic RKO algorithm. Compared to other algorithms, the recommended IRKO algorithm is superior in discovering the optimal results for all selected optimization problems. The runtime of IRKO is less than 0.5 s for most of the 23 benchmark problems and stands first for most of the selected problems, including real-world optimization problems.     

HYBRID MULTIMODAL OPTIMIZATION WITH CLUSTERING GENETIC STRATEGIES

Abstract

Two-stage hybrid multimodal optimization approaches that combine cluster identification techniques in genetic algorithms with sharing and gradient-based local search methods are proposed. The multimodal optimization comprises the use of a sharing function implementation in genetic searches to pursue multiple local optima and subsequent executions of local searches to locate each local optimum when an extreme-containing region is identified. A new cluster identification technique is proposed for automatic and adaptive identification of the locations and sizes of design clusters in genetic algorithms with sharing. The first stage of the hybrid multimodal optimization is to use sharing-enhanced genetic algorithms for the identification of the near-optimum designs inside extreme-containing regions. The second stage simply involves consecutive employment of efficient gradient-based local searches by using the near-optimum designs as initial designs. Two strategies defining the coupling of the genetic search and local searches are proposed. The proposed hybrid optimization strategies are tested in a number of illustrative multimodal optimization problems.     

A parallel particle swarm optimization algorithm for multi-objective optimization problems

In this article, a new proposal of using particle swarm optimization algorithms to solve multi-objective optimization problems is presented. The algorithm is constructed based on the concept of Pareto dominance, as well as a state-of-the-art ‘parallel’ computing technique that intends to improve algorithmic effectiveness and efficiency simultaneously. The proposed parallel particle swarm multi-objective evolutionary algorithm (PPS-MOEA) is tested through a variety of standard test functions taken from the literature; its performance is compared with six noted multi-objective algorithms. The computational experience gained from the first two experiments indicates that the algorithm proposed in this article is extremely competitive when compared with other MOEAs, being able to accurately, reliably and robustly approximate the true Pareto front in almost every tested case. To justify the motivation behind the research of the parallel swarm structure, the computational results of the third experiment confirm the PPS-MOEA's merit in solving really high-dimensional multi-objective optimization problems.     

Deterministic oscillatory search: a new meta-heuristic optimization algorithm

The paper proposes a new optimization algorithm that is extremely robust in solving mathematical and engineering problems. The algorithm combines the deterministic nature of classical methods of optimization and global converging characteristics of meta-heuristic algorithms. Common traits of nature-inspired algorithms like randomness and tuning parameters (other than population size) are eliminated. The proposed algorithm is tested with mathematical benchmark functions and compared to other popular optimization algorithms. The results show that the proposed algorithm is superior in terms of robustness and problem solving capabilities to other algorithms. The paradigm is also applied to an engineering problem to prove its practicality. It is applied to find the optimal location of multi-type FACTS devices in a power system and tested in the IEEE 39 bus system and UPSEB 75 bus system. Results show better performance over other standard algorithms in terms of voltage stability, real power loss and sizing and cost of FACTS devices.     

Dynamic multi-swarm particle swarm optimizer using parallel PC cluster systems for global optimization of large-scale multimodal functions

This article presents a novel parallel multi-swarm optimization (PMSO) algorithm with the aim of enhancing the search ability of standard single-swarm PSOs for global optimization of very large-scale multimodal functions. Different from the existing multi-swarm structures, the multiple swarms work in parallel, and the search space is partitioned evenly and dynamically assigned in a weighted manner via the roulette wheel selection (RWS) mechanism. This parallel, distributed framework of the PMSO algorithm is developed based on a master–slave paradigm, which is implemented on a cluster of PCs using message passing interface (MPI) for information interchange among swarms. The PMSO algorithm handles multiple swarms simultaneously and each swarm performs PSO operations of its own independently. In particular, one swarm is designated for global search and the others are for local search. The first part of the experimental comparison is made among the PMSO, standard PSO, and two state-of-the-art algorithms (CTSS and CLPSO) in terms of various un-rotated and rotated benchmark functions taken from the literature. In the second part, the proposed multi-swarm algorithm is tested on large-scale multimodal benchmark functions up to 300 dimensions. The results of the PMSO algorithm show great promise in solving high-dimensional problems.     

Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems

An efficient optimization algorithm called teaching–learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ?-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.     

A comparative study of the scalability of alternative metamodelling techniques

Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. The accuracy of these metamodels varies with the scale and complexity of the underlying model. In this article, three metamodelling methods are evaluated with respect to their capabilities for modelling high-dimensional, nonlinear, multimodal functions. Methods analyzed include kriging, radial basis functions, and support vector regression. Each metamodelling technique is used to model a set of single output functions with dimensionality ranging from fifteen to fifty independent variables and modality ranging from one to ten local maxima. The number of points used to train the models is increased until a predetermined error threshold is met. Results show that kriging metamodels perform most consistently across a variety of functions, although radial basis functions and support vector regression are very competitive for highly multimodal functions and functions with large local gradients, respectively. Support vector regression metamodels consistently offer the shortest build and prediction times when applied to large scale multimodal problems.     

Accelerating adaptive trade‐off model using shrinking space technique for constrained evolutionary optimization

Adaptive trade‐off model (ATM) is a constraint‐handling mechanism proposed recently. The main advantages of this model are its simplicity and adaptation. Moreover, it can be easily embedded into evolutionary algorithms for solving constrained optimization problems. This paper proposes a novel method for constrained optimization, which aims at accelerating the ATM using shrinking space technique. Eighteen benchmark test functions and five engineering design problems are used to test the performance of the method proposed. Experimental results suggest that combining the ATM with the shrinking space technique is very beneficial. The method proposed can promptly converge to competitive results without loss of the quality and the precision of the final results. Performance comparisons with some other state‐of‐the‐art approaches from the literature are also presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.     

Plant Identification Using Fitness-Based Position Update in Whale Optimization Algorithm

Since the beginning of time, humans have relied on plants for food, energy, and medicine. Plants are recognized by leaf, flower, or fruit and linked to their suitable cluster. Classification methods are used to extract and select traits that are helpful in identifying a plant. In plant leaf image categorization, each plant is assigned a label according to its classification. The purpose of classifying plant leaf images is to enable farmers to recognize plants, leading to the management of plants in several aspects. This study aims to present a modified whale optimization algorithm and categorizes plant leaf images into classes. This modified algorithm works on different sets of plant leaves. The proposed algorithm examines several benchmark functions with adequate performance. On ten plant leaf images, this classification method was validated. The proposed model calculates precision, recall, F-measurement, and accuracy for ten different plant leaf image datasets and compares these parameters with other existing algorithms. Based on experimental data, it is observed that the accuracy of the proposed method outperforms the accuracy of different algorithms under consideration and improves accuracy by 5%.     

Enhanced Heap-Based Optimizer Algorithm for Solving Team FormationProblem

Team Formation (TF) is considered one of the most significant problems in computer science and optimization. TF is defined as forming the best team of experts in a social network to complete a task with least cost. Many real-world problems, such as task assignment, vehicle routing, nurse scheduling, resource allocation, and airline crew scheduling, are based on the TF problem. TF has been shown to be a Nondeterministic Polynomial time (NP) problem, and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms. This paper proposes two improved swarm-based algorithms for solving team formation problem. The first algorithm, entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm (HBOSA), uses a single crossover operator to improve the performance of a standard heap-based optimizer (HBO) algorithm. It also employs the simulated annealing (SA) approach to improve model convergence and avoid local minima trapping. The second algorithm is the Chaotic Heap-based Optimizer Algorithm (CHBO). CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space. During HBO’s optimization process, a logistic chaotic map is used. The performance of the two proposed algorithms (HBOSA) and (CHBO) is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills. Furthermore, the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer (HBO), Developed Simulated Annealing (DSA), Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Genetic Algorithm (GA). Finally, the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database (IMDB). The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance, with fast convergence to the global minimum.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.