Real-parameter Numerical Optimization Research Articles

A self-learning differential evolution algorithm with population range indicator

The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization.

Differential evolution with stage stratification method and dual balanced mutation strategy for real-parameter numerical optimization

Traditional differential evolution (DE) algorithms have functional limitations in effectively addressing increasingly intricate numerical optimization problems. The key to responding to this challenge is to strike a suitable balance between exploration and exploitation. Exploration is used to find the global optimal solution, and exploitation is used to improve the accuracy of the global optimal solution. Therefore, this study introduces a novel differential evolution algorithm with a stage stratification method and a dual balanced mutation strategy framework, named SbmDE. To enhance the balance between convergence and diversity, the population is stratified into exploration and exploitation layers based on the size of the fitness value and evolutionary period. In the exploitation layer, a hybridization mutation is applied as the first mutation. A novel dual improved mutation operation is proposed and applied to the exploration layer. For the first mutation, the hybridization mutation is used in the same manner as for the exploitation layer. For the secondary mutation, two improved mutation strategies are proposed to alleviate premature convergence at the early stage of evolution and to enhance the local neighborhood search at a later stage, named DE/ranking-to-rand/1 and DE/best-current-dev/1. Experiments were conducted on the CEC2017 benchmark suite, which contains 29 single-objective real-parameter numerical optimization problems, to evaluate the performance of the proposed algorithm. Compared with 11 state-of-the-art algorithms, the results demonstrate the superiority of the proposed algorithm, which does not increase the time complexity. Additionally, based on the four engineering design problems, the proposed algorithm is fully competent in solving practical constrained optimization problems.

Reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy

The particle swarm optimization (PSO) algorithm has been one of the most effective methods for solving various engineering optimization problems. Most existing PSO variants frequently use fixed operators, the adoption of a fixed operator learning mode may restrict the intelligence level of each particle, thus reducing the performance of PSO in solving optimization issues with complicated fitness landscapes. To address single goal real-parameter numerical optimization while overcoming the above shortcoming, this paper proposes a reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy (NRLPSO). In NRLPSO, a dynamic oscillation inertial weight (DOW) strategy that provides particles with dynamic adjustment ability in different situations is designed. To resolve the operator selection conundrum of exploration and exploitation, a reinforcement learning-based velocity vector generation (VRL) strategy is developed. At each iteration, particles select the velocity update model based on reinforcement learning, and VRL helps to thoroughly search the problem space. A velocity updating mechanism based on cosine similarity (VCS) is applied to control the velocity learning mode to determine more promising solutions. Furthermore, to alleviate the problem of premature convergence, a local update strategy with neighborhood differential mutation (NDM) is employed to increase the diversity of the algorithm. To verify the efficiency of the proposed algorithm, the CEC2017 and CEC2022 test suites are implemented, and nine classic or state-of-the-art PSO variants are comprehensively tested. The experimental results show that NRLPSO outperforms the popular PSO variants in terms of convergence speed and accuracy. Since NRLPSO utilizes the DE mutations, it is compared with the representative LSHADE variant algorithm - LSHADE_SPACMA. Although LSHADE_SPACMA is better than NRLPSO concerning algorithm stability and convergence accuracy, we will refine our work in the future to enhance the performance in all aspects.

Towards a parameterless out-of-the-box population size control for evolutionary and swarm-based algorithms for single objective bound constrained real-parameter numerical optimization

We present an innovative step towards a parameterless out-of-the-box population size control for evolutionary and swarm-based algorithms for single objective bound constrained real-parameter numerical optimization. To the best of our knowledge, our approach is the first parameterless out-of-the-box parameter control for such a kind of technique. It is easy to implement and to use, since it does not require the adjustment of any parameter. The general idea is to increment the velocity of the population change if the best fitness stagnates, and decrement it otherwise. Then, in order to effectively change the population size, a mechanism of removal/addition of individuals inspired by the selection methods of evolutionary algorithms is executed. Our experimental results provide evidence that our controller is not only compatible with any evolutionary or swarm-based algorithm for single objective bound constrained real-parameter numerical optimization, but that it also performs well in many scenarios.

Joint Opposite Selection (JOS): A premiere joint of selective leading opposition and dynamic opposite enhanced Harris’ hawks optimization for solving single-objective problems

In this paper, we proposed Joint Opposite Selection (JOS) operator that is a joint of two opposition learning techniques: the Selective Leading Opposition (SLO) and the Dynamic Opposite (DO). SLO uses a linearly decreasing threshold value to determine the close distance dimension of the search agents. DO provides the search agents chances to expand their abilities in the search space. We applied JOS to the Harris Hawks Optimization (HHO), the performance is increased because JOS balances the capability of exploration phase by using SLO and exploitation phase by using DO. The new algorithm, named Harris’ Hawks Optimization-Joint Opposite Selection (HHO-JOS), is also proposed in this research as an enhanced version of HHO to solve single-objective problems. When the hawks deploy JOS, SLO assists the hawks to succeed in exploitation phase by changing their close distance dimension and DO tries to diverse the search space range of the hawks in the exploration phase using a Random Jump Strategy (RJS). The sufficient Jumping rate (Jr) of DO in HHO-JOS is 0.25, according to our experimental results. The proposed algorithm was included in a competition conducted on 30 benchmark functions of CEC 2014 and 29 benchmark functions of CEC 2017. Both benchmarks contain collections of single-objective problems for real parameter numerical optimization. The problems were employed to evaluate and compare the proposed HHO-JOS to the original HHO, three variations of OBLs embedded in the original HHO, and 31 nature-inspired algorithms by using a scoring metric. The results of the competition showed that the premiere JOS on HHO consistently achieves robustness performance on CEC 2014 and CEC 2017. Comprehensive statistical analysis also demonstrated that HHO-JOS can compete with many leading optimization algorithms. Therefore, we can conclude that the proposed joint opposite selection is well-matched to HHO and succeeds in elevating HHO-JOS.

BSO20: efficient brain storm optimization for real-parameter numerical optimization

Brain storm optimization (BSO) is an emerging global optimization algorithm. The primary idea is to divide the population into different clusters, and offspring are generated within a cluster or between two clusters. However, the problems of inefficient clustering strategy and insufficient exploration exist in BSO. In this paper, a novel and efficient BSO is proposed, called BSO20 (proposed in 2020). BSO20 pays attention to both the clustering strategy and the mutation strategy. First, we propose a hybrid clustering strategy, which combines two clustering strategies, i.e., nearest-better clustering and random grouping strategy. The size of the subpopulation clustered by two strategies is dynamically adjusted as the population evolves. Second, a modified mutation strategy is used in BSO20 to share information within a cluster or among multiple clusters to enhance the ability of exploration. BSO20 is tested on the problems of the 2017 IEEE Congress on Evolutionary Computation competition on real parameter numerical optimization. BSO20 is compared with several variants of BSO and two variants of particle swarm optimization, and the experimental results show that BSO20 is competitive.

Atomic orbital search: A novel metaheuristic algorithm

In this paper, the Atomic Orbital Search (AOS) is proposed as a novel metaheuristic algorithm for optimization purposes. The main concept of this algorithm is based on some principles of quantum mechanics and the quantum-based atomic model in which the general configuration of electrons around nucleus is in perspective. In order to evaluate the performance of this algorithm, a total number of 20 unconstrained mathematical test functions are utilized with different dimensions of 2–100 while a maximum number of 150,000 function evaluations is considered with 100 independent optimization runs for statistical purposes. A complete statistical analysis is also conducted by utilization of the Kolmogorov Smirnov, Wilcoxon and the Kruskal Wallis tests while 8 metaheuristics are also utilized as alternatives for comparative purposes. The latest Competitions on Evolutionary Computation (CEC) regarding the single objective real-parameter numerical optimization (CEC 2017) including 30 benchmark test functions is also considered in which the capability of the proposed algorithm is compared to the most state−of-the−art algorithms in the optimization field. In addition, a total number of 5 constrained engineering design problems are utilized as design examples including some of the constrained optimization problems of the recent Competitions on Evolutionary Computation (CEC 2020). The obtained results of the AOS algorithm in dealing with the constraint problems are compared to the results of different standard, improved and hybrid metaheuristic algorithms from the literature. The obtained results demonstrate that the proposed AOS algorithm provides very outstanding results in dealing with the mathematical and engineering design problems.

Chaos Game Optimization: a novel metaheuristic algorithm

In this paper, a novel metaheuristic algorithm called Chaos Game Optimization (CGO) is developed for solving optimization problems. The main concept of the CGO algorithm is based on some principles of chaos theory in which the configuration of fractals by chaos game concept and the fractals self-similarity issues are in perspective. A total number of 239 mathematical functions which are categorized into four different groups are collected to evaluate the overall performance of the presented novel algorithm. In order to evaluate the results of the CGO algorithm, three comparative analysis with different characteristics are conducted. In the first step, six different metaheuristic algorithms are selected from the literature while the minimum, mean and standard deviation values alongside the number of function evaluations for the CGO and these algorithms are calculated and compared. A complete statistical analysis is also conducted in order to provide a valid judgment about the performance of the CGO algorithm. In the second one, the results of the CGO algorithm are compared to some of the recently developed fractal- and chaos-based algorithms. Finally, the performance of the CGO algorithm is compared to some state-of-the-art algorithms in dealing with the state-of-the-art mathematical functions and one of the recent competitions on single objective real-parameter numerical optimization named “CEC 2017” is considered as numerical examples for this purpose. In addition, a computational cost analysis is also conducted for the presented algorithm. The obtained results proved that the CGO is superior compared to the other metaheuristics in most of the cases.

Harris Hawks optimization with information exchange

The basic Harris Hawks optimization algorithm cannot take full advantage of the information sharing capability of the Harris Hawks while cooperatively searching for prey, and it is difficult to balance the exploration and development capacities of this algorithm. These factors limit the Harris Hawks optimization algorithm, such as in terms of premature convergence and ease of falling into a local optimum. To this end, an improved Harris Hawks optimization algorithm based on information exchange is proposed to optimize the continuous function and its application to engineering problems. First, an individual Harris Hawk obtains information from the shared area of cooperative foraging and the location area of collaborators, thereby realizing information exchange and sharing. Second, a nonlinear escaping energy factor with chaos disturbance is designed to better balance the local searching and the global searching of the algorithm. Finally, a numerical experiment is conducted with four benchmark test functions and five CEC-2017 real-parameter numerical optimization problems as well as seven practical engineering problems. The results show that the proposed algorithm outperforms the basic Harris Hawks optimization algorithm and other intelligence optimization algorithms in terms of the convergence rate, solution accuracy, and robustness.

Adaptive inertia weight Bat algorithm with Sugeno-Function fuzzy search

Bat algorithm (BA) turns into the most generally utilized meta-heuristic algorithm to solve the different sort of global optimization problems. In the optimization of continuous data, BA experiences one of the prominent difficulties called premature convergence. In order to tackle premature convergence, this study exhibits a new version of BA called Adaptive inertia weight Bat algorithm with Sugeno-Function Fuzzy Search (ASF-BA). The proposed algorithm ASF-BA brings two major adjustments in the standard BA. Firstly, we incorporated an adaptive inertia weight to boost up the velocity rate of bats effectively. Secondly, we replaced the random searching method of standard BA with Sugeno-Function fuzzy search, which used Sugeno-Function decline curves to dynamically adjust the fitness of each bat according to their own experience and experience of their neighbour bats. We compared ASF-BA with several old fashioned and new fashioned optimization algorithms. ASF-BA is also tested against top hybridized and enhanced version of DE algorithms. The CEC 2017 benchmark (30 real parameter numerical optimization problems ), CEC 2017 ( 28 constrained optimization problems) and 19 additional benchmark problems have been used to examine and compare the performance of ASF-BA with other state of the art variants. Contrasted with the existing BA and other leading variants of BA, DE, and PSO on CEC 2017 constrained and numerical benchmarks, the ASF-BA is excellent to the state-of-art variants of BA, DE, and PSO in terms of stability, convergence speed and solution quality. The ASF-BA sets stable support for resolving optimization problems of intelligent and expert systems. Furthermore, we also examined the performance of proposed ASF-BA for the weight optimization of Feed Forward Neural Networks (FFNN) and compared ASF-BA with Back Propagation Algorithm (BPA), BA and PSO. ASF-BA achieved 94 % of maximum accuracy. The experimental outcomes reveal that the suggested algorithm executed especially reliable and effective than the existing state of the art variants.

An improved whale optimization algorithm with armed force program and strategic adjustment

In this paper, we propose a new whale army optimization algorithm with a view to solving multifarious optimization problems. The key novelty of our approach is to modify the original whale optimization algorithm to make it effective to solve the complicated, large-scale and constrained optimization problems. Our modifications mainly embody two aspects: the beneficial strategic adjustment to set key parameters and to help establish base principles in the original optimizer and the introduction of armed force program which classifies the search whales into different categories to achieve efficient cooperation. We evaluate the performance of the proposed algorithm, using three simple benchmark test functions over thirty CEC-2014 real-parameter numerical optimization problems and three constraint engineering design problems. The test results indicate that this algorithm can provide a faster local convergence rate, a higher convergence accuracy, and a lower computational complexity in comparison to traditional whale optimization algorithms and other sophisticated state of the art whale optimizers. Performance wise, it also surpasses many advanced methods for large-scaled complex functions. Furthermore, in this paper we propose a variant of whale army optimization algorithm to specifically address and solve optimizing constrained problems with a high degree of precision.

Improved Self-adaptive Search Equation-based Artificial Bee Colony Algorithm with competitive local search strategy

Abstract The search equations and the local search procedures used in Artificial Bee Colony (ABC) algorithm are two key components that affect the performance of the algorithm. However, there is no search equation or local search that provides good results for all problem types. In this article, an ABC algorithm called “Self-adaptive Search Equation-based Artificial Bee Colony” (SSEABC) is proposed which can determine the appropriate local search procedure and the search equation internally during execution. SSEABC integrates three strategies into the canonical ABC algorithm. The first strategy is a self-adaptive strategy that determines the appropriate search equations for a particular problem by eliminating improper ones from a pool consisting of randomly generated search equations. The second strategy is a competitive local search selection. It decides the most effective local search procedure by comparing the performances of SSEABC, Mtsls1 and IPOP-CMA-ES. The third strategy is an incremental population size strategy, which is based on adding new food sources located around the best-so-far food source position after a predefined number of iterations. This helps to increase convergence speed. The SSEABC algorithm is tested on benchmark functions proposed in the CEC'14 abd CEC'17 competition on single objective bound constrained real-parameter numerical optimization. SSEABC is compared with several ABC variants, competitor algorithms of CEC'14 and CEC'17, and several state-of-the-art algorithms. Finally, we applied SSEABC to the infinite impulse response (IIR) system identification problem as an engineering application. The results showed the superiority of the SSEABC algorithm.

Particle state change algorithm

The matter state change, which is a common phenomenon in nature, shows the process that the matter how to reach the optimal state in the environment. This paper presents a novel particle state change model (PSCM) inspired by mimicking the process of the matter state change. Based on PSCM, a novel particle state change (PSC) algorithm is proposed for solving continuous optimization problems. As a new algorithm, PSC has many differences from other similar nature-inspired algorithms in terms of the basic principle models, mathematical formalization and properties. This paper considers three states of the matter, namely gas state, liquid state and solid state. In a certain circumstance, the matter always converts from an unstable state into a stable state. It is similar to find the optimal solution of an optimization problem. The proposed algorithm also has the advantages in the respects of higher intelligence, effectiveness and lower computation complexity. And the convergence property of PSC is discussed in detail. In order to illustrate the ability of solving optimization problems in continuous domain, the new proposed algorithm is tested on basic function optimization, CEC2016 single-objective real-parameter numerical optimization and CEC2016 learning-base real-parameter single-objective optimization, and compared with eleven existing algorithms. The numerous simulations have shown the effectiveness and suitability of the proposed approach.

A hybrid evolutionary algorithm based on tissue membrane systems and CMA-ES for solving numerical optimization problems

In this paper, a new hybrid algorithm is proposed to solve the single objective real-parameter numerical optimization problems, named as CETMS. The proposed CETMS is based on tissue membrane systems(TMS), and the evolution strategy with covariance matrix adaptation (CMA-ES) algorithm is employed to find the optimal solution in each cell of TMS. Some features of Tissue Membrane Systems, such as membrane structure, evolution mechanism and communication mechanism among cells, are introduced into CETMS. In addition, the optimal information of different cells can be shared by communication mechanism of TMS after the appointed cycle. The simulation experiments are conducted on thirty benchmark functions on the CEC14 test suite, which evaluate the performance of the proposed algorithm on solving single objective real-parameter numerical optimization problems. Numerical results show that the proposed CETMS has a very good performance in comparison with some of the state-of-the-art algorithms.

Hybrid achievement oriented computational chemotaxis in bacterial foraging optimization: a comparative study on numerical benchmark

The social foraging behavior of Escherichia coli bacteria has been recently used for solving complex real-world search and optimization problems. Bacterial foraging optimization algorithm (BFOA) is an important global optimization method inspired from this behavior. In this paper, a novel method called chemotaxis differential evolution optimization algorithm (CDEOA), which augments BFOA with conditional introduction of differential evolution (DE) and Random Search operators, is proposed. Introduction of these operators is done considering the number of successful run and unsuccessful tumble steps of bacteria. CDEOA was compared with the classical BFOA, two variants of BFOA which use DE operators [Adaptive Chemotactic Bacterial Swarm Foraging Optimization with Differential Evolution Strategy (ACBSFO_DES)], chemotaxis differential evolution (CDE), and the classical DE on all 30 numerical functions of the 2014 Congress on Evolutionary Computation (CEC 2014) Special Session and Competition on Single Objective Real Parameter Numerical Optimization suite. CDEOA was also compared with four state-of-the-art DE variants that competed in CEC 2014. Statistics of the computer simulations over this benchmark suite indicate that CDEOA outperforms, or is comparable to, its competitors in terms of the quality of final solution and its convergence rates for high-dimensional problems.

A Novel Artificial Bee Colony Algorithm with an Overall-Degradation Strategy and Its Performance on the Benchmark Functions of CEC 2014 Special Session

The artificial bee colony (ABC) algorithm has been a well-known swarm intelligence algorithm, which assimilates the cooperating behavior of bees when seeking for nectar sources. Aiming to improve the conventional ABC algorithm, we focus on the re-initialization phase. In this paper, an overall-degradation-oriented artificial bee colony (OD-ABC) algorithm is proposed, pursuing to fight against premature convergence. This is achieved through re-initializing majority of the employed bees at one time, rather than generating at most one scout bee in each iteration. In this work, our OD-ABC algorithm is compared against the conventional ABC algorithms using 24 benchmark functions that origin from the CEC 2014’s competition on single objective real-parameter numerical optimization. The numerical results show that the OD-ABC algorithm is effective and thus can be employed to fight against premature convergence.