High-dimensional Multimodal Functions Research Articles

Improved Driving Training-Based Optimization Algorithm Using Levy Flight and Crowding Distance Techniques

This study presents an improved version of the Driving Training-Based Optimization (DTBO) algorithm, the Improved Driving Training-Based Optimization (IDTBO). The work addresses fundamental issues in selecting drivers and learners for the conventional DTBO, which substantially impact the algorithm's accuracy and convergence speed. Two significant improvements are proposed: including the crowding distance technique for more diverse driver and learner selection and incorporating the Levy Flight distribution for better exploration and local optima avoidance. The IDTBO's performance is evaluated using twelve benchmark functions, including unimodal and high-dimensional multimodal optimization functions. The results indicate that IDTBO performs exceptionally well, with more extraordinary exploitation ability on unimodal functions and consistent achievement of the global optima. The proposed IDTBO demonstrated exceptional exploration capabilities on high-dimensional multimodal functions and performed competitively with other algorithms in the literature. From six functions, the IDTBO obtained zero optimal values. Again, the rate of convergence analysis demonstrates that IDTBO finds optimal solutions in fewer iterations, demonstrating its capacity to balance exploration and exploitation. To assess the strength of the IDTBO in solving real-world problems, the improved DTBO is further tested on two practical benchmark engineering problems. The IDTBO again produced a competitive performance against other algorithms in the literature. The study shows that IDTBO is a valuable metaheuristic algorithm that can tackle various real-world optimization problems.

Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm

The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated. It attained the top rank in 115 out of 161 benchmark functions in finding optimal value, encompassing unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, as well as the CEC 2019 test suite and CEC 2014 test suite dimensions of 10, 30, 50, and 100 and Zigzag Pattern benchmark functions, this suggests that the HO demonstrates a noteworthy proficiency in both exploitation and exploration. Moreover, it effectively balances exploration and exploitation, supporting the search process. In light of the results from addressing four distinct engineering design challenges, the HO has effectively achieved the most efficient resolution while concurrently upholding adherence to the designated constraints. The performance evaluation of the HO algorithm encompasses various aspects, including a comparison with WOA, GWO, SSA, PSO, SCA, FA, GOA, TLBO, MFO, and IWO recognized as the most extensively researched metaheuristics, AOA as recently developed algorithms, and CMA-ES as high-performance optimizers acknowledged for their success in the IEEE CEC competition. According to the statistical post hoc analysis, the HO algorithm is determined to be significantly superior to the investigated algorithms. The source codes of the HO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/160088-hippopotamus-optimization-algorithm-ho.

Mother optimization algorithm: a new human-based metaheuristic approach for solving engineering optimization

This article’s innovation and novelty are introducing a new metaheuristic method called mother optimization algorithm (MOA) that mimics the human interaction between a mother and her children. The real inspiration of MOA is to simulate the mother’s care of children in three phases education, advice, and upbringing. The mathematical model of MOA used in the search process and exploration is presented. The performance of MOA is assessed on a set of 52 benchmark functions, including unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, and the CEC 2017 test suite. The findings of optimizing unimodal functions indicate MOA’s high ability in local search and exploitation. The findings of optimization of high-dimensional multimodal functions indicate the high ability of MOA in global search and exploration. The findings of optimization of fixed-dimension multi-model functions and the CEC 2017 test suite show that MOA with a high ability to balance exploration and exploitation effectively supports the search process and can generate appropriate solutions for optimization problems. The outcomes quality obtained from MOA has been compared with the performance of 12 often-used metaheuristic algorithms. Upon analysis and comparison of the simulation results, it was found that the proposed MOA outperforms competing algorithms with superior and significantly more competitive performance. Precisely, the proposed MOA delivers better results in most objective functions. Furthermore, the application of MOA on four engineering design problems demonstrates the efficacy of the proposed approach in solving real-world optimization problems. The findings of the statistical analysis from the Wilcoxon signed-rank test show that MOA has a significant statistical superiority compared to the twelve well-known metaheuristic algorithms in managing the optimization problems studied in this paper.

Red Panda Optimization Algorithm: An Effective Bio-Inspired Metaheuristic Algorithm for Solving Engineering Optimization Problems

This paper presents a new bio-inspired metaheuristic algorithm called Red Panda Optimization (RPO) that imitates the natural behaviors of red pandas in nature. The main design idea of RPO is derived from two characteristic natural behaviors of red pandas: (i) foraging strategy, and (ii) climbing trees to rest. The proposed RPO approach is mathematically modeled in two phases of exploration based on the simulation of red pandas’ foraging strategy and exploitation based on the simulation of red pandas’ movement in climbing trees. The main advantage of the proposed approach is that there is no control parameter in its mathematical modeling, and for this reason, it does not need a parameter adjustment process. The performance of RPO is evaluated on fifty-two standard benchmark functions including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types as well as CEC 2017 test suite. The optimization results obtained by the proposed RPO approach are compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that RPO, by maintaining the balance between exploration and exploitation, is effective in solving optimization problems and its performance is superior over competitor algorithms. Based on the analysis of the optimization results, RPO has provided more successful performance compared to the competitor algorithms in 100% of unimodal functions, 100% of high-dimensional multimodal functions, 100% of fixed-dimensional multimodal functions, and 86.2% of CEC 2017 test suite benchmark functions. Also, the statistical analysis of the Wilcoxon rank sum test shows that the superiority of RPO in the competition with the compared algorithms is significant from a statistical point of view. In addition, the results of implementing RPO on four engineering design problems confirms the ability of the proposed approach to handle real-world optimization applications.

A new optimization algorithm based on average and subtraction of the best and worst members of the population for solving various optimization problems.

In this paper, a novel evolutionary-based method, called Average and Subtraction-Based Optimizer (ASBO), is presented to attain suitable quasi-optimal solutions for various optimization problems. The core idea in the design of the ASBO is to use the average information and the subtraction of the best and worst population members for guiding the algorithm population in the problem search space. The proposed ASBO is mathematically modeled with the ability to solve optimization problems. Twenty-three test functions, including unimodal and multimodal functions, have been employed to evaluate ASBO’s performance in effectively solving optimization problems. The optimization results of the unimodal functions, which have only one main peak, show the high ASBO’s exploitation power in converging towards global optima. In addition, the optimization results of the high-dimensional multimodal functions and fixed-dimensional multimodal functions, which have several peaks and local optima, indicate the high exploration power of ASBO in accurately searching the problem-solving space and not getting stuck in nonoptimal peaks. The simulation results show the proper balance between exploration and exploitation in ASBO in order to discover and present the optimal solution. In addition, the results obtained from the implementation of ASBO in optimizing these objective functions are analyzed compared with the results of nine well-known metaheuristic algorithms. Analysis of the optimization results obtained from ASBO against the performance of the nine compared algorithms indicates the superiority and competitiveness of the proposed algorithm in providing more appropriate solutions.

Human behavior-based optimization: a novel metaheuristic approach to solve complex optimization problems

Optimization techniques, specially evolutionary algorithms, have been widely used for solving various scientific and engineering optimization problems because of their flexibility and simplicity. In this paper, a novel metaheuristic optimization method, namely human behavior-based optimization (HBBO), is presented. Despite many of the optimization algorithms that use nature as the principal source of inspiration, HBBO uses the human behavior as the main source of inspiration. In this paper, first some human behaviors that are needed to understand the algorithm are discussed and after that it is shown that how it can be used for solving the practical optimization problems. HBBO is capable of solving many types of optimization problems such as high-dimensional multimodal functions, which have multiple local minima, and unimodal functions. In order to demonstrate the performance of HBBO, the proposed algorithm has been tested on a set of well-known benchmark functions and compared with other optimization algorithms. The results have been shown that this algorithm outperforms other optimization algorithms in terms of algorithm reliability, result accuracy and convergence speed.

A Scalable MapReduce-enabled Glowworm Swarm Optimization Approach for High Dimensional Multimodal Functions

Glowworm Swarm Optimization (GSO) is one of the common swarm intelligence algorithms, where GSO has the ability to optimize multimodal functions efficiently. In this paper, a parallel MapReduce-based GSO algorithm is proposed to speedup the GSO optimization process. The authors argue that GSO can be formulated based on the MapReduce parallel programming model quite naturally. In addition, they use higher dimensional multimodal benchmark functions for evaluating the proposed algorithm. The experimental results show that the proposed algorithm is appropriate for optimizing difficult multimodal functions with higher dimensions and achieving high peak capture rates. Furthermore, a scalability analysis shows that the proposed algorithm scales very well with increasing swarm sizes. In addition, an overhead of the Hadoop infrastructure is investigated to find if there is any relationship between the overhead, the swarm size, and number of nodes used.

An Improved Particle Swarm Optimization Algorithm

Particle swarm optimization (PSO) algorithm has the ability of global optimization , but it often suffers from premature convergence problem, especially in high-dimensional multimodal functions. In order to overcome the premature property and improve the global optimization performance of PSO algorithm, this paper proposes an improved particle swarm optimization algorithm , called IPSO. The simulation results of eight unimodal/multimodal benchmark functions demonstrate that IPSO is superior in enhancing the global convergence performance and avoiding the premature convergence problem to SPSO no matter on unimodal or multimodal high-dimensional (100 real-valued variables) functions.

Hybrid optimization algorithm based on chaos, cloud and particle swarm optimization algorithm

As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization (PSO) is applied to solve high-dimensional multi-modal functions, a hybrid optimization algorithm based on the cat mapping, the cloud model and PSO is proposed. While the PSO algorithm evolves a certain of generations, this algorithm applies the cat mapping to implement global disturbance of the poorer individuals, and employs the cloud model to execute local search of the better individuals; accordingly, the obtained best individuals form a new swarm. For this new swarm, the evolution operation is maintained with the PSO algorithm, using the parameter of pop_distr to balance the global and local search capacity of the algorithm, as well as, adopting the parameter of mix_gen to control mixing times of the algorithm. The comparative analysis is carried out on the basis of 4 functions and other algorithms. It indicates that this algorithm shows faster convergent speed and better solving precision for solving functions particularly those high-dimensional multi-modal functions. Finally, the suggested values are proposed for parameters pop_distr and mix_gen applied to different dimension functions via the comparative analysis of parameters.

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.

A study on the effect of v<SUB align=right>max in particle swarm optimisation with high dimension

Velocity threshold vmax is an important parameter of particle swarm optimisation. Different from other parameters, it affects the algorithm performance by restricting the moving size and direction of each particle. However, the current results are all with small dimensions no larger than 30. Because of the scientific development, many optimisation tasks are complex, high dimensional multi-modal functions. Therefore, in this paper, the authors investigate the selection principle of vmax with high dimension on numerical optimisation problems. To make a deep insight, the test suit consists of three different type benchmarks: unimodel, multi-modal functions with a few local optima and multi-modal functions with many local optima. Simulation results show the 10% of the upper bound of the domain may generally obtain the satisfied solution within the allowed iterations.

Study on Improvement of Memory Cell Control in Hybridization of Immune Algorithm and Gradient Search for Multiple Solution Search

Many evolutionary computation methods have been proposed and applied to real world problems. But gradient methods are still effective in problems involving real-coded parameters. In addition, it is desirable to find not only an optimal solution but also plural optimal and semi-optimal solutions in most real world problems. Although a hybrid algorithm combining Immune Algorithm (IA) and Quasi-Newton method (QN) has been proposed for multiple solution search, its memory cell control sometimes fails to keep semi-optimal solutions whose evaluation value is not so high. In addition, because the hybrid algorithm applies QN only to memory cell candidates, QN can be used as local search operator only after global search by IA. This paper proposes an improved memory cell control which restricts existence of redundant memory cells, and a QN application method which uses QN even in early search stage. Experimental results have shown that the hybrid algorithm involving the proposed improvements can find optimal and semi-optimal solutions with high accuracy and efficiency even in high-dimensional multimodal functions involving epistasis.