Multiobjective Differential Evolution for Higher-Dimensional Multimodal Multiobjective Optimization

In multimodal multiobjective optimization problems(MMOPs),there are several Pareto optimal solutions corre-sponding to the identical objective vector.This paper proposes a new differential evolution algorithm to solve MMOPs with higher-dimensional decision variables.Due to the increase in the dimensions of decision variables in real-world MMOPs,it is diffi-cult for current multimodal multiobjective optimization evolu-tionary algorithms(MMOEAs)to find multiple Pareto optimal solutions.The proposed algorithm adopts a dual-population framework and an improved environmental selection method.It utilizes a convergence archive to help the first population improve the quality of solutions.The improved environmental selection method enables the other population to search the remaining decision space and reserve more Pareto optimal solutions through the information of the first population.The combination of these two strategies helps to effectively balance and enhance conver-gence and diversity performance.In addition,to study the per-formance of the proposed algorithm,a novel set of multimodal multiobjective optimization test functions with extensible decision variables is designed.The proposed MMOEA is certified to be effective through comparison with six state-of-the-art MMOEAs on the test functions.

Synergistic Swarm Optimization Algorithm

This research paper presents a novel optimization method called the Synergistic Swarm Optimization Algorithm(SSOA).The SSOA combines the principles of swarmintelligence and synergistic cooperation to search for optimal solutions efficiently.A synergistic cooperation mechanism is employed,where particles exchange information and learn from each other to improve their search behaviors.This cooperation enhances the exploitation of promising regions in the search space while maintaining exploration capabilities.Furthermore,adaptive mechanisms,such as dynamic parameter adjustment and diversification strategies,are incorporated to balance exploration and exploitation.By leveraging the collaborative nature of swarm intelligence and integrating synergistic cooperation,the SSOAmethod aims to achieve superior convergence speed and solution quality performance compared to other optimization algorithms.The effectiveness of the proposed SSOA is investigated in solving the 23 benchmark functions and various engineering design problems.The experimental results highlight the effectiveness and potential of the SSOA method in addressing challenging optimization problems,making it a promising tool for a wide range of applications in engineering and beyond.Matlab codes of SSOA are available at:https://www.mathworks.com/matlabcentral/fileexchange/153466-synergistic-swarm-optimization-algorithm.

Empirical Review of Standard Benchmark Functions Using Evolutionary Global Optimization

We have employed a recent implementation of genetic algorithms to study a range of standard benchmark functions for global optimization. It turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters. The latter properties seem to be simulated better by two other types of benchmark functions. One type is designed to be deceptive, exemplified here by Lunacek’s function. The other type offers additional advantages of markedly increased complexity and of broad tunability in search space characteristics. For the latter type, we use an implementation based on randomly distributed Gaussians. We advocate the use of the latter types of test functions for algorithm development and benchmarking.

An Improved Bald Eagle Search Algorithm with Cauchy Mutation and Adaptive Weight Factor for Engineering Optimization

The Bald Eagle Search algorithm(BES)is an emerging meta-heuristic algorithm.The algorithm simulates the hunting behavior of eagles,and obtains an optimal solution through three stages,namely selection stage,search stage and swooping stage.However,BES tends to drop-in local optimization and the maximum value of search space needs to be improved.To fill this research gap,we propose an improved bald eagle algorithm(CABES)that integrates Cauchy mutation and adaptive optimization to improve the performance of BES from local optima.Firstly,CABES introduces the Cauchy mutation strategy to adjust the step size of the selection stage,to select a better search range.Secondly,in the search stage,CABES updates the search position update formula by an adaptive weight factor to further promote the local optimization capability of BES.To verify the performance of CABES,the benchmark function of CEC2017 is used to simulate the algorithm.The findings of the tests are compared to those of the Particle Swarm Optimization algorithm(PSO),Whale Optimization Algorithm(WOA)and Archimedes Algorithm(AOA).The experimental results show that CABES can provide good exploration and development capabilities,and it has strong competitiveness in testing algorithms.Finally,CABES is applied to four constrained engineering problems and a groundwater engineeringmodel,which further verifies the effectiveness and efficiency of CABES in practical engineering problems.

A Chaos Sparrow Search Algorithm with Logarithmic Spiral and Adaptive Step for Engineering Problems

The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence speed and difficulty in jumping out of the local optimum.In order to overcome these shortcomings,a chaotic sparrow search algorithm based on logarithmic spiral strategy and adaptive step strategy(CLSSA)is proposed in this paper.Firstly,in order to balance the exploration and exploitation ability of the algorithm,chaotic mapping is introduced to adjust the main parameters of SSA.Secondly,in order to improve the diversity of the population and enhance the search of the surrounding space,the logarithmic spiral strategy is introduced to improve the sparrow search mechanism.Finally,the adaptive step strategy is introduced to better control the process of algorithm exploitation and exploration.The best chaotic map is determined by different test functions,and the CLSSA with the best chaotic map is applied to solve 23 benchmark functions and 3 classical engineering problems.The simulation results show that the iterative map is the best chaotic map,and CLSSA is efficient and useful for engineering problems,which is better than all comparison algorithms.

θ-PSO: a new strategy of particle swarm optimization

Particle swarm optimization (PSO) is an efficient, robust and simple optimization algorithm. Most studies are mainly concentrated on better understanding of the standard PSO control parameters, such as acceleration coefficients, etc. In this paper, a more simple strategy of PSO algorithm called θ-PSO is proposed. In θ-PSO, an increment of phase angle vector replaces the increment of velocity vector and the positions are decided by the mapping of phase angles. Benchmark testing of nonlinear func- tions is described and the results show that the performance of θ-PSO is much more effective than that of the standard PSO.

Non-dominated sorting quantum particle swarm optimization and its application in cognitive radio spectrum allocation

In order to solve discrete multi-objective optimization problems, a non-dominated sorting quantum particle swarm optimization (NSQPSO) based on non-dominated sorting and quantum particle swarm optimization is proposed, and the performance of the NSQPSO is evaluated through five classical benchmark functions. The quantum particle swarm optimization (QPSO) applies the quantum computing theory to particle swarm optimization, and thus has the advantages of both quantum computing theory and particle swarm optimization, so it has a faster convergence rate and a more accurate convergence value. Therefore, QPSO is used as the evolutionary method of the proposed NSQPSO. Also NSQPSO is used to solve cognitive radio spectrum allocation problem. The methods to complete spectrum allocation in previous literature only consider one objective, i.e. network utilization or fairness, but the proposed NSQPSO method, can consider both network utilization and fairness simultaneously through obtaining Pareto front solutions. Cognitive radio systems can select one solution from the Pareto front solutions according to the weight of network reward and fairness. If one weight is unit and the other is zero, then it becomes single objective optimization, so the proposed NSQPSO method has a much wider application range. The experimental research results show that the NSQPS can obtain the same non-dominated solutions as exhaustive search but takes much less time in small dimensions; while in large dimensions, where the problem cannot be solved by exhaustive search, the NSQPSO can still solve the problem, which proves the effectiveness of NSQPSO.

An improved self-adaptive membrane computing optimization algorithm and its applications in residue hydrogenating model parameter estimation

In order to solve the non-linear and high-dimensional optimization problems more effectively, an improved self-adaptive membrane computing(ISMC) optimization algorithm was proposed. The proposed ISMC algorithm applied improved self-adaptive crossover and mutation formulae that can provide appropriate crossover operator and mutation operator based on different functions of the objects and the number of iterations. The performance of ISMC was tested by the benchmark functions. The simulation results for residue hydrogenating kinetics model parameter estimation show that the proposed method is superior to the traditional intelligent algorithms in terms of convergence accuracy and stability in solving the complex parameter optimization problems.

A New Class of Hybrid Particle Swarm Optimization Algorithm

A new class of hybrid particle swarm optimization （PSO） algorithm is developed for solving the premature convergence caused by some particles in standard PSO fall into stagnation. In this algorithm, the linearly decreasing inertia weight technique （LDIW） and the mutative scale chaos optimization algorithm （MSCOA） are combined with standard PSO, which are used to balance the global and local exploration abilities and enhance the local searching abilities, respectively. In order to evaluate the performance of the new method, three benchmark functions are used. The simulation results confirm the proposed algorithm can greatly enhance the searching ability and effectively improve the premature convergence.

Adaptive mutation sparrow search algorithm-Elman-AdaBoost model for predicting the deformation of subway tunnels

A novel coupled model integrating Elman-AdaBoost with adaptive mutation sparrow search algorithm(AM-SSA),called AMSSAElman-AdaBoost,is proposed for predicting the existing metro tunnel deformation induced by adjacent deep excavations in soft ground.The novelty is that the modified SSA proposes adaptive adjustment strategy to create a balance between the capacity of exploitation and exploration.In AM-SSA,firstly,the population is initialized by cat mapping chaotic sequences to improve the ergodicity and randomness of the individual sparrow,enhancing the global search ability.Then the individuals are adjusted by Tent chaotic disturbance and Cauchy mutation to avoid the population being too concentrated or scattered,expanding the local search ability.Finally,the adaptive producer-scrounger number adjustment formula is introduced to balance the ability to seek the global and local optimal.In addition,it leads to the improved algorithm achieving a better accuracy level and convergence speed compared with the original SSA.To demonstrate the effectiveness and reliability of AM-SSA,23 classical benchmark functions and 25 IEEE Congress on Evolutionary Computation benchmark test functions(CEC2005),are employed as the numerical examples and investigated in comparison with some wellknown optimization algorithms.The statistical results indicate the promising performance of AM-SSA in a variety of optimization with constrained and unknown search spaces.By utilizing the AdaBoost algorithm,multiple sets of weak AMSSA-Elman predictor functions are restructured into one strong predictor by successive iterations for the tunnel deformation prediction output.Additionally,the on-site monitoring data acquired from a deep excavation project in Ningbo,China,were selected as the training and testing sample.Meanwhile,the predictive outcomes are compared with those of other different optimization and machine learning techniques.In the end,the obtained results in this real-world geotechnical engineering field reveal the feasibility of the proposed hybrid algorithm model,illustrating its power and superiority in terms of computational efficiency,accuracy,stability,and robustness.More critically,by observing data in real time on daily basis,the structural safety associated with metro tunnels could be supervised,which enables decision-makers to take concrete control and protection measures.

Wind Driven Butterfly Optimization Algorithm with Hybrid Mechanism Avoiding Natural Enemies for Global Optimization and PID Controller Design

This paper presents a Butterfly Optimization Algorithm(BOA)with a wind-driven mechanism for avoiding natural enemies known as WDBOA.To further balance the basic BOA algorithm's exploration and exploitation capabilities,the butterfly actions were divided into downwind and upwind states.The algorithm of exploration ability was improved with the wind,while the algorithm of exploitation ability was improved against the wind.Also,a mechanism of avoiding natural enemies based on Lévy flight was introduced for the purpose of enhancing its global searching ability.Aiming at improving the explorative performance at the initial stages and later stages,the fragrance generation method was modified.To evaluate the effectiveness of the suggested algorithm,a comparative study was done with six classical metaheuristic algorithms and three BOA variant optimization techniques on 18 benchmark functions.Further,the performance of the suggested technique in addressing some complicated problems in various dimensions was evaluated using CEC 2017 and CEC 2020.Finally,the WDBOA algorithm is used proportional-integral-derivative(PID)controller parameter optimization.Experimental results demonstrate that the WDBOA based PID controller has better control performance in comparison with other PID controllers tuned by the Genetic Algorithm(GA),Flower Pollination Algorithm(FPA),Cuckoo Search(CS)and BOA.

Hybrid Modified Chimp Optimization Algorithm and Reinforcement Learning for Global Numeric Optimization

Chimp Optimization Algorithm(ChOA)is one of the most efficient recent optimization algorithms,which proved its ability to deal with different problems in various do-mains.However,ChOA suffers from the weakness of the local search technique which leads to a loss of diversity,getting stuck in a local minimum,and procuring premature convergence.In response to these defects,this paper proposes an improved ChOA algorithm based on using Opposition-based learning(OBL)to enhance the choice of better solutions,written as OChOA.Then,utilizing Reinforcement Learning(RL)to improve the local research technique of OChOA,called RLOChOA.This way effectively avoids the algorithm falling into local optimum.The performance of the proposed RLOChOA algorithm is evaluated using the Friedman rank test on a set of CEC 2015 and CEC 2017 benchmark functions problems and a set of CEC 2011 real-world problems.Numerical results and statistical experiments show that RLOChOA provides better solution quality,convergence accuracy and stability compared with other state-of-the-art algorithms.

Enhanced Moth-flame Optimization Based on Cultural Learning and Gaussian Mutation

This paper presents an Enhanced Moth-Flame Optimization （EMFO） technique based on Cultural Learning （CL） and Gaussian Mutation （GM）. The mechanism of CL and the operator of GM are incorporated to the original algorithm of Moth-Flame Optimization （MFO）. CL plays an important role in the inheritance of historical experiences and stimulates moths to obtain information from flames more effectively, which helps MFO enhance its searching ability. Furthermore, in order to overcome the disadvantage of trapping into local optima, the operator of GM is introduced to MFO. This operator acts on the best flame in order to generate several variant ones, which can increase the diversity. The proposed algorithm of EMFO has been comprehensively evaluated on 13 benchmark functions, in comparison with MFO. Simulation results verify that EMFO shows a significant improvement on MFO, in terms of solution quality and algorithmic reliability.

Modified chaotic ant swarm to function optimization

The chaotic ant swarm algorithm （CAS） is an optimization algorithm based on swarm intelligence theory, and it is inspired by the chaotic and self-organizing behavior of the ants in nature. Based on the analysis of the properties of the CAS, this article proposes a variation on the CAS called the modified chaotic ant swarm （MCAS）, which employs two novel strategies to significantly improve the performance of the original algorithm. This is achieved by restricting the variables to search ranges and making the global best ant to learn from different ants＇ best information in the end. The simulation of the MCAS on five benchmark functions shows that the MCAS improves the precision of the solution.

A Hybrid Moth Flame Optimization Algorithm for Global Optimization

The Moth Flame Optimization(MFO)algorithm shows decent performance results compared to other meta-heuristic algorithms for tackling non-linear constrained global optimization problems.However,it still suffers from obtaining quality solution and slow convergence speed.On the other hand,the Butterfly Optimization Algorithm(BOA)is a comparatively new algorithm which is gaining its popularity due to its simplicity,but it also suffers from poor exploitation ability.In this study,a novel hybrid algorithm,h-MFOBOA,is introduced,which integrates BOA with the MFO algorithm to overcome the shortcomings of both the algorithms and at the same time inherit their advantages.For performance evaluation,the proposed h-MFOBOA algorithm is applied on 23 classical benchmark functions with varied complexity.The tested results of the proposed algorithm are compared with some well-known traditional meta-heuristic algorithms as well as MFO variants.Friedman rank test and Wilcoxon signed rank test are employed to measure the performance of the newly introduced algorithm statistically.The computational complexity has been measured.Moreover,the proposed algorithm has been applied to solve one constrained and one unconstrained real-life problems to examine its problem-solving capability of both type of problems.The comparison results of benchmark functions,statistical analysis,real-world problems confirm that the proposed h-MFOBOA algorithm provides superior results compared to the other conventional optimization algorithms.

A new parameter setting-based modified differential evolution for function optimization

The population-based efficient iterative evolutionary algorithm(EA)is differential evolution(DE).It has fewer control parameters but is useful when dealing with complex problems of optimization in the real world.A great deal of progress has already been made and implemented in various fields of engineering and science.Nevertheless,DE is prone to the setting of control parameters in its performance evaluation.Therefore,the appropriate adjustment of the time-consuming control parameters is necessary to achieve optimal DE efficiency.This research proposes a new version of the DE algorithm control parameters and mutation operator.For the justifiability of the suggested method,several benchmark functions are taken from the literature.The test results are contrasted with other literary algorithms.