Mutation Strategies Of Differential Evolution Research Articles

An adapted Black Widow Optimization Algorithm for Financial Portfolio Optimization Problem with cardinalty and budget constraints

Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz’s 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.

DEMFFA: a multi-strategy modified Fennec Fox algorithm with mixed improved differential evolutionary variation strategies

The Fennec Fox algorithm (FFA) is a new meta-heuristic algorithm that is primarily inspired by the Fennec fox's ability to dig and escape from wild predators. Compared with other classical algorithms, FFA shows strong competitiveness. The “No free lunch” theorem shows that an algorithm has different effects in the face of different problems, such as: when solving high-dimensional or more complex applications, there are challenges such as easily falling into local optimal and slow convergence speed. To solve this problem with FFA, in this paper, an improved Fenna fox algorithm DEMFFA is proposed by adding sin chaotic mapping, formula factor adjustment, Cauchy operator mutation, and differential evolution mutation strategies. Firstly, a sin chaotic mapping strategy is added in the initialization stage to make the population distribution more uniform, thus speeding up the algorithm convergence speed. Secondly, in order to expedite the convergence speed of the algorithm, adjustments are made to the factors of the formula whose position is updated in the first stage, resulting in faster convergence. Finally, in order to prevent the algorithm from getting into the local optimal too early and expand the search space of the population, the Cauchy operator mutation strategy and differential evolution mutation strategy are added after the first and second stages of the original algorithm update. In order to verify the performance of the proposed DEMFFA, qualitative analysis is carried out on different test sets, and the proposed algorithm is tested with the original FFA, other classical algorithms, improved algorithms, and newly proposed algorithms on three different test sets. And we also carried out a qualitative analysis of the CEC2020. In addition, DEMFFA is applied to 10 practical engineering design problems and a complex 24-bar truss topology optimization problem, and the results show that the DEMFFA algorithm has the potential to solve complex problems.

Differential Evolution Using Enhanced Mutation Strategy Based on Random Neighbor Selection

Symmetry in a differential evolution (DE) transforms a solution without impacting the family of solutions. For symmetrical problems in differential equations, DE is a strong evolutionary algorithm that provides a powerful solution to resolve global optimization problems. DE/best/1 and DE/rand/1 are the two most commonly used mutation strategies in DE. The former provides better exploitation while the latter ensures better exploration. DE/Neighbor/1 is an improved form of DE/rand/1 to maintain a balance between exploration and exploitation which was used with a random neighbor-based differential evolution (RNDE) algorithm. However, this mutation strategy slows down convergence. It should achieve a global minimum by using 1000 × D, where D is the dimension, but due to exploration and exploitation balancing trade-offs, it can not achieve a global minimum within the range of 1000 × D in some of the objective functions. To overcome this issue, a new and enhanced mutation strategy and algorithm have been introduced in this paper, called DE/Neighbor/2, as well as an improved random neighbor-based differential evolution algorithm. The new DE/Neighbor/2 mutation strategy also uses neighbor information such as DE/Neighbor/1; however, in addition, we add weighted differences after various tests. The DE/Neighbor/2 and IRNDE algorithm has also been tested on the same 27 commonly used benchmark functions on which the DE/Neighbor/1 mutation strategy and RNDE were tested. Experimental results demonstrate that the DE/Neighbor/2 mutation strategy and IRNDE algorithm show overall better and faster convergence than the DE/Neighbor/1 mutation strategy and RNDE algorithm. The parametric significance test shows that there is a significance difference in the performance of RNDE and IRNDE algorithms at the 0.05 level of significance.

X-MODE: Extended Multi-operator Differential Evolution algorithm

During past years, multi-operator optimization techniques gained vast attention due to their flexible structure and self-adaptation. They yielded promising results when compared with the single-operator based methods. However, the existing multi-operator models can be further improved regarding exploration–exploitation equilibrium. Therefore, we propose a novel multi-operator algorithm for solving single-objective optimization problems that categorize differential evolution mutation strategies according to the purpose each of them fulfills. A new mutation scheme is also presented to promote the mutation across search space boundaries. A novel extended crossover technique is proposed in this study to retain the properties of applied mutation strategies, as well as develop the potential of the standard crossover function. The model is afterward evaluated on the CEC2020 benchmark test-suite. The proposed algorithm has overwhelming results while comparing single-operator and multi-operator algorithms for several classes of functions. It has been observed from the study that proposed mutation and crossover techniques help improve the efficiency of MODE variants.

Differential Evolution with Adaptive Grid-Based Mutation Strategy for Multi-Objective Optimization

Differential Evolution (DE) has been extensively adopted for multi-objective optimization due to its efficient and straightforward framework. In DE, the mutation operator influences the evolution of the population. In this paper, an adaptive Grid-based Multi-Objective Differential Evolution is proposed to address multi-objective optimization (ad-GrMODE). In ad-GrMODE, an adaptive grid environment is employed to perform a mutation strategy in conjunction with performance indicators. The grid reflects the convergence and diversity performance together but is associated with the user-specified parameter “div”. To solve this problem, we adaptively tune the parameter “div”. Among the DE mutation strategies, “DE/current-to-best/1” is applied extensively in single-objective optimization. This paper extends the application of “DE/current-to-best/1” to multi-objective optimization. In addition, a two-stage environmental selection is adopted in ad-GrMODE, where in the first stage, one-to-one selection between the parent and its corresponding offspring solution is performed. In addition, to preserve elitism, a stochastic selection is adopted with respect to performance metrics. We conducted experiments on 16 benchmark problems, including the DTLZ and WFG, to validate the performance of the proposed ad-GrMODE algorithm. Besides the benchmark problem, we evaluated the performance of the proposed method on real-world problems. Results of the experiments show that the proposed algorithm outperforms the eight state-of-the-art algorithms.

Comparative Study on the Synthesis of Path-Generating Four-Bar Linkages Using Metaheuristic Optimization Algorithms

Four-bar linkages are one of the most widely used mechanisms in industries. This paper presents a comparative study on the accuracy and efficiency of the optimum synthesis of path-generating four-bar linkages using five metaheuristic optimization algorithms. The utilized metaheuristic methods included two swarm intelligence-based algorithms, i.e., particle swarm optimization and hybrid particle swarm optimization, and three evolutionary-based algorithms, i.e., differential evolution, ensemble of parameters and mutation strategies in differential evolution, and linearly ensemble of parameters and mutation strategies in differential evolution. The objective function to be minimized is the sum of squares of the distance between the generated points and the precision points of a coupler point. The optimal design of four-bar linkages must meet the Grashof’s criteria and exhibit sequential constraints that can prevent the occurrence of order defect. This study investigated five representative cases of the dimensional synthesis of four-bar path generators with and without prescribed timing and compared the optimal solutions of the utilized five metaheuristic methods to those of previously reported algorithms in literature. The improved metaheuristic methods exhibited superior optimal solution and enhanced reliability compared to the original methods. Moreover, three improved metaheuristic methods were not only easy implemented, but also more efficient for solving the optimal synthesis problems, particularly for high dimensional problems.

An adaptive differential evolution framework based on population feature information

Differential Evolution (DE) is an effective global optimization algorithm, and many existing adaptive variants of it have been proposed to solve engineering problems. It is well known that population feature information that refers to some mathematical statistic feature information of all individuals in the dimension of decision space, and it can reflect the features of the problem to be solved. However, the population feature information has not been fully utilized by DE’s adaptive variants. As a result, those adaptive variants do not obtain promising performance in optimizing nonlinear, non-differentiable and non-separable multi-modal problems. To make adequate extraction and effective use of population feature information, we propose an adaptive differential evolution framework based on population feature information in this paper, named PFI for short. In the PFI framework, the population feature information consists of the standard deviation of fitness value and the sum of standard deviation of each dimension of population. Besides, population feature information archive is designed to store the population feature information and success parameters, and the utilization mechanism of population feature information assigns historical success parameters with high population feature similarity to the current corresponding population. Four widely used mutation strategies of DE are incorporated into the PFI framework to evaluate its performance by optimizing CEC2005, CEC2015, CEC2020 benchmark functions and two real world applications to verify the performance of the PFI framework. Experiment results have demonstrated that PFI framework can significantly improve the performance of 4 popular mutation strategies of DE.

Combined heat and power economic dispatch using an adaptive cuckoo search with differential evolution mutation

In power system operation, the combined heat and power economic dispatch (CHPED) is an attractive and momentous optimization problem where the major objective is to find an optimal generation schedule of heat and power to meet the heat and power demands with the minimum cost, while satisfying various practical operation constraints. This paper puts forward an adaptive cuckoo search with differential evolution mutation (ACS-DEM) for solving the CHPED problem. Compared with the basic cuckoo search (CS), there are three main improvements in the proposed ACS-DEM. The first improvement is that adaptive parameters are employed and therefore no parameter adjustment is required. The second is the incorporation of a Gaussian sampling strategy into the global search phase of the algorithm to increase the exploration capability. The third is the introduction of an improved differential evolution mutation strategy into the local search phase to replace the simple biased random walk in the basic CS, thus discouraging the blindness and enhancing the exploitation capability. The outstanding performance of ACS-DEM is first confirmed through the test suite from the 2017 Conference on Evolutionary Computation and then demonstrated on several CHPED problems. The obtained dispatch schedules from ACS-DEM are feasible and in most cases exhibit a distinct improvement over the results offered by six other CS-based algorithms, one state-of-the-art differential evolution algorithm, as well as recent works in this field.

Differential evolution with mixed mutation strategy based on deep reinforcement learning

The performance of differential evolution (DE) algorithm significantly depends on mutation strategy. However, there are six commonly used mutation strategies in DE. It is difficult to select a reasonable mutation strategy in solving the different real-life optimization problems. In general, the selection of the most appropriate mutation strategy is based on personal experience. To address this problem, a mixed mutation strategy DE algorithm based on deep Q-network (DQN), named DEDQN is proposed in this paper, in which a deep reinforcement learning approach realizes the adaptive selection of mutation strategy in the evolution process. Two steps are needed for the application of DQN to DE. First, the DQN is trained offline through collecting the data about fitness landscape and the benefit (reward) of applying each mutation strategy during multiple runs of DEDQN tackling the training functions. Second, the mutation strategy is predicted by the trained DQN at each generation according to the fitness landscape of every test function. Besides, a historical memory parameter adaptation mechanism is also utilized to improve the DEDQN. The performance of the DEDQN algorithm is evaluated by the CEC2017 benchmark function set, and five state-of-the-art DE algorithms are compared with the DEDQN in the experiments. The experimental results indicate the competitive performance of the proposed algorithm.

A Hybrid Differential Symbiotic Organisms Search Algorithm for UAV Path Planning.

Unmanned aerial vehicle (UAV) path planning is crucial in UAV mission fulfillment, with the aim of finding a satisfactory path within affordable time and moderate computation resources. The problem is challenging due to the complexity of the flight environment, especially in three-dimensional scenarios with obstacles. To solve the problem, a hybrid differential symbiotic organisms search (HDSOS) algorithm is proposed by combining the mutation strategy of differential evolution (DE) with the modified strategies of symbiotic organism search (SOS). The proposed algorithm preserves the local search capability of SOS, and at the same time has impressive global search ability. The concept of traction function is put forward and used to improve the efficiency. Moreover, a perturbation strategy is adopted to further enhance the robustness of the algorithm. Extensive simulation experiments and comparative study in two-dimensional and three-dimensional scenarios show the superiority of the proposed algorithm compared with particle swarm optimization (PSO), DE, and SOS algorithm.

Nature-Inspired Hybrid Multi-objective Optimization Algorithms in Search of Near-OGRs to Eliminate FWM Noise Signals in Optical WDM Systems and their Performance Comparison

Nowadays, the multi-objective optimizing algorithms which are inspired by nature are widely used in solving the many objectives of NP-complete engineering and industrial design problems. To eliminate one of the prevailing nonlinear optical noise mechanisms, i.e., four-wave mixing noise signals in the optical wavelength division multiplexing (WDM) systems, several unequally spaced channel-allocation algorithms were found that require increased bandwidth than the equally spaced channel-allocation. One of the bandwidths efficient, a USCA algorithm can be designed by considering the optimal Golomb rulers (OGRs) in optical WDM systems. Two nature-inspired multi-objective optimization algorithms (MOAs), namely multi-objective big bang–big crunch (MOBB-BC) optimization algorithm and multi-objective firefly optimization algorithm (MOFA), to solve NP-complete OGR problem in an optical WDM system are proposed here. Additionally, the algorithms MOBB-BC and MOFA are hybridized by introducing differential evolution (DE) based mutation and random walk features in their standard forms. These two features have the potential to explore new search space for MOAs to search for OGRs in a reasonable time. The algorithms presented here solve the two objectives in optical WDM systems, one is the occupied length by the ruler, and the other is total channel bandwidth obtained by OGRs. The obtained results suggest that the considered nature-inspired MOAs are computationally better than the other algorithms to search near-OGRs. To assert the improvement in the MOAs further, the non-parametric Friedman statistical analysis test is employed. The results conclude that for large mark values, the hybridization of MOFA with both DE mutation and Levy-flight strategies potentially performs better than the MOBB-BC and its hybrid forms to search OGR sequences. The hybrid algorithm MOBB-BC can explore OGRs up to 8-marks and near-OGRs for 9 to 20-marks with a maximum computation time of 27 h, whereas hybrid MOFA can examine up to 16-mark OGRs, but finds 17 to 20-mark near-OGRs with the maximum computation time of 20 h. The success rate of the proposed hybrid MOFA to search best OGRs up to 20-marks is 80%, whereas for hybrid algorithm MOBB-BC is 40%.

A local surrogate-based parallel optimization for analog circuits

Computationally expensive simulations make challenges for analog/RF circuit and electromagnetic device design automation, where efficiency is a key issue. Both surrogate-based optimization and parallel computing play an important role in addressing this challenge. However, most surrogate-based parallel optimizations use global surrogate models for the entire database or multiple local surrogate models for individuals. Under the condition of limited computing capability, multi-constraints and the curse of dimensionality creates great difficulty in building such accurate surrogate models for large-scale analog/RF circuits. In order to address this problem, a Local Surrogate-based Parallel Optimization (LSPO) for analog/RF circuits is proposed. The state-of-the-art surrogate model-aware evolutionary search (SMAS) framework is used as the foundation of LSPO. The combination of three differential evolution mutation strategies and its self-adaptive adoption mechanism helps SMAS search for the optimal design in a parallel computing environment. Through experiments on a two-stage operational amplifier, a biased-based two-stage operational amplifier, and three benchmark problems with different complexity, it is proved that the LSPO can give a comparative solution in a shorter time, and show better optimization ability than the parallel differential evolution algorithm and state-of-the-art surrogate-based optimization method.

An adaptive mutation strategy for differential evolution algorithm based on particle swarm optimization

Differential evolution (DE) algorithm is a very effective algorithm used for solving wide range of optimization problems. However, the performance of DE is dependent on the control parameters and to choose the right parameter value and tuning of these parameters is a challenging task. Therefore, a novel variant of differential evolution algorithm based on particle swarm optimization (DEPSO) is proposed to improve the overall performance of Differential evolution algorithm. In our proposed approach, we are using DE mutation strategy during the initial phase of evolution and therefore enlarge its search space possibly to the extent that helps in finding more encouraging results and thus avoid premature convergence. During the subsequent phase of evolution process, this value of sigmoid function reduces with the increase of number of iterations. In this scenario, there is a greater probability of operating PSO mutation strategy and thus this sigmoid function helps in improving the precision and convergence speed. The Performance of our proposed algorithm is tested with 10 benchmark test functions on 50 and 25 dimensions set, also tested with 11 test functions on 30- and 100-dimension test functions. We have also tested our proposed algorithm with 8 test functions on high dimension set as 500- and 1000-dimensions. The performance comparison shows that our proposed variant is giving significant improvement in convergence speed and thus avoiding premature convergence. Average performance of DEPSO is better than classical DE, PSO and other algorithms in comparison.

A path planning method for UAVs based on multi-objective pigeon-inspired optimisation and differential evolution

Inspired by the behaviour of pigeon flocks, an improved method of path planning and autonomous formation for unmanned aerial vehicles based on the pigeon-inspired optimisation and differential evolution is proposed in this paper. Firstly, the mathematical model for UAV path planning is devised as a multi-objective optimisation with three indices, i.e., the length of a path, the sinuosity of a path, and the risk of a path. Then, the method integrated by pigeon-inspired optimisation and mutation strategies of differential evolution is developed to optimise feasible paths. Besides, Pareto dominance is applied to select the global best position of a pigeon. Finally, a series of simulation results compared with standard particle swarm optimisation algorithm and standard differential evolution algorithm show the effectiveness of our method.

A novel mutation strategy selection mechanism for differential evolution based on local fitness landscape

The performance of differential evolution (DE) algorithm highly depends on the selection of mutation strategy. However, there are six commonly used mutation strategies in DE. Therefore, it is a challenging task to choose an appropriate mutation strategy for a specific optimization problem. For a better tackle this problem, in this paper, a novel DE algorithm based on local fitness landscape called LFLDE is proposed, in which the local fitness landscape information of the problem is investigated to guide the selection of the mutation strategy for each given problem at each generation. In addition, a novel control parameter adaptive mechanism is used to improve the proposed algorithm. In the experiments, a total of 29 test functions originated from CEC2017 single-objective test function suite which are utilized to evaluate the performance of the proposed algorithm. The Wilcoxon rank-sum test and Friedman rank test results reveal that the performance of the proposed algorithm is better than the other five representative DE algorithms.

Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem

The optimization performance of differential evolution(DE) algorithm significantly depends on control parameters and mutation strategy. However, it is difficult to set suitable control parameters and select reasonable mutation strategy for DE in solving an actual engineering optimization problem. To solve these problems, a new optimal mutation strategy based on the complementary advantages of five mutation strategies is designed to develop a novel improved DE algorithm with the wavelet basis function, named WMSDE, which can improve the search quality, accelerate convergence and avoid fall into local optimum and stagnation. In the proposed WMSDE, the initial population is divided into several subpopulations to exchange search information between the different subpopulations and improve the population diversity to a certain extent. The wavelet basis function and normal distribution function are used to control the scaling factor and the crossover rate respectively in order to ensure the diversity of solutions and accelerate convergence. The new optimal mutation strategy is used to improve the local search ability and ensure the global search ability. Finally, the proposed WMSDE is compared with five state-of-the-art DE variants by 11 benchmark functions. The experiment results indicate that the proposed WMSDE can avoid premature convergence, balance local search ability and global search ability, accelerate convergence, improve the population diversity and the search quality. Additionally, a real-world airport gate assignment problem is employed to further prove the effectiveness of the proposed WMSDE. The results show that it can effectively solve the complex airport gate assignment problem, and obtain airport gate assignment rate of 97.6%.

Adaptive differential evolution with a new joint parameter adaptation method

Differential evolution (DE) is a population-based metaheuristic algorithm that has been proved powerful in solving a wide range of real-parameter optimization tasks. However, the selection of the mutation strategy and control parameters in DE is problem dependent, and inappropriate specification of them will lead to poor performance of the algorithm such as slow convergence and early stagnation in a local optimum. This paper proposes a new method termed as Joint Adaptation of Parameters in DE (JAPDE). The key idea lies in dynamically updating the selection probabilities for a complete set of pairs of parameter generating functions based on feedback information acquired during the search by DE. Further, for mutation strategy adaptation, the Rank-Based Adaptation (RAM) method is utilized to facilitate the learning of multiple probability distributions, each of which corresponds to an interval of fitness ranks of individuals in the population. The coupling of RAM with JAPDE results in the new RAM-JAPDE algorithm that enables simultaneous adaptation of the selection probabilities for pairs of control parameters and mutation strategies in DE. The merit of RAM-JAPDE has been evaluated on the benchmark test suit proposed in CEC2014 in comparison to many well-known DE algorithms. The results of experiments demonstrate that the proposed RAM-JAPDE algorithm outperforms or is competitive to the other related DE variants that perform mutation strategy and control parameter adaptation, respectively.

Estimation of Software Development Effort: A Differential Evolution Approach

Several software effort estimation techniques based on mathematical formulations have been proposed, however there is little consensus on the best technique for effort estimation, which can predict the estimated effort optimally for any given project. Much research has been carried out in finding out the most suitable parameter values for accurate effort estimation. This research investigates the efficacy of Differential Evolution algorithms in improving the parameter values for algorithmic models like CoCoMo and CoCoMo II. Parameter values were obtained by using the three successful mutation strategies in Differential Evolution. The proposed methodology was tested on two datasets from the Promise Repository. Test results were compared with the original CoCoMo and CoCoMo II models based on MMRE. The proposed differential evolution approach predicted the estimated effort more accurately than the original models for the two datasets under consideration.

Efficient Design Optimization of High-Performance MEMS Based on a Surrogate-Assisted Self-Adaptive Differential Evolution

High-performance microelectromechanical systems (MEMS) are playing a critical role in modern engineering systems. Due to computationally expensive numerical analysis and stringent design specifications nowadays, both the optimization efficiency and quality of design solutions become challenges for available MEMS shape optimization methods. In this paper, a new method, called self-adaptive surrogate model-assisted differential evolution for MEMS optimization (ASDEMO), is presented to address these challenges. The main innovation of ASDEMO is a hybrid differential evolution mutation strategy combination and its self-adaptive adoption mechanism, which are proposed for online surrogate model-assisted MEMS optimization. The performance of ASDEMO is demonstrated by a high-performance electro-thermo-elastic micro-actuator, a high-performance corrugated membrane micro-actuator, and a highly multimodal mathematical benchmark problem. Comparisons with state-of-the-art methods verify the advantages of ASDEMO in terms of efficiency and optimization ability.

Differential evolution using cooperative ranking-based mutation operators for constrained optimization

Abstract Differential evolution (DE) is a widely used heuristic algorithm for numerical optimization over continuous space. As the core operator, the mutation operator has a great effect on DE's performance. In this paper, we propose a cooperative ranking-based mutation strategy (CRM) for DE when solving constrained optimization problems (COPs). In CRM, two different ranking criteria are adopted in a cooperative way to move the population towards a feasible global optimum with a faster convergence speed. The first criterion is objective function value-based criterion which is applied for feasible solutions to converge towards the global optimum. The second criterion is overall constraint violation-based criterion which is applied for infeasible solutions to search for feasible regions. The proposed CRM is integrated into the basic DE and two advanced DE variants. The comparison results showed that the DE variants with CRM have a faster convergence speed than the non-CRM-based variants in the majority of test problems. This approach is a promising strategy to improve the search ability of DE variants when solving COPs.