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In this paper, we study swarm intelligence computation for constrained optimization problems and propose a new hybrid PSO-DE algorithm based on feasibility rules. Establishing individual feasibility rules as a way to determine whether the position of an individual satisfies the constraint or violates the degree of the constraint, which will determine the choice of the individual optimal position and the global optimal position in the particle population. First, particle swarm optimization (PSO) is used to act on the top 50% of individuals with higher degree of constraint violation to update their velocity and position. Second, Differential Evolution (DE) is applied to act on the individual optimal position of each individual to form a new population. The current individual optimal position and the global optimal position are updated using the feasibility rules, thus forming a hybrid PSO-DE intelligent algorithm. Analyzing the convergence and complexity of PSO-DE. Finally, the performance of the PSO-DE algorithm is tested with 12 benchmark functions of constrained optimization and 57 engineering optimization problems, the numerical results show that the proposed algorithm has good accuracy, effectiveness and robustness. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper aims to improve premature convergence and low precision of the differential evolution algorithm. An adaptive constrained differential evolution algorithm based on a probability interval update mechanism (PIMDE) is proposed. First, the interval probability update mechanism is developed to adaptively generate the mutation probability value, and the hybrid mutation strategy is formulated by effectively selecting complementary mutation strategies based on the mutation probability. Subsequently, the adaptive mechanism is employed to dynamically adjust the mutation strategy and parameters; as a result, the global detection and local search ability of the algorithm can be balanced, and the search efficiency of the algorithm can be enhanced. To verify determine the performance of the proposed algorithm, ten standard constrained optimization problems and five engineering optimization problems are analyzed. As revealed from experimental results, PIMDE can effectively solve COPs with high precision and robustness. [ABSTRACT FROM AUTHOR]

In order to solve the dynamic emission economic dispatch (DEED) problem with high-dimensional and large scale constraints, this paper proposed an adaptive multiobjective differential evolutionary algorithm (ADEA). The ADEA designed an adaptive differential crossover module, developed an improving current to best 1 crossover scheme to enhance the diversity of population. These strategies improved the exploration and exploitation ability of the ADEA, it also applied a repair strategy to deal with the equality and inequality constrains in DEED problem. Numerical experiments tested the effectiveness of ADEA on 10-unit system, and compared with several peer algorithms. Simulation results indicate that ADEA has good convergence. The uniformity and ductility of the Pareto front obtained by ADEA is better than that of the compared algorithms. It provides a more efficient scheduling decision-making method for power system dispatcher by a fuzzy decision method. [ABSTRACT FROM AUTHOR]

This paper proposes an improved memetic algorithm relying on ring neighborhood topology for constrained optimization problems based on our previous work in Cai et al. (Soft Comput (in press), ). The main motivation of using ring neighborhood topology is to provide a good balance between effective exploration and efficient exploitation, which is a very important design issue for memetic algorithms. More specifically, a novel variant of invasive weed optimization (IWO) as the local refinement procedure is proposed in this paper. The proposed IWO variant adopts a neighborhood-based dispersal operator to achieve more fine-grained local search through the estimation of neighborhood fitness information relying on the ring neighborhood topology. Furthermore, a modified version of differential evolution (DE), known as 'DE/current-to-best/1', is integrated into the improved memetic algorithm with the aim of providing a more effective exploration. Performance of the improved memetic algorithm has been comprehensively tested on 13 well-known benchmark test functions and four engineering constrained optimization problems. The experimental results show that the improved memetic algorithm obtains greater competitiveness when compared with the original memetic approach Cai et al. in (Soft Comput (in press), ) and other state-of-the-art algorithms. The effectiveness of the modification of each component in the proposed approach is also discussed in the paper. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named C ε -LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed C ε -LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of C ε -LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that C ε -LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme. [ABSTRACT FROM AUTHOR]

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

This paper proposes a (μ + λ)-differential evolution and an improved adaptive trade-off model for solving constrained optimization problems.The proposed (μ + λ)-differential evolution adopts three mutation strategies (i.e., rand/1 strategy, current-to-best/1 strategy, and rand/2 strategy) and binomial crossover to generate the offspring population. Moreover, the current-to-best/1 strategy has been improved in this paper to further enhance the global exploration ability by exploiting the feasibility proportion of the last population. Additionally, the improved adaptive trade-off model includes three main situations: the infeasible situation, the semi-feasible situation, and the feasible situation. In each situation, a constraint-handlingmechanism is designed based on the characteristics of the current population. By combining the (μ + λ)-differential evolution with the improved adaptive trade-off model, a generic method named (μ + λ)-constrained differential evolution ((μ + λ)-CDE) is developed. The (μ + λ)-CDE is utilized to solve 24 well-known benchmark test functions provided for the special session on constrained real-parameter optimization of the 2006 IEEE Congress on Evolutionary Computation (CEC2006). Experimental results suggest that the (μ + λ)-CDE is very promising for constrained optimization, since it can reach the best known solutions for 23 test functions and is able to successfully solve 21 test functions in all runs. Moreover, in this paper, a self-adaptive version of (μ + λ)-CDE is proposed which is the most competitive algorithm so far among the CEC2006 entries. [ABSTRACT FROM AUTHOR]

When solving constrained multiobjective optimization problems, it is crucial to deal with several conflicting objectives and various constraints simultaneously. To address these two issues, a constrained multiobjective differential evolution algorithm with an infeasible-proportion control mechanism is presented in this paper. Specifically, two populations are cooperatively employed in the evolution process. The first population is used to solve the original problem, that is, to explore the constrained Pareto front, while the second population is created to search for high-quality objective function information. Furthermore, differential evolution with two specific mutation strategies is employed to update each population. Cooperative strategies can not only balance diversity and convergence but also realize information exchange between the two populations provide new evolutionary directions. In addition, an infeasible-proportion control mechanism is used to gradually decrease the proportion of infeasible solutions in the second population. This enables the main population to pass through the infeasible region barrier in the early evolution stage and facilitates the search for a constrained Pareto front in the later evolution stage. Systematic experiments on 65 benchmark test functions show that the proposed algorithm is superior to or at least comparable to five well-established constrained multiobjective optimization methods. [ABSTRACT FROM AUTHOR]

In attempting to overcome the limitation of current methods to solve complicated constrained optimization problems, this paper proposes an adaptive hybrid particle swarm optimization multi-objective optimization (AHPSOMO) algorithm. In the early stage, this algorithm initializes the individuals in a population in an even manner using good point set (GPS) theory so that the diversity of the population can be guaranteed. In the process of local search, differential evolution (DE) algorithm is introduced for updating local optimal individuals. Particle swarm optimization method is further adopted to conduct global search as per the multi-objective approach. The results of simulation tests on 24 classic test functions and three engineering constrained optimization problems show that compared with other algorithms, our proposed algorithm is effective and feasible, which can offer highly accurate solutions with good robustness. [ABSTRACT FROM AUTHOR]

Dynamic economic dispatch with valve-point effects (DED_ vpe) is a high-dimensional constrained optimization problem with non-convex and non-smooth characteristics. Hybrid methods are one of the most advanced methods to solve the problem. However, most of these methods improve the solution accuracy at the expense of algorithm robustness. This paper proposes an adaptive hybrid backtracking search optimization algorithm (AHBSA) for solving the DED_ vpe. The core idea of AHBSA lies in designing a suitable coupling structure based on the current best individual (called optimal partial coupling). The structure hybridizes an improved BSA mutation operator and the DE/best/1 operator with equal probability. The improved BSA mutation operator uses the current best individual and the historical population to update individual position, called BSA/best/old. It is also the first research work of extending BSA to the problem. In addition, an adaptive parameter control mechanism is proposed to select an appropriate 'mixrate' value for achieving better coupling. The performance of AHBSA is validated on six DED test cases of three systems. Experimental results demonstrate that, compared with some representative methods, AHBSA not only reduces the fuel cost but also ensures the robustness of the algorithm. • A hybrid method AHBSA is proposed to solve DED problem with valve-point effects. • An optimal partial coupling structure is designed in AHBSA. • BSA is the first attempt at solving DED problem. • Results on six benchmark DED test cases show AHBSA is competitive. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a damage detection technique combining proper orthogonal decomposition (POD) with self-adaptive differential evolution algorithm for structural health monitoring considering environmental variability and measurement noises. The damage detection methodology consists of three stages. Identification of the exact time instant of damage and exact spatial location of damage using proper orthogonal modes constitutes the first two stages. The damage severity assessment is the third stage and is formulated as a constrained optimisation problem, solved using newly proposed self-adaptive differential evolution algorithm. Numerical simulation studies indicate that the proposed method is robust and can be used effectively in SHM applications. [Copyright &y& Elsevier]

Abstract: Many practical problems can be formulated as constrained optimization problems. Due to the simple concept and easy implementation, the penalty function method has been one of the most common techniques to handle constraints. However, the performance of this technique greatly relies on the setting of penalty factors, which are usually determined by manual trial and error, and the suitable penalty factors are often problem-dependent and difficult to set. In this paper, a differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems. First, a special penalty function is designed to handle the constraints. Second, a co-evolution model is presented and differential evolution (DE) is employed to perform evolutionary search in spaces of both solutions and penalty factors. Thus, the solutions and penalty factors evolve interactively and self-adaptively, and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously. Simulation results based on several benchmark functions and three well-known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method. [Copyright &y& Elsevier]

• Present the effective transmission positional workspace (ETPW) of Rec4 mechanism. • Construct the constrained optimization model to maximize the volume of ETPW. • Differential evolution is used to solve the constrained optimization problem. A 4-RUP a R parallel mechanism (named as Rec4) with Schöenflies motion has been taken as the research object, and its dimensional synthesis problem has been solved by intelligence algorithms. Using screw theory as a mathematical tool, this paper establishes two indices (i.e., the input transmission index and the output transmission index) to evaluate motion and force transmission performance of mechanism, and presents the definition and numerical calculation method of effective transmission positional workspace (ETPW). A constrained optimization model is constructed to formulate the design problem of dimensional parameters on the maximizing volume of ETPW, and differential evolution (DE) algorithm is employed to solve this problem. A real case of dimensional optimization design is given, and the results show that the proposed model and algorithm are feasible and effective. Furthermore, a comparative test on global optimization capability to solve the dimensional design case is carried out with genetic algorithm (GA), particle swarm optimization (PSO), and DE algorithm, and the numerical experiments demonstrate that DE outperforms GA and PSO in terms of performance indices. [ABSTRACT FROM AUTHOR]

In recent years, evolutionary computation (EC) has gained increasing attention in the field of production optimization due to its powerful global search ability and derivative-free characteristic. However, state constraints are much more challenging to handle in comparison with the explicit constraints. To alleviate this difficulty, this paper presents a framework called surrogate-assisted differential evolution with an effective constraint-handling technique—the feasibility rule with the incorporation of objective function information (SADE-FROFI). The novel constraint-handling technique used in this work achieves an effective balance between constraints and objective function by revising the well-known feasibility rule (FR), which can effectively maintain the diversity of population and help the population jump out of local optimal solution. Moreover, to address the computationally time-consuming issue of numerical simulator, a multi-surrogate strategy is introduced specially for state constraints. Two benchmark functions are tested to verify the effectiveness of new constraint-handling technique (FROFI). The efficacy of the proposed method is validated on two synthetic reservoir models, named three-channel model and PUNQ-S3 model, respectively. The experimental results demonstrated that the proposed method can find better solutions on the basis of satisfying all constraints in comparison with several existing methods. • A new constrained production optimization framework is proposed based on surrogate-assisted algorithm and novel constraint-handling technique. • The new methodology is successfully applied to two constrained production optimization problems. • The optimization results of two reservoir models show the great performance of the proposed method. [ABSTRACT FROM AUTHOR]

Disasters have caused significant losses to humans in the past decades. It is essential to learn about the disaster situation so that rescue works can be conducted as soon as possible. Unmanned aerial vehicle (UAV) is a very useful and effective tool to improve the capacity of disaster situational awareness for responders. In the paper, UAV path planning is modelled as the optimization problem, in which fitness functions include travelling distance and risk of UAV, three constraints involve the height of UAV, angle of UAV, and limited UAV slope. An adaptive selection mutation constrained differential evolution algorithm is put forward to solve the problem. In the proposed algorithm, individuals are selected depending on their fitness values and constraint violations. The better the individual is, the higher the chosen probability it has. These selected individuals are used to make mutation, and the algorithm searches around the best individual among the selected individuals. The well-designed mechanism improves the exploitation and maintains the exploration. The experimental results have indicated that the proposed algorithm is competitive compared with the state-of-art algorithms, which makes it more suitable in the disaster scenario. [ABSTRACT FROM AUTHOR]

Single objective optimization algorithms are the foundation of establishing more complex methods, like constrained optimization, niching and multi-objective algorithms. Therefore, improvements to single objective optimization algorithms are important because they can impact other domains as well. This paper proposes a method using turning-based mutation that is aimed to solve the problem of premature convergence of algorithms based on SHADE (Success-History based Adaptive Differential Evolution) in high dimensional search space. The proposed method is tested on the Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions for all SHADE, L-SHADE, and jSO algorithms. The effectiveness of the method is verified by population diversity measure and population clustering analysis. In addition, the new versions (Tb-SHADE, TbL-SHADE and Tb-jSO) using the proposed turning-based mutation get apparently better optimization results than the original algorithms (SHADE, L-SHADE, and jSO) as well as the advanced DISH and the jDE100 algorithms in 10, 15, and 20 dimensional functions, but only have advantages compared with the advanced j2020 algorithm in 5 dimensional functions. [ABSTRACT FROM AUTHOR]

Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both unconstrained search and optimization algorithms. However, if some constraint handling techniques (CHTs) are incorporated in their frameworks, then they can be used to solve constrained optimization problems (COPs). In an early work, an ensemble of constraint handling techniques (ECHT) is probabilistically hybridized with the basic version of DE. The ECHT consists of four different CHTs: superiority of feasible solutions, self-adaptive penalty, ε -constraint handling technique and stochastic ranking. This paper employs ECHT in the selection schemes, where offspring competes with their parents for survival to the next generation, of JADE and SaDE. As a result, JADE-ECHT and SaDE-ECHT are developed, which are the constrained variants of JADE and SaDE. Both algorithms are tested on 24 COPs and the experimental results are collected and compared according to algorithms' evaluation criteria of CEC'06. Their comparison, in terms of feasibility rate (FR) and success rate (SR), shows that SaDE-ECHT surpasses JADE-ECHT in terms of FR, while JADE-ECHT outperforms SaDE-ECHT in terms of SR. [ABSTRACT FROM AUTHOR]