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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]

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]

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]

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]

• 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]