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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]

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]

Differential evolution (DE) algorithm has attracted considerable attention because of its effectiveness and simplicity. However, previous studies have validated that DE still suffers from some limitations such as premature convergence and slow convergence especially dealing with multimodal optimization problems. To address these concerning issues, we propose an innovative optimization method named particle swarm-differential evolution algorithm with multiple random mutation (MRPSODE) in this paper. The proposed MRPSODE algorithm is based on multiple random mutation framework cooperating with mean particle swarm mutation strategy, DE/current-to-rand/1 mutation strategy and disturbance strategy. Firstly, we incorporate the modified mean particle swarm mutation strategy into DE algorithm to improve the global convergence ability. Secondly, DE/current-to-rand/1 mutation strategy is adopted to increase the population diversity and produce perturbations to avoid the algorithm trapping into a local optimum. Thirdly, we propose a disturbance strategy to help the population escape from local optima, so as to enhance the exploration ability. Finally, to ensure that the proposed algorithm can get satisfactory solutions with a fast convergence speed, we design a multiple random mutation framework, in which these three mutation strategies can effectively play their advantages and make up for the shortcomings of others. To evaluate the performance of the proposed algorithm, three different experiments are constructed on twenty-nine classical benchmark functions. The simulation results demonstrate that, (1) MRPSODE significantly outperforms conventional PSO and DE algorithms, (2) MRPSODE can achieve better performance than nine well-known DE variants in terms of solution quality and robustness, (3) MRPSODE is superior to nine latest heuristic-based algorithms. Furthermore, MRPSODE is successfully applied to seven typical constrained optimization problems and performs better than almost all compared methods. • A hybrid particle swarm differential evolution algorithm with multiple random mutation (MRPSODE) is proposed. • Three different mutation strategies are incorporated into DE algorithm to improve the optimization performance. • A random mutation framework is proposed to combine these three different mutation strategies. • Three kinds of experiments are conducted to validate the effectiveness of the MRPSODE. • The MRPSODE is successfully applied to seven constrained optimization problems. [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]

Summary: This article presents an advanced hybrid algorithm (haDEPSO) for nonlinear constrained function optimization problem. It consists of the advised advanced differential evolution, that is, aDE (wherein a novel mutation, crossover, and selection strategy is introduced, to avoid premature convergence) and particle swarm optimization, namely, aPSO (in which novel gradually varying parameters is utilized, to escape stagnation). The proposed haDEPSO achieve better results as aDE and aPSO provides diverse convergence characteristic to the solution space. Moreover, in haDEPSO distinct population is merged with other in a predefined way, to balance between exploration and exploitation. Efficiency of the proposed hybrid haDEPSO along with its integrating component aDE and aPSO are inspected on IEEE CEC'2006 constrained benchmark functions and IEEE CEC'2011 real world problems. According to the comparison results, the proposed methods achieved better results than traditional DE and PSO with their hybrids as well as over many state‐of‐the‐art algorithms. [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]