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This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents’ states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents’ states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents’ states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents’ states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

Abstract: To overcome the main drawbacks of (μ + λ)-constrained differential evolution ((μ + λ)-CDE) [45], this paper proposes an improved version of (μ + λ)-CDE, named ICDE, to solve constrained optimization problems (COPs). ICDE mainly consists of an improved (μ + λ)-differential evolution (IDE) and a novel archiving-based adaptive tradeoff model (ArATM). Therein, IDE employs several mutation strategies and the binomial crossover of differential evolution (DE) to generate the offspring population. Moreover, a new mutation strategy named “current-to-rand/best/1” is proposed by making use of the current generation number in IDE. Since the population may undergo three situations during the evolution (i.e., the infeasible situation, the semi-feasible situation, and the feasible situation), like (μ + λ)-CDE, ArATM designs one constraint-handling mechanism for each situation. However, unlike (μ + λ)-CDE, in the constraint-handling mechanism of the infeasible situation, the hierarchical nondominated individual selection scheme is utilized, and an individual archiving technique is proposed to maintain the diversity of the population. Furthermore, in the constraint-handling mechanism of the semi-infeasible situation, the feasibility proportion of the combined population consisting of the parent population and the offspring population is used to convert the objective function of each individual. It is noteworthy that ICDE adopts a fixed tolerance value for the equality constraints. In addition, in this paper two criteria are used to compute the degree of constraint violation of each individual in the population, according to the difference among the violations of different constraints. By combining IDE with ArATM, ICDE has the capability to maintain a good balance between the diversity and the convergence of the population during the evolution. The performance of ICDE has been tested on 24 well-known benchmark test functions collected for the special session on constrained real-parameter optimization of the 2006 IEEE Congress on Evolutionary Computation (IEEE CEC2006). The experimental results demonstrate that ICDE not only overcomes the main drawbacks of (μ + λ)-CDE but also obtains very competitive performance compared with other state-of-the-art methods for constrained optimization in the community of constrained evolutionary optimization. [Copyright &y& Elsevier]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel Constrained Optimization based on Modified Differential Evolution algorithm (COMDE). In the new algorithm, a new directed mutation rule, based on the weighted difference vector between the best and the worst individuals at a particular generation, is introduced. The new directed mutation rule is combined with the modified basic mutation strategy DE/rand/1/bin, where only one of the two mutation rules is applied with the probability of 0.5. The proposed mutation rule is shown to enhance the local search ability of the basic Differential Evolution (DE) and to get a better trade-off between convergence rate and robustness. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability is utilized to balance the global exploration and local exploitation. COMDE also includes a modified constraint handling technique based on feasibility and the sum of constraints violations. A new dynamic tolerance technique to handle equality constraints is also adopted. The effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in COMDE has been experimentally investigated. The effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of COMDE have been analyzed and evaluated by different experiments. Numerical experiments on 13 well-known benchmark test functions and five engineering design problems have shown that the new approach is efficient, effective and robust. The comparison results between the COMDE and the other 28 state-of-the-art evolutionary algorithms indicate that the proposed COMDE algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final solution. [Copyright &y& Elsevier]