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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]

Many real-world applications can be modelled as dynamic constrained optimization problems (DCOPs). Due to the fact that objective function and/or constraints change over time, solving DCOPs is a challenging task. Although solving DCOPs by evolutionary algorithms has attracted increasing interest in the community of evolutionary computation, the design of benchmark test functions of DCOPs is still insufficient. Therefore, we propose a test suite for DCOPs. A dynamic unconstrained optimization benchmark with good time-varying characteristics, called moving peaks benchmark, is chosen to be the objective function of our test suite. In addition, we design adjustable dynamic constraints, by which the size, number, and change severity of the feasible regions can be flexibly controlled. Furthermore, the performance of three dynamic constrained optimization evolutionary algorithms is tested on the proposed test suite, one of which is presented in this paper, named dynamic constrained optimization differential evolution (DyCODE). DyCODE includes three main phases: 1) the first phase intends to enter the feasible region from different directions promptly via a multi-population search strategy; 2) in the second phase, some excellent individuals chosen from the first phase form a new population to search for the optimal solution of the current environment; and 3) the third phase combines the memory individuals of the first two phases with some randomly generated individuals to re-initialize the population for the next environment. From the experiments, one can understand the strengths and weaknesses of the three compared algorithms for solving DCOPs in depth. Moreover, we also give some suggestions for researchers to apply these three algorithms on different occasions. [ABSTRACT FROM AUTHOR]