Application of differential evolution-based constrained optimization methods to district energy optimization and comparison with dynamic programming

Metaheuristic optimization methods, as model-free approaches, are expected to be applicable to practical issues (e.g., engineering problems). Although optimization methods have been proposed or improved through many different theoretical studies, they should be tested using not only certain benchmark functions, but also other models representing practical situations, such as those involving discrete control variables and equality or inequality constraints. Hence, in this study, differential evolution based constrained optimization methods were applied to district energy optimization. To obtain theoretical results, several different types of proposed methods were compared with dynamic programming and genetic algorithm. In addition, a parametric study was conducted to evaluate the effects of the population size, mutation rate, and random jumping rate. The proposed method, namely, ε-constrained differential evolution with random jumping II, proved capable of producing results that differ from the theoretical results by only 2.1% within a computation time 1/457 of that required by dynamic programming. In addition, the method was superior to genetic algorithm which had been often adopted as a metaheuristic method in engineering problems because the result of the proposed method was 460,417 yen/day and that of genetic algorithm was 660,424 yen/day. Therefore, the proposed method has high potential to provide comprehensive district energy optimization within a realistic computational time.