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Many real-world problems are modeled as multi-objective optimization problems whose optimal solutions change with time. These problems are commonly termed dynamic multi-objective optimization problems (DMOPs). One challenge associated with solving such problems is the fact that the Pareto front or Pareto set often changes too quickly. This means that the optimal solution set at period t may likely vary from that at (t+1), and this makes the process of optimizing such problems computationally expensive to implement. This article proposes the use of adaptive mutation and crossover operators for the non-dominated sorting genetic algorithm III (NSGA-III). The aim is to find solutions that can adapt to fitness changes in the objective function space over time. The proposed approach improves the capability of NSGA-III to solve multi-objective optimization problems with solutions that change quickly in both space and time. Results obtained show that this method of population reinitialization can effectively optimize selected benchmark dynamic problems. In addition, we test the capability of the proposed algorithm to select robust solutions over time. We recognize that DMOPs are characterized by rapidly changing optimal solutions. Therefore, we also test the ability of our proposed algorithm to handle these changes. This is achieved by evaluating its performance on selected robust optimization over time (ROOT) and robust Pareto-optimality over time (RPOOT) benchmark problems.

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This paper investigates the effect of selected strategies of distributed energy resources (DER) on an energy cost function that optimizes the distribution of distributed energy resources for a mid-rise apartment building. This is achieved through comparing parameter optimization results for both a high-level and low-level optimizer, respectively. The optimization process is carried out using the following approach: (1) a two-objective function is constructed with one objective function similar to that of the high-level optimizer (DER-CAM); (2) an evolutionary algorithm (EA) with modified selection capability is used to optimize the two-objective function problem in (1) for four selected cases of DER utilization that were previously optimized in DER-CAM; and (3) the optimization results of the low-level optimizer are compared with the outcome of DER-CAM optimization for the four selected cases. This is done to establish the capability of DER-CAM as an effective tool for optimal distributed energy resource allocation. Results obtained reveal the effect of load shifting and solar photovoltaic (PV) panels with power exporting capability on the optimization of the cost function. The Pareto-based MOEA approach has also proved to be effective in observing the interactions between objective function parameters. Mean inverted generational distance (MIGD) values obtained over 10 runs for each of the four cases that were considered show that a DER combination of PV panel, battery storage, heat pump, and load shifting outperforms the other strategies in 70% of the total simulation runs.

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