Scalarization techniques are a popular method for articulating preferences in solving multi-objective optimization problems. These techniques, however, have so far proven to be ill-suited in finding a preference-driven approximation that still captures the Pareto front in its entirety. Therefore, we propose a new concept that defines an optimal distribution of points on the front given a specific scalarization function. It is proven that such an approximation exists for every real-valued problem irrespective of the shape of the corresponding front under some very mild conditions. We also show that our approach works well in obtaining an equidistant approximation of the Pareto front if no specific preference is articulated. Our analysis is complemented by the presentation of a new algorithm that implements the aforementioned concept. We provide in-depth simulation results to demonstrate the performance of our algorithm. The analysis also reveals that our algorithm is able to outperform current state-of-the-art algorithms on many popular benchmark problems.

Abstract. The optimization of operating times and operation modes of devices and systems that consume or generate electricity in buildings by building energy management systems promises to alleviate problems arising in today's electricity grids. Conflicting objectives may have to be pursued in this context, giving rise to a multi-objective optimization problem. This paper presents the optimization of appliances as well as heating and air-conditioning devices in two distinct settings of smart buildings, a residential and a commercial building, with respect to the minimization of energy costs, CO2 emissions, discomfort, and technical wearout. We propose new encodings for appliances that are based on a combined categorization of devices respecting both, the optimization of operating times as well as operation modes, e.g., of hybrid devices. To identify an evolutionary algorithm that promises to lead to good optimization results of the devices in our real-world lab environments, we compare four state-of-the-art algorithms in realistic simulations: ESPEA, NSGA-II, NSGA-III, and SPEA2. The results show that ESPEA and NSGA-II significantly outperform the other two algorithms in our scenario.

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