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In evolutionary multiobjective optimization, it is very important to be able to visualize approximations of the Pareto front (called approximation sets) that are found by multiobjective evolutionary algorithms. While scatter plots can be used for visualizing 2-D and 3-D approximation sets, more advanced approaches are needed to handle four or more objectives. This paper presents a comprehensive review of the existing visualization methods used in evolutionary multiobjective optimization, showing their outcomes on two novel 4-D benchmark approximation sets. In addition, a visualization method that uses prosection (projection of a section) to visualize 4-D approximation sets is proposed. The method reproduces the shape, range, and distribution of vectors in the observed approximation sets well and can handle multiple large approximation sets while being robust and computationally inexpensive. Even more importantly, for some vectors, the visualization with prosections preserves the Pareto dominance relation and relative closeness to reference points. The method is analyzed theoretically and demonstrated on several approximation sets.

Abstract. This paper presents a comprehensive comparison between the performance of state-of-the-art genetic algorithms NSGA-II, SPEA2 and IBEA and their differential evolution based variants DEMO NS-II , DEMO SP2 and DEMO IB . Experimental results on 16 numerical multiobjective test problems show that on the majority of problems, the algorithms based on differential evolution perform significantly better than the corresponding genetic algorithms with regard to applied quality indicators. This suggests that in numerical multiobjective optimization, differential evolution explores the decision space more efficiently than genetic algorithms.

Nowadays, Renewable Energy Sources (RES) are attracting more and more interest. Thus, many countries aim to increase the share of green energy and have to face with several challenges (e.g., balancing, storage, pricing). In this paper, we address the balancing challenge and present the MIRABEL project which aims to prototype an Energy Data Management System (EDMS) which takes benefit of flexibilities to efficiently balance energy demand and supply. The EDMS consists of millions of heterogeneous nodes that each incorporates advanced components (e.g., aggregation, forecasting, scheduling, negotiation). We describe each of these components and their interaction. Preliminary experimental results confirm the feasibility of our EDMS.

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