On local minima in distributed energy scheduling

Abstract

Abstract-Distributed energy scheduling constitutes a tough task for optimization algorithms, as the underlying problem structure is highdimensional, multimodal and non-linear. For this reason, metaheuristics and especially distributed algorithms have been in the focus of research for several years with promising results. The modeling of the distributed energy units' flexibility is a specific research task, with different concepts like comfort-level based approaches, enumeration of possible schedules, and continuous schedule representation using machine learning and decoder techniques. Although a continuous representation of flexibility has shown better results regarding the global optimization goal, there have been hints that the susceptibility to local minima traps enlarges compared to the enumeration of distinct schedules. In this contribution, we present an exemplary system for predictive scheduling of distributed energy units consisting of a continuous flexibility modelling approach and a fully distributed planning heuristic. A prestudy is presented, where we analyze the problem structure regarding local minima and describe planned work to reduce the heuristic's susceptibility to be kept in these.

Towards fully Decentralized Multi-Objective Energy Scheduling

“…The model has already been used and evaluated in different projects, e. g. [13], [46], [50], [51]. We started with a rather small setting of four agents and 96-dimensional schedules resulting in a 384-dimensional search space which has already been evaluated to be highly multi-modal and ragged [52]. As goal, two objectives were set: F 1 denotes the deviation of the joint schedule from the desired target schedule ( • 2 ) and f 2 equalizes the run of the co-generation plants by minimizing peak loads: with µ being the mean power over the whole planning horizon.…”

Dynamic communication topologies for distributed heuristics in energy system optimization algorithms

“…Regarding the application domain of distributed control in cyber-physical energy systems, search spaces will have to be analyzed in detail. Given the complexity and non-linearity of the resulting system of systems though, high modality and rugged surfaces seem to be characteristic for many use cases with distributed energy resources, controllable loads and storage systems [36]. So far, communication topologies for distributed heuristics have been selected mostly independently from solution space characteristics.…”

Ant colony optimization for feasible scheduling of step-controlled smart grid generation

“…Most works propose using heuristics as an appropriate means for attacking scheduling problems within the smart grid. In (Nieße et al 2017), a systematic analysis of the occurrence of local minima for decentralized predictive scheduling problems has been conducted. The used approach of fitness landscape analysis is especially suitable for analytically difficult, non-linear objectives, decentralized problems, or complex relations between objective and constraints.…”

“…Surprisingly, not many a priori studies on practical problems are published. Some examples can be found in (Tavares et al 2008;Rapp 2019;Nieße et al 2017).…”

“…Many different procedures have so far been proposed for analyzing the landscape of fitness (Pitzer and Affenzeller 2012). As a starting point, we used an approach by (Vassilev et al 2000) that has already been used in energy management-related questions (Nieße et al 2017). Given an optimization problem, a landscape L is defined by the search space S , a neighborhood relation N and an error function (equivalently: the fitness) .…”