Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Abstract

Many optimization problems admit a number of local optima, among which there is the global optimum. For these problems, various heuristic optimization methods have been proposed. Comparing the results of these solvers requires the definition of suitable metrics. In the electrical energy systems literature, simple metrics such as best value obtained, the mean value, the median or the standard deviation of the solutions are still used. However, the comparisons carried out with these metrics are rather weak, and on these bases a somehow uncontrolled proliferation of heuristic solvers is taking place. This paper addresses the overall issue of understanding the reasons of this proliferation, showing a conceptual scheme that indicates how the assessment of the best solver may result in the unlimited formulation of new solvers. Moreover, this paper shows how the use of more refined metrics defined to compare the optimization result, associated with the definition of appropriate benchmarks, may make the comparisons among the solvers more robust. The proposed metrics are based on the concept of firstorder stochastic dominance and are defined for the cases in which: (i) the globally optimal solution can be found (for testing purposes); and (ii) the number of possible solutions is so large that practically it cannot be guaranteed that the global optimum has been found. Illustrative examples are provided for a typical problem in the electrical energy systems area -distribution network reconfiguration. The conceptual results obtained are generally valid to compare the results of other optimization problems.2

Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the ‘Rush to Heuristics’

“…In practice, taking three algorithms A, B, and C, it may happen that, for different problems, A is better than B, B is better than C, and C is better than A. The same concept is shown in [29] by indicating that the relation between the solvers is non-transitive, namely, if algorithm A is better than algorithm B for some problems, and algorithm B is better than algorithm C, this does not imply that algorithm A is better than algorithm C. Another paradox that is shown in [92] is the so-called "survival of the fittest".…”

“…In the power and energy domain, metaheuristic optimization is widely used to solve many problems referring to operation, planning, control, forecasting, reliability, security, and demand management. A set of typical problems that are solved with metaheuristic optimization have been considered in [27][28][29], including unit commitment, economic dispatch, optimal power flow, distribution system reconfiguration, power system planning, distribution system planning, load forecasting, and maintenance scheduling. Table 1 shows a selection of the metaheuristics most applied to these typical problems.…”

“…Table 1. Most used metaheuristic algorithms used to solve some power and energy systems problems [28,29]. Concerning the information coding, the most successful implementations of genetic algorithms do not use binary coding of the strings, but use representations that are adapted to the application, and the crossover and mutation operators are re-defined accordingly [13].…”

“…The quality of the algorithms can then be determined by calculating the percentage of the best solutions, averaged over a given number of executions of each algorithm [13]. The series of the best solutions obtained during the execution of the algorithm in the given time is typically considered for applying a performance metric [29,92].…”

Optimal Routing an Ungrounded Electrical Distribution System Based on Heuristic Method with Micro Grids Integration

“…There are several heuristics methods that can be used to solve an optimisation problem, in the paper [25] a scheme is explained the pros and cons of the "best solvers", based on the analysis of a considerable amount of articles. The efficiency and closeness to the global optimum solution of some heuristic solvers are tested in [26], where implemented a Home Energy Management solved through five heuristic algorithms.…”