Decomposition-based Multi-objective Algorithm Research Articles

Radar placement optimization based on adaptive multi-objective meta-heuristics

Airspace surveillance is a significant issue for many countries to control and manage their airspace. The number of radars used and their coverage rate are the main issues to consider in this case. Therefore, this paper addresses the problem of finding the best radar locations to obtain the highest coverage rate with the least possible number of radars in a certain region. The radar placement problem is considered as a multi-objective optimization problem with two objectives: the number of radars and the coverage rate. To perfectly solve this optimization problem, a set of multi-objective meta-heuristic approaches based on simulated annealing, memory-based steady-state genetic algorithm, a decomposition-based multi-objective algorithm with differential evolution, and non-dominated sorting genetic algorithm (NSGA-II) are utilized. Algorithms are tested on a dataset created using DTED-1 map elevation data for two different selected regions. Based on the results, the NSGA-II algorithm achieves the best results and the highest coverage ratios among the tested algorithms. Two improved versions of the NSGA-II algorithm are also proposed to enhance its performance and make it more suitable for solving this optimization problem. The experimental results show that a coverage rate of 98% could be achieved with a small number of radars, and by increasing the number of radars, it exceeds 99%.

An Improved MOEA/D Algorithm for the Solution of the Multi-Objective Optimal Power Flow Problem

The optimal power flow (OPF) is an important tool for the secure and economic operation of the power system. It attracts many researchers to pay close attention. Many algorithms are used to solve the OPF problem. The decomposition-based multi-objective algorithm (MOEA/D) is one of them. However, the effectiveness of the algorithm decreases as the size of the power system increases. Therefore, an improved MOEA/D (IMOEA/D) is proposed in this paper to solve the OPF problem. The main goal of IMOEA/D is to speed up the convergence of the algorithm and increase species diversity. To achieve this goal, three improvement strategies are introduced. Firstly, the competition strategy between the barnacle optimization algorithm and differential evolution algorithm is adopted to overcome the reduced species diversity. Secondly, an adaptive mutation strategy is employed to enhance species diversity at the latter stage of iteration. Finally, the selective candidate with similarity selection is used to balance the exploration and exploitation capabilities of the proposed algorithm. Simulation experiments are performed on IEEE 30-bus and IEEE 57-bus test systems. The obtained results show that the above three measures can effectively improve the diversity of the population, and also demonstrate the competitiveness and effectiveness of the proposed algorithm for the OPF problem.

Multiple Classifiers-Assisted Evolutionary Algorithm Based on Decomposition for High-Dimensional Multiobjective Problems

Surrogate-assisted multiobjective evolutionary algorithms (MOEAs) have advanced the field of computationally expensive optimization, but their progress is often restricted to low-dimensional problems. This manuscript presents a multiple classifiers-assisted evolutionary algorithm based on decomposition, which is adapted for high-dimensional expensive problems in terms of the following two insights. Compared to approximation-based surrogates, the accuracy of classification-based surrogates is robust for few high-dimensional training samples. Furthermore, multiple local classifiers can hedge the risk of overfitting issues. Accordingly, the proposed algorithm builds multiple classifiers with support vector machines (SVMs) on a decomposition-based multiobjective algorithm, wherein each local classifier is trained for a corresponding scalarization function. Experimental results confirm that the proposed algorithm is competitive to the state-of-the-art algorithms and computationally efficient as well.