Evaluation of the absolute forms of cost functions in optimization using a novel evolutionary algorithm - Mohammadi, Adel; Nariman-zadeh, Nader; Payan, Meghdad; Jamali, Ali (Soft computing (Berlin, Germany), 2023)
Many ordinary approaches in optimization are mathematical-based. Due to the limitations of such methods, optimal problems have been commonly defined in single-objective and quadratic forms, leading to non-optimal solutions based on the main design requirements. In order to address these issues, this paper presents a new type of genetic programming (GP) called “multi-objective archived-based genetic programming (MAGP)”. The absolute forms of cost functions, which are unsolvable using the conventional methods, could be assessed herein through the suggested algorithm. It is shown that in addition to the possibility of obtaining optimal single-objective solutions, It is shown that in addition to the possibility of obtaining optimal single-objective solutions, some very fruitful non-dominant solutions on the Pareto fronts would be acquired, providing the designer with a set of optimal analytical solutions which could be selected depending on the design requirements. For example, in the case studies examined in this paper, around 30,000 and 14,000 non-dominant solutions were obtained for linear and nonlinear problems, respectively, indicating the high performance of the novel proposed MAGP algorithm in acquiring non-dominant solutions in optimization problems. Generally, it is observed that obtaining and comparing optimal solutions in the quadratic form are basically unreliable and as a consequence, an optimal control problem must be analyzed in its absolute form of indices.