The use of evolutionary algorithms to tackle the energy economy parameter-dependent multi-objective optimization problem in fuel-cell hybrid electric vehicles

Abstract

Many real-world applications seek the optimal parameter settings to enhance the performance of specific targets. For example, to travel from point A to point B in the least amount of time. In some cases, one function’s improvement causes the worsening of another, leading to searching for the combination of these design parameters that provides a balanced trade-off between these objective functions. For instance, to have the best fuel consumption efficiency while reducing the traveling time from point A to point B. These kinds of problems are named multi-objective optimization problems (MOPs). Furthermore, an extension of these problems where external parameters influence the behavior of the objective functions are named parameter-dependent MOPs (PMOPs). The essence of these parameters is that they cannot be controlled by the decision-maker and are independent of the optimization process. In the latter example, the environmental temperature or the traffic density are denoted as independent parameters. Despite the state-of-the-art proposals to tackle PMOPs, the lack of further research regarding these problems is addressed. Therefore, the scope of this work is based on expanding the application fields of evolutionary algorithms for tackling a real-world PMOP application. The energy economy problem in fuel-cell hybrid electric vehicles (FCHEVs) can be stated as a PMOP, where some design parameters involved in the performance optimization of the fuel consumption and total mechanical power produced by the electric motor are subject to the total vehicle’s mass. By implementing an evolutionary algorithm embedded with a generated surrogate model for emulating the responses of the objective functions, broader solutions in terms of speed and quality can be produced. A FCHEV is modeled using the MATLAB Simulink software toolbox. Then, we generate several surrogate models for reducing computational time by using the Latin hypercube sampling to build the training and testing data. Subsequently, the Bayesian correlated t-test is performed to select the best surrogate model out of four available choices. Afterward, the Parameter-dependent island-based multi-indicator algorithm (P-IMIA) is proposed to take advantage of the information on the family of fronts simultaneously instead of tackling one front at a time. In addition, P-IMIA is compared to the state-of-the-art adaptations by utilizing the Wilcoxon rank sum test and the Bayesian correlated t-test. The obtained results showed that the proposed algorithm surpasses the speed of convergence of the state-of-the-art adaptations and maintains a competitive quality concerning the encountered optimal solutions sets. Besides, introducing a surrogate model approach for emulating the objective function responses for the evolutionary optimization provides quality solutions when comparing them to the MATLAB simulation model responses.