Development of a memetic algorithm for Dynamic Multi-Objective Optimization and its applications for online neural network modeling of UAVs

Abstract

Dynamic multi-objective optimization (DMO) is one of the most challenging class of optimization problems where the objective functions change over time and the optimization algorithm is required to identify the corresponding Pareto optimal solutions with minimal time lag. DMO has received very little attention in the past and none of the existing multi-objective algorithms perform satisfactorily on test problems and a handful of such applications have been reported. In this paper, we introduce a memetic algorithm (MA) and illustrate its performance for online neural network (NN) identification of the multi-input multi-output unmanned aerial vehicle (UAV) system. As a typical case, the longitudinal model of the UAV is considered and the performance of a NN trained with the memetic algorithm is compared to another trained with Levenberg-Marquardt training algorithm using mini-batches. The memetic algorithm employs an orthogonal epsilon-constrained formulation to deal with multiple objectives and a sequential quadratic programming (SQP) solver is embedded as its local search mechanism to improve the rate of convergence. The performance of the memetic algorithm is presented for two benchmarks Fisherpsilas Discriminant Analysis (FDA), FDA1 and modified FDA2 before highlighting its benefits for online NN model identification for UAVs. Observations from our recent work indicated that Mean Square Error (MSE) alone may not always be a good measure for training the networks. Hence the MSE and maximum absolute value of the instantaneous error is considered as objectives to be minimized which requires a Dynamic MO algorithm. The proposed memetic algorithm is aimed to solve such identification problems and the same can be extended to control problems.