Multi-Objective Constrained Optimization using Discrete Mechanics and NSGA-II Approach

A novel approach to solve multi-objective optimization problems of complex mechanical systems is proposed based on evolutionary algorithm. Discrete mechanics derives structure preserving constraint equations and objective functions. Standard non-linear optimization techniques used to obtain optimal solution to these equations fails to find global optimum solution and also requires system satisfying initial guess. Multi-objective optimization technique like non-dominated sorting genetic algorithm-II (NSGA-II) finds global optimal solution without giving any initial guess for multiple conflicting objectives. This method is numerically illustrated by optimizing an underactuated mechanical system called 2D SpiderCrane system. In SpiderCrane, fast and precise payload positioning is to be achieved while keeping payload swing minimum along the trajectory. Minimizing the time of operation requires greater amount of force which may lead to unacceptable payload sway, while decreasing forces increases the time of operation. Proposed control law to optimize this conflicting multi-objectives is validated with simulation results.