Biased Dyadic Crossover for Variable-Length Multi-Objective Optimal Control Problems

This paper presents an enabling technique for social cooperation suitable for variable-length multi-objective direct optimal control problems. Using this approach, individualistic mesh-refinement may be performed across a population of discretised optimal control solutions within a real-coded evolutionary algorithm. Structural homology between individual solutions is inferred via the exploitation of non-uniform dyadic grid structures. Social actions, including genetic crossover, are enabled by identifying nodal intersections between parent vectors in normalised time. Several alternative crossover techniques are discussed, where effectiveness is evaluated based on the likelihood of producing dominating solutions with respect to the current archive. Each technique is demonstrated and compared using a simple numerical test case representing the controlled descent of a Lunar-landing vehicle. Of the examined methods, it is found that a hybrid one/two-point crossover, biased towards higher levels of grid resolution consistently outperforms those based on more traditional, unbiased crossover.