Topology of Anticipatory Populations for Evolutionary Dynamic Multi-Objective Optimization
Iason Hatzakis, David Robert Wallace · 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2006
In this paper we study the size and distribution of the anticipatory population used in a feed-forward prediction strategy to improve the method’s performance. The feed-forward prediction strategy for the solution of time-changing optimization problems with evolutionary algorithms has been detailed in prior art, and involves the combination of a forecasting technique with a population-based algorithm. Forecasting is used to create an estimate for the location of the moving optimum at the next time step, using as input the history of past optima discovered by the algorithm. An anticipatory population of individuals, the prediction set, is placed in the neighborhood of the forecast in order to accelerate discovery of the next optimum. This exploitation of past information can increase solution performance in problems where there is an amount of predictability in the objective’s temporal change pattern. The overall dynamic optimization concept combines the feed-forward prediction strategy with a method for balancing convergence and diversity in the population, so that dynamic problems lacking predictability in their change pattern can also be solved. The current work involves two approaches aimed at enhancing the effect of the prediction set. First, we investigate ways of populating the forecast neighborhood as opposed to simply placing a single individual on the forecast coordinates. The intention is to include the next time step’s optimum in the area of the prediction set even when the forecast error is large, thereby increasing the probability of discovering the optimum. We create prediction sets in the form of a hypercube and a Latin hypercube around the forecast coordinates, dimensioned in proportion to the expected forecast error. The hypercube was found to perform well for a design vector of low dimension, whereas the Latin hypercube appeared to be the best overall choice due to its better scaling properties as the design vector’s dimension increases. Second, we address the question of selecting which members of the non-dominated front to track and forecast. An intermediate point is proposed, defined as the non-dominated solution closest to the ideal point, together with the extremities of the Pareto front (anchor points). Prediction sets using these points were found to increase the algorithm’s performance.