Hybrid Multi-Gradient Explorer Algorithm for Global Multi-Objective Optimization
Vladimir Sevastyanov · 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference · 2010
Hybrid Multi-Gradient Explorer (HMGE) algorithm for global multi-objective optimization of objective functions considered in a multi-dimensional domain is presented (patent pending). The proposed hybrid algorithm relies on genetic variation operators for creating new solutions, but in addition to a standard random mutation operator, HMGE uses a gradient mutation operator, which improves convergence. Thus, random mutation helps find global Pareto frontier, and gradient mutation improves convergence to the Pareto frontier. In such a way HMGE algorithm combines advantages of both gradient-based and GA-based optimization techniques: it is as fast as a pure gradient-based MGE algorithm, and is able to find the global Pareto frontier similar to genetic algorithms (GA). HMGE employs Dynamically Dimensioned Response Surface Method (DDRSM) for calculating gradients. DDRSM dynamically recognizes the most significant design variables, and builds local approximations based only on the variables. This allows one to estimate gradients by the price of 4-5 model evaluations without significant loss of accuracy. As a result, HMGE efficiently optimizes highly non-linear models with dozens and hundreds of design variables, and with multiple Pareto fronts. HMGE efficiency is 2-10 times higher when compared to the most advanced commercial GAs.