Derivative-free Efficient Global Optimization on High-dimensional Simplex

In this paper, we develop a novel derivative-free deterministic greedy algorithm for global optimization of any objective function of parameters belonging to a unit-simplex. Main principle of the proposed algorithm is making jumps of varying step-sizes within the simplex parameter space and searching for the best direction to move in a greedy manner. Unlike most of the other existing methods of constraint optimization, here the objective function is evaluated at independent directions within an iteration. Thus incorporation of parallel computing makes it even faster. Requirement of parallelization grows only in the order of the dimension of the parameter space, which makes it more convenient for solving high-dimensional optimization problems in simplex parameter space using parallel computing. A comparative study of the performances of this algorithm and other existing algorithms have been shown for some moderate and high-dimensional optimization problems along with some transformed benchmark test-functions on simplex. Around 20 – 300 folds improvement in computation time has been achieved using the proposed algorithm over Genetic algorithm with more accurate solution.