Block Differential Evolution

In order to solve huge-scale optimization problems, many evolutionary algorithms have been proposed. In this paper, we introduce Block Differential Evolution (BDE) algorithm. The BDE can be categorized into the class of memory-efficient optimization algorithms. The main contribution is to solve large and huge-scale problems effectively and efficiently by reducing the problem dimension by utilizing a dimension-blocking scheme. With respect to the block size times reduced memory usage, furthermore, the proposed algorithm is computationally more efficient because DE operations (i.e., mutation, crossover, and selection) are performed on much smaller vector sizes. In fact, the employed blocking approach helps us to map the higher-dimensional problems into a lower-dimensional one which is more convenient to process during the optimization steps. There is a great demanding potential for the proposed approach to be utilized in embedded systems with low computational resources as a compressed optimization algorithm. This strategy is instantiated and evaluated on some well-known benchmark problems and compared with the baseline classic DE algorithm; the reported results are promising and encouraging for conducting further investigations. To the best of our knowledge, that is the first time a variable blocking scheme has been used in any meta-heuristic algorithm. A detailed explanation of the geometrical behavior of the proposed blocking approach is provided which explains how in a higher search space, a blocking approach is meaningful and applicable to accelerate convergence rate while the memory saving is huge. The reported results in this paper show the experiments on Large-Scale Global Optimization Problems proposed in CEC-2013 benchmark suite with 1,000, 10,000, and 100,000 dimensions and clearly are evidence of the possibility of satisfying two conflicting objectives, namely, efficiency and effectiveness, simultaneously. In order to utilize CEC-2013 benchmark problems for the huge dimensions 10,000D and 100,000D, some modifications and expansions have been done. The proposed approach can be utilized in another population-based optimization algorithm (swarm or evolutionary), and it is not restricted to the DE algorithm. In this paper, DE has been used as a parent algorithm for our conducted case study.