Differential evolution with thresheld convergence

During the search process of differential evolution (DE), each new solution may represent a new more promising region of the search space (exploration) or a better solution within the current region (exploitation). This concurrent exploitation can interfere with exploration since the identification of a new more promising region depends on finding a (random) solution in that region which is better than its target solution. Ideally, every sampled solution will have the same relative fitness with respect to its nearby local optimum-finding the best region to exploit then becomes the problem of finding the best random solution. However, differential evolution is characterized by an initial period of exploration followed by rapid convergence. Once the population starts converging, the difference vectors become shorter, more exploitation is performed, and an accelerating convergence occurs. This rapid convergence can occur well before the algorithm's budget of function evaluations is exhausted; that is, the algorithm can converge prematurely. In thresheld convergence, early exploitation is 'held' back by a threshold function, allowing a longer exploration phase. This paper presents a new adaptive thresheld convergence mechanism which helps DE achieve large performance improvements in multi-modal search spaces.