Differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.
Most of the mathematical optimization algorithms require a derivative of optimization problems to operate. The majority of meta-heuristics are gradient-free. This means meta-heuristics (including DE) does not require the optimization problem to be differentiable, as is required by classic optimization methods such as gradient descent and quasi-newton methods.
Multi-trial vector-based differential evolution (MTDE) is distinguished by introducing an adaptive movement step designed based on a new multi-trial vector approach named MTV, which combines different search strategies in the form of trial vector producers (TVPs). In the developed MTV approach, the TVPs are applied on their dedicated subpopulation, which are distributed by a winner-based distribution policy, and share their experiences efficiently by using a life-time archive. The MTV can be deployed by different types of TVPs, particularly, we use the MTV approach in the MTDE algorithm by three TVPs: representative based trial vector producer, local random based trial vector producer, and global best history-based trial vector producer. (Credits to Dr. Mohammad H. Nadimi-Shahraki )