A proportional, integral and derivative differential evolution algorithm for global optimization

The proportional, integral, and derivative differential evolution algorithm (PID-DE) is proposed as a new type of interdisciplinary metaheuristic evolutionary algorithm in this paper. The inspiration of PID-DE is derived from the classical proportional, integral, and derivative control method in engineering, and it is used in the framework of the differential evolution (DE) algorithm. To begin, the mathematical models of proportional search, integral search, and derivative search are established as the fundamental search operations. Five different types of optimizers that use a combination of these three basic operations and an additional mutation operation are presented. The selection and crossover methods in DE are then modified to maintain population diversity while also improving global search capacity, and a feedback strategy is established to adaptively adjust the subgroup member of each optimizer. Following that, an integrated high-accuracy, rapid-convergence, and stable metaheuristic is invented using the comprehensive information utilization principle and flexible parameter determination method. Five groups of experiments are studied to assess the overall performance of the proposed algorithm. The first test comprises 12 standard benchmark functions with minimum optima. In Tests 2 and 3, the 52 functions of Congress on Evolutionary Computation (CEC) 2014 and CEC 11 are evaluated using PID-DE under standard test conditions. Besides, three classic real-world engineering design problems and the CEC 2020 test suit are studied for the constrained optimization test. The experimental tests validate PID-DE's higher accuracy and faster convergence speed in numerical optimization when compared with the representative approaches and top algorithms in the CEC competitions.