Inspired by the mechanism of generation and restriction among five elements in Chinese traditional culture, we present a novel Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO). During the optimization process of MOFECO, we use individuals to represent the elements. At each iteration, we first divide the population into several cycles, each of which contains several individuals. Secondly, for every individual in each cycle, we judge whether to update it according to the force exerted on it by other individuals in the cycle. In the case of an update, a local or global update is selected by a dynamically adjustable probability P s ; otherwise, the individual is retained. Next, we perform combined mutation operations on the updated individuals, so that a new population contains both the reserved and updated individuals for the selection operation. Finally, the fast non-dominated sorting method is adopted on the current population to obtain an optimal Pareto solution set. The parameters’ comparison of MOFECO is given by an experiment and also the performance of MOFECO is compared with three classic evolutionary algorithms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization algorithm (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and two latest algorithms Knee point-driven Evolutionary Algorithm (KnEA) and Non-dominated Sorting and Local Search (NSLS) on solving test function sets Zitzler et al’s Test suite (ZDT), Deb et al’s Test suite (DTLZ), Walking Fish Group (WFG) and Many objective Function (MaF). The experimental results indicate that the proposed MOFECO can approach the true Pareto-optimal front with both better diversity and convergence compared to the five other algorithms.
A LP Relaxation based Matheuristic for Multi-objective Integer Programming