Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

CAutoCSD-Evolutionary Search and Optimisation Enabled Computer Automated Control System Design

This paper attempts to set a unified scene for various linear time-invariant (LTI) control system design schemes, by transforming the existing concept of “computer-aided control system design” (CACSD) to novel “computer-automated control system design” (CAutoCSD). The first step towards this goal is to accommodate, under practical constraints, various design objectives that are desirable in both time and frequency domains. Such performance-prioritised unification is aimed at relieving practising engineers from having to select a particular control scheme and from sacrificing certain performance goals resulting from pre-commitment to such schemes. With recent progress in evolutionary computing based extra-numeric, multi-criterion search and optimisation techniques, such unification of LTI control schemes becomes feasible, analytical and practical, and the resultant designs can be creative. The techniques developed are applied to, and illustrated by, three design problems. The unified approach automatically provides an integrator for zero-steady state error in velocity control of a DC motor, and meets multiple objectives in the design of an LTI controller for a non-minimum phase plant and offers a high-performance LTI controller network for a non-linear chemical process.