A configuration space evolutionary algorithm with local minimizer for weighted circles packing problem

Abstract

The weighted circles packing (WCP) problem typically aims for arranging some circular objects into a larger rectangular (or circular) container with the constraint of non-overlapping. The WCP problem derives from the layout design of the very large-scale integration (VLSI) and the plant machine equipment layout. It has wide applications in engineering practice. The problem considers two different objectives: minimizing the area of the envelope container and minimizing the sum of weighted distances associated with the given circular objects. Based on the quasi-physical strategy, the WCP problem becomes an unconstrained optimization problem. Then, a novel multi-objective evolutionary algorithm (MOEA) called configuration space evolutionary algorithm with local minimizer (CSE_LM) is proposed to solve the problem. Unlike the traditional MOEAs, the unique aspects of the CSE_LM mainly include a special evolutionary mechanism of configuration library (population), a convergence strategy of introducing a gradually decreasing configuration library radius, and a nearest and farthest candidate solution method to maintain diversity and uniformity of configurations. Furthermore, a novel mechanism of introducing the minimization of an extrusive elastic potential energy as an additional objective in the layout system is developed to handle the interference among circular objects. Experiment results for four typical instances show the validity of the CSE_LM for the WCP.