Abstract
In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard problem, which justifies heuristics methods for its resolution in larger instances. The main feature of our heuristic is based on the selection of the next circle to be placed inside the container according to the position of the system's center of mass. Our approach has been tested on a series of instances up to 55 circles and compared with the literature. Computational results show good performance in terms of solution quality and computational time for the proposed algorithm.
Highlights
1 INTRODUCTION We study how to install unequal disks in a rotating circular container, which is an adaptation of the model for the two-dimensional (2D) unequal circle packing problem with balance behavioral constraints
We compare our approach with a series of hybrid nature-inspired approaches based on simulated annealing and particle swarm optimization (Xiao et al 2007; Lei, 2009), a hybrid approach based on simulated annealing, neighborhood search mechanism and the adaptive gradient method (Liu et al 2010), a hybrid tabu search algorithm and gradient method (Liu et al 2011), a series of heuristics based on energy landscape paving, gradient method and local search (Liu & Li, 2010; Liu et al 2010, 2015), and a series of algorithms based on quasi-physical approaches, gradient method and local search (Huang & Chen, 2006; He et al 2013; Liu et al 2015)
We have presented a new heuristic called center-of-mass-based placing technique for packing unequal circles into a 2D circular container with additional balance constraints
Summary
We study how to install unequal disks in a rotating circular container, which is an adaptation of the model for the two-dimensional (2D) unequal circle packing problem with balance behavioral constraints. In Liu & Li (2010) the LOP is converted into an unconstrained optimization problem which is solved by the basin filling algorithm presented by them, together with the improved energy landscape paving method, the gradient method based on local search and the heuristic configuration update mechanism. Liu et al (2010) presented a simulated annealing heuristic for solving the LOP by incorporating the neighborhood search mechanism and the adaptive gradient method. The algorithm begins with a random initial configuration and applies the gradient method with an adaptive step length to search for the minimum energy configuration He et al (2013) proposed a hybrid approach based on coarse-to-fine quasiphysical optimization method, where improvement is made by adapting the quasi-physical descent and the tabu search procedures.
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