Population Based Heuristics Approaches for Packing Circles in a Circular Container

Abstract

In this Thesis we mainly deal with packing problems. Packing problems have mathematical as well as practical application point of interest. Population based heuristic algorithms like Evolutionary algorithm, Genetic algorithms etc. frequently used for such Non Polynomial (NP) hard problems. But packing circles into a circular container is relatively new. Here, we present Population based Basin Hopping (PBH) rather than Monotonic heuristic search approach like Monotonic Basin Hopping (MBH) to solve the problem of packing identical circles within a minimum size of circular container. For the evolution among the population we will also present two dissimilarity measures. Extensive computational experiments have been performed for analyzing the problem as well as for choosing an appropriate way the parameter values for the proposed methods. From the experiments, It is observed that the population based basin hopping approach is comparable for solving packing problem. Moreover when the problem has many narrow basin, then population based basin hopping may perform better than MBH approach. Also several improvements with respect to the best results reported in the literature have been detected.

It is worthwhile to mention here that MBH heuristic approaches are successfully implemented for solving equal circles problems. For the presence of combinatorial part, due to unequal radii, simple extension of MBH approach is not the appropriate way to co-opt the problem of packing nonidentical circles within a smallest circular container. Here, we present a modified Monotonic Basin Hopping heuristic approach to solve the problem. As well as some new perturbation moves are proposed which are suitable for the case of unequal circles packing problems. Several improvements with respect to the best results reported in the literature have been detected.