Solving combinatorial optimization problems using a new algorithm based on gravitational attraction
Webster, Barry Lynn
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This dissertation represents the culmination of research into the development of a new algorithm for locating optimal solutions to difficult problems. This new algorithm is founded upon one of the most basic concepts in nature - so basic that it is in fact one of the four primary forces in physics: gravity. It is called the Gravitational Emulation Local Search algorithm, or GELS. Four variants of the algorithm were developed, representing combinations of two basic methods of operation and two modes of search space exploration. Following development, a series of experiments were conducted to assess the capabilities of this new algorithm. Three test problems were used (Traveling Salesman, Bin Packing, and File Assignment). Instances of these problems were generated using several different problem sizes, then solved using three well-known comparison algorithms (Hill Climbing, Genetic Algorithm, and Simulated Annealing) in addition to the four variants of GELS. The outcomes of the experiments were rigorously analyzed using a variety of statistical techniques. The results of the analyses showed that GELS was able to perform on a par with, and in many cases better than, the much more mature and extensively studied comparison algorithms. One of the GELS combinations achieved the best performance rating of any algorithm in solving instances of Bin Packing, and finished in a virtual tie with Simulated Annealing for solving instances of File Assignment and for general purpose performance. Two of the four GELS combinations were also shown to outperform Hill Climbing and the Genetic Algorithm. GELS also performed its task efficiently. Two of the four combinations were shown to be more efficient in locating their solutions than any of the comparison algorithms except Hill Climbing (a greedy algorithm known to produce solutions in very few steps). The solutions produced by GELS were thus not only of comparable or better quality than those of the comparison algorithms, but usually were arrived at more efficiently.