Sensitivity analysis of certain time -dependent matroid base models solved by genetic algorithms
Since the advent of the computer, computer scientists have studied evolutionary systems with the idea that evolution could be used as an optimization tool for engineering problems. John Holland invented genetic algorithms (GA's) in the 1960s . The genetic algorithm paradigm is an adaptive methodology based on Darwinian natural selection and genetic inheritance. It applies operations of selection (based on survival of the fittest), crossover (i.e., mating) and mutation to a given population of potential solutions to generate a new, more fit population of potential solutions. After a number of generations the process converges to an optimal or near optimal solution. Although his goal was not to design algorithms to solve specific problems, but rather to formally study the phenomenon of adaptation as it occurs in nature, Holland developed ways in which the mechanisms of natural adaptation might be implemented in computer systems. Holland's 1975 book “Adaptation in Natural and Artificial Systems” presented the genetic algorithm as a construct of biological evolution and gave a theoretical framework for using the genetic algorithm . All of these genetic algorithms performed optimization on problems where the costs were fixed with no dependency on time. Researchers Gargano and Edelson  have developed five theoretical models to study the use of genetic algorithms (GA) on optimal matroid base models whereby the matroid element costs are not fixed, but are time dependent. To date, only one has actually been coded and executed but without further analysis . As stated previously, what is unique about these models is that matroid element costs are not fixed, but are time dependent. It is important to understand the impact of certain factors on the performance of genetic algorithms. Many factors such as population size, reproduction operators, fitness function, and encoding methods have a significant impact on the performance of the algorithm. Researchers have studied the impact on genetic algorithm's performance from various factors including problem encoding, crossover and mutation operators, population size, crossover and mutation rate, and stop criterion [DeJong, 1975; Grefenstette, 1986; Dengiz, Altiparmak, and Smith, 1997] . This dissertation is designed to study the performance of genetic algorithms where the costs are not fixed but time dependent. Using two of the models developed by Gargano and Edelson, this dissertation set out to implement these models and study the factors that influence the performance of these types of genetic algorithms. Not only will the study focus on the classical factors such as population size, problem size, crossover and mutation rate but also new factors brought about by the fact that element costs are time dependent. These new factors which influence these types of genetic algorithms are the structure of the cost table and the introduction of slack time.
DeCicco, Joseph, "Sensitivity analysis of certain time -dependent matroid base models solved by genetic algorithms" (2002). ETD Collection for Pace University. AAI3064834.
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