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Multiobjective Optimization Using The Niche Pareto Genetic Algorithm

Authors:
Jeffrey Horn at Northern Michigan University
Jeffrey Horn
Nicholas Nafpliotis
Nicholas Nafpliotis
Nicholas Nafpliotis
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David E. Goldberg
David E. Goldberg
David E. Goldberg
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Abstract and Figures

Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives (i.e., attributes or criteria) have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The most recent development in the field of decision analysis has yielded a rigorous technique for combining attributes multiplicatively (thereby incorporating nonlinearity), and for handling uncertainty in the attribute values. But MultiAttribute Utility Analysis (MAUA) provides only a mapping from a vector-valued objective function to a scalar-valued function, and does not address the difficulty of searching large problem spaces. Genetic algorithms (GAs), on the other hand, are well suited to searching intractably large, poorly understood problem spaces, but have mostly been used to optimize a single objective. The direct combination of MAUA and GAs is a logical next step...
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Comparison Set Individuals
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... Now, recently the indicator-based algorithms are proposed. The most popular Pareto-based approaches such as multiple objective GA [11], niched Pareto genetic algorithm (NPGA) [12], and non-dominated sorting genetic algorithm (NSGA) [13] were immediately tested on multiple real time applications and gain the publicity. However, they exclude elitism and therefore cannot guarantee that the non-dominated solutions obtained during the search are preserved. ...
... It has been reviewed that bit flip mutation is used in most of the MOEAs. Few exceptions are observed as below: some MOEAs are adopted hybrid mutation in [12], shift mutation in [48], adaptive mutation in [53], probability mutation in [58], and crowding mutation in [63]. ...
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... This algorithm works on the concept of the tournament selection method. Horn et. al 1993Horn et. al ,1994 [16,26] proposed the NPGA by using the concept of tournament selection method based on Pareto dominance. In NSGA, the populations set is in the hierarchy in nature and consider only one set of the population at a time this may take more time to classify the population. In NPGA, the two individuals are selected randomly ...
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... The presented method follows four individual main steps which are: data preprocessing, training of individual models, evaluation of the trained models, and population update based on the evolutionary processes. Specifically, MEvA-X, except the main framework of the EA with the known operators (Selection, Crossover, Mutation), implements a niched Pareto frontier ranking scheme which makes it appropriate for searching big feature spaces without converging to one local minimum (Horn et al., 1994). The niches are essentially different peaks (local maxima) in the objective function and this method keeps a relative balance between the distribution of the solution in these valleys to preserve pluralism and promote the searching of the feature space. ...
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