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A new metaheuristic, known as Global Bacteria Optimization (GBO), is known to solve multi-objective optimization problems and results from previous work has shown improvement over those solutions generated by other metaheuristics, such as genetic algorithms (GA), evolutionary algorithms (EA) and swarm algorithms (PSO). This metaheuristic is inspired on bacteria phototaxis behavior, where the solution space is reduced and gets far closer to the Pareto optima solutions. In this paper, the analytical aspect of the solution to multi-objective problems is approached, where it has been demonstrated how two mathematical functions, when minimized, produce Pareto Optima solutions. A review of the MCDM theory states the conditions that are required for two or more functions to reach their optimal solutions simultaneously. Metrics, such as extreme points and spacing, were compared to exact solutions obtained by MCDM techniques programmed in GAMS, proving that GBO not only produce Pareto Optima solutions, but robustness is also obtained.
Keywords: Metaheuristics; Multi-objective Optimization Problems; MCDM; Partial derivatives; GBO; Extreme Points; Spacing
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