A New Treatment Solution of Interval Nonlinear Programming Problems: A Case Study of Green Fuel Production

Abstract

Green fuel is growing in popularity in recent years. Bio-reactive waste converted to green fuel through anaerobic digestion technology. The performance of biogas unit has been optimized and formulated as interval programming problems as function of inlet feed rate, retention time fermentation temperature and pH. A new treatment for solving the interval nonlinear programming problem (INPP) is discussed. All the intervals in the INPP are replaced by new variables. This the modified nonlinear programming problem (MIPP). We presented three hybrid evolutionary algorithms (EAs) which are chaotic genetic algorithm (CGA), chaotic particle swarm optimization (CPSO) and chaotic firefly algorithm (CFA) to solve MIPP. The Karush–Kuhn–Tucker (KKT) conditions for MIPP are gotten. These equations are solved as algebraic equations. Its solutions may be represented as a function of new variables to get the stability set of first kind. The staring points in EAs is gotten by the Newton method. Finally, the comparison between the stability set of first kind, CGA, CPSO and CFA are presented with discussion. An empirical optimization model of biogas production has been constructed with accuracy of 90%.