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problem has inequality constraints, the Kuhn-Tucker conditions can be used to identify the optimum solution. 5.4.4.2 Numerical method optimization This optimization technique can be categorized according to specific method, as follows: Linear programming: Studies the case in which the objective function f is linear and the set A, where A is the design variable space, is specified using only linear equalities and inequalities. Integer programming: Studies linear programs in which some or all variables are constrained to take on integer values. Quadratic programming: Allows the objective function to have quadratic terms, while the set A must be specified with linear equalities and inequalities. Nonlinear programming: Studies the general case in which the objective function or the constraints or both contain nonlinear parts. Stochastic programming: Studies the case in which some of the constraints depend on random variables. Dynamic programming: Studies the case in which the optimization strategy is based on splitting the problem into smaller sub-problems. Combinatorial optimization: Concerns problems where the set of feasible solutions is discrete or can be reduced to a discrete one. Evolutionary algorithm: Involves numerical methods based on random search. 5.4.4.3 Evolutionary algorithm An evolutionary algorithm utilizes techniques inspired by biological evaluation reproduction,mutation,recombination, andselection.Candidate solutionsto the optimization problem play the role of individuals in a population, and the fitness function determines the environment within which the solutions “live.” Evolutionary algorithm methods include genetic algorithms (GAs), artificial neural networks (ANNs), and fuzzy logic [93]. These approaches are discussed further below. Each of the approaches is available in toolboxes developed by Math Works and can thus be used easily with MATLAB software. 65PDF Image | Energy Systems for Multigeneration Purposes
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