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Answer :
Final answer:
The Evolutionary Solving method in Excel Solver is used for solving nonlinear problems with local optimal solutions. It's based on genetic algorithms, helping address complex optimization problems.
Explanation:
Solving nonlinear problems with local optimal solutions is performed using Evolutionary Solving method, in Excel Solver, which is based on more classical optimization techniques. This method uses concepts from genetic algorithms and natural evolution. It helps to resolve complex optimization problems which are non-smooth, discontinuous or even highly complex. An example of its application could be to find the optimal design of a product within a set of constraints, or maximize profit in a business setting given a certain capital.
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Nonlinear programming involves optimizing a nonlinear objective function subject to nonlinear constraints. Excel Solver uses the Generalized Reduced Gradient (GRG) algorithm to solve nonlinear programming problems. This algorithm is a variant of the more well-known Newton's method for optimization, but with modifications to handle nonlinear constraints.
Solving nonlinear problems with local optimal solutions can be performed using various optimization techniques, including gradient descent, Newton's method, and simulated annealing, among others. However, in Excel Solver, which is a widely used optimization tool, local optimal solutions are typically found using the more classical optimization technique of nonlinear programming.
The GRG algorithm iteratively computes the gradient and Hessian of the objective function, and then uses this information to update the decision variable values. The algorithm then checks whether the updated solution satisfies the nonlinear constraints. If it does, the algorithm terminates. Otherwise, the algorithm modifies the constraints and repeats the process until a feasible solution is found.
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