# Comparison of Optimization Algorithms

Comparison of Optimization Algorithms Problem A: Consider the following three optimization problems: Numerically find the minimum (=optimal) feasible design vector x for each of the three problems using a gradient-based search technique of your choice  For each run (2runs) record the starting point you used, the iteration history (objective value on y-axis and iteration number on x-axis), the final point at which the algorithm terminated and whether or not the final solution is feasibleProblem B: Repeat problem a but this time using a heuristic technique of your choice Explain how you tuned the heuristic algorithm. compare convergence history of both method and frequency at which the technique gets trapped in a local maximum1. The Rosenbrock Function his function is known as the banana function because of its shape; it is described mathematically in Equation 1. In this problem, there are two design variables with lower and upper limits of [?5,5]. The Rosenbrock function has a known global minimum at [1,1] with an optimal function value of zero. Minimize f(x) = 100 (x2 ?(x1)^2)^2  + (1?x1) ^2 2. The Eggcrate Function: This function is described mathematically in Equation 2. In this problem, there are two design variables with lower and upper bounds of [?2?,2?]. The Eggcrate function has a known global minimum at [0,0] with an optimal function value of zero. Minimize f(x) = (x 1 )^2 + (x2)^2 +25 ((sin^2) x1 +(sin^2) x2)3.Golinskis Speed Reducer :This hypothetical problem represents the design of a simple gearbox such as might be used  in a light airplane between the engine and propeller to allow each to rotate at its most efficient speed. The objective is to minimize the speed reducers weight while satisfying the 11 constraints imposed by gear and shaft design practices. A known feasible solution obtained by a sequential quadratic programming (SQP) approach (Matlabs fmincon) is a 2994.34 kg gearbox with the following values for the seven design variables: [3.5000,0.7000,17,7.3000,7.7153,3.3502,5.2867]. This is a feasible solution with four active constraints, but is it an optimal solution?Hide

Price (USD)
\$