Optimization Assignment

CHPTER 2: OPTIMIZATION
Optimization is a scientific approach to solve for the best solution for a problem. Its applications emerge in many different areas is real-life. For instance, you need to minimize the labor cost in a business or to maximize the profit of a product. On the other hand in an airline company, you need to minimize the flight time of a plane or the fuel cost. In basic words, in an optimization issue, you need to either minimize or maximize the result (the objective or cost function). Of course, you can't generally optimize a situation without some particular constraints. For example, how does a worldwide petroleum refiner choose where to purchase raw petroleum, where to ship it for processing, what products to convert it to,

LIMITATION ON LINEAR PROGRAMMING
4.2. LIMITATION ON NONLINEAR PROGRAMMING
Nonlinear optimization problems are naturally harder to solve than linear problems, and there are less assurances about what sort of solution Solver can find. Suppose the smooth nonlinear problem is convex, the Solver will usually find the globally optimal solution. In any case if the problem is non-convex, Solver will only find a locally optimal solution, close to the starting values of the decision variables, when the Solve is clicked.

At the point when dealing a non-convex problem, it is better to run the Solver starting from a few different sets of initial values for the decision variables. Since Solver follows the trail from the starting value (guided by the curvature of the objective function and constraints and direction) to the last solution values, it will usually stop at peek or valley nearest to the starting value you supply. By beginning from more than one point, it’s possible to build the chances that the best possible "ideal solution" is discovered.

A simple way to do this is to choose the Use MultiStart check box on the GRG Nonlinear tab of the Solver Options dialog: See Multistart Methods for Global Optimization for more

Since it is not able to calculate the gradient of a function at points where the function is discontinuous, or to process curvature details at point where the function is non-smooth, it can't assure that any solution it finds to such a problem is genuinely optimal. Practically, the GRG system can sometimes manage discontinuous or non-smooth functions that are incidental to the problem, however as a general statement, this Solving method needs smooth nonlinear functions for the objective and constraints. Let say, the model includes discontinuous or non-smooth functions, your easiest way is by using Evolutionary Solving method to discover a "good"