Numerical Approach for Solving a Difficult Nonlinear Programming problem by a Meta Heuristic Algorithm
Subject Areas :علی اصغر توفیق 1 , منیره السادات محمودی 2
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Keywords: Minimum Volume Ellipsoid Covering a Finite Set of Points problem Simulated Annealing Algorithm,
Abstract :
Since exact algorithms are able to find the optimal solution exactly, they are not effective for solving the complicated and difficult optimization problem and the time of problem solving is increased exponentially; moreover approximate algorithms are able to find the approximate solution (which is very near to the optimal solution) for very complicated and difficult optimization problem in a short period of time. One of the well-known nonlinear programming problems is finding minimum volume ellipsoid covering a finite set of points problem. This problem is solvable for two dimensional space, however heuristic methods are even used to solve it in two dimensional space are very difficult. It would be difficult to achieve the exact solution for three dimensions or more because of huge volume of calculation. In this paper, SA algorithm is used and the problem is solved in two and three dimensions; in addition it can be used for n dimensions as well.
