Decision variables. In a linear program, the variables are a set of quantities to be determined for solving the problem; i.e., the problem is solved when the best values of the variables have been identified. The variables are sometimes called decision variables because the problem is to decide what value each variable should take. Usually, the variables represent the amount of a resource to use or the level of some activity. For instance, a variable might represent the number of acres to cut from a particular part of the forest during a given period.
Keywords Travelling Salesman Problem, Genetic Algorithm, Selection, Sequential Constructive Crossover, Mutation I. INTRODUCTION Optimization is the process of making something better. An optimization problem is the problem of finding the best solution from all available solution spaces. The terminology “best” solution implies that there is more than one solution. Travelling salesman problem also results in more than one solution but the aim is to find the best solution in a reduced time and the performance is also increased.
Besides that, it solves optimization problems over discrete structures. Artificial intelligence, software engineering, , mathematics and machine learning are several fields which have been applying the combinatorial optimization techniques. From the literature studies, according to F. Neumann, C. Witt, the goal of combinatorial optimization problem is either minimizing or maximizing a
For the solution of nonlinear system of equations, we use multigrid method with FAS scheme. FAS involve an inner and an outer iteration; the outer iteration is the FAS correction scheme, while the inner iteration is usually a standard relaxation method such as Gauss-Seidel iteration
I also know how to find the probability with given statements and conditional statements. I know how to use tree diagrams to see the possible outcomes of events. For example, if I flip a coin, I know the probability of getting a head is a half or the probability of rolling a four on a six-sided die is 1/6. I know that probability plays an important role in decision-making and in economies with regards to business predications. The idea of this dilemma and the probability of decisions being made that are either to people’s advantage or not to their advantage, interests me and for that reason, along with my preference for economics, I want to do further research in the mathematics behind the high probability of disadvantageous decisions being made.
System of Non-Linear Equations Start this lesson by answering the warm-up questions below. This is to assess the ideas or concepts related to Non-linear and Linear equations. Activity 1.5.a Linear Against Non-Linear Equations Answer the following questions below: 1. Determine if the equation is linear or not a. 2x + 3y – 4 = 0 b. xy + 2 = 0 c. x = y d. y = 0 e. x = 2y + 3 2.
So several researchers generally have recourse to heuristic methods. For the packing problem, the two-dimensional container can be square, circle, semicircle, polygon, cubs and rectangle and the items can be rectangles, circles or irregular. However, as an NP-hard problem, there is no exact algorithm to obtain optimality in polynomial time unless N = NP, and researchers have resorted to heuristics or approximation methods. As a well-known NP-hard problem, the circle packing problem We consider two-dimensional (2D) circle packing problem (CPP) where items are circles. is to pack n given items with no overlap into a two-dimensional container such that the container size is minimized.
When either the system state dynamics or the observation dynamics is nonlinear, the conditional probability density functions that provide the minimum mean-square estimate are no longer Gaussian. The optimal non-linear filter transmits these non-Gaussian functions and evaluate their mean, which represents a high computational burden. A non-optimal approach to solve the problem, in the frame of linear filters, is the Extended Kalman filter (EKF) or the Unscented Kalman filter (UKF). The EKF or UKF implements a Kalman filter for a system dynamics that results from the linearization of the original nonlinear filter dynamics around the previous state estimates. This research develops an algorithm for the application of the Smooth Transition Autoregressive (STAR) methodology by Terasvirta (1994) to the estimation of the state equation of the Kalman filtering technique.
There are two main approaches in solving continuous-time portfolio optimization problem. One is the stochastic control approach and the other is the martingale approach. In the stochastic control approach, an optimal solution is conjectured by guessing a solution to the HJB equation. It is necessary to verify that the conjectured solution is in fact solution to the original problem. Korn and kraft  pointed out, the verification is often skipped since it is mathematically demanding for kim and omberg examined the finiteness of conjectured value function very carefully, but they could not provide verification conditions.
Researcher does well a lot work on this problem to find an optimized solution for this problem but no one able provide accurate solution to solve this problem. Many scientists tried several approaches but everyone got the solution by its own way by using different algorithms one of the approaches was used “ a multilevel graph portioning scheme to solve travel sales man problem” although traveling sales man problem is not a simple problem because it belong to NP-Complete class problem. they tried to solve this problem by using multilevel graph partitioning scheme in which they used vertices and edge to represent the graph but in this problem its several weaknesses one of them is the arbitrary initial portioning of the vertex set that is capable of can affecting the desire result quality. Most popular paradigm is the arbitrary initial partitioning of a vertices, it can a have major affect quality of a solution. Comprehensive methods depend on characteristics of the whole graph and not depend on the arbitrary initial partitioning.