Linear programming which is also known as “Linear Optimization” is a way to achieve best outcomes in a Mathematical Model using different linear solutions .Linear Programming is a special case of Mathematical Optimization .Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries. The method of Linear Programming was originally developed by American mathematicians between 1945 and 1955 to solve problems arising in economic planning ad industries .The problems involve constraints, quantity of raw material available in the industry. Linear Programming problems are generally solved by graphical representation if…
And who wants to site on a chair that has no sitting scaffold, even though it needs less material to be manufactured? But hold one a second. How about the aesthetic aspects of this bridge shown below? Nobody have ever thought about this design before! Topology Optimization may be an architectural tool rather a material saving script. In fact,the current approach is to ease and sharpen the results of the topology optimization process to make them applicable into reality despite its funky outputs…
such that we achieve a maximal outflow? What is the maximal load of the factory? How long does it take to process a certain type of snack or cookie? The question we ask is how to control the flow through the network so that a maximum number of goods can be produced and storage costs are minimized. In a simulation only the product flow propagates according to user-defined distribution rates. The simplest choice is equally distributed rates i.e. the arriving goods are consistently fed in parallel…
Literature Survey According to wikipedia, the origins of TSP is yet not known. It was first found in a handbook in 1832 without any prior mathematical statements . It was later formulated by mathematician W.R Hamilton and Thomas Kirkman. The general form of TSP was first studied by Karl Menger in the 30’s. We denote by messenger problem (since in practice this question should be solved by each postman, anyway also by many travelers) the task to find, for ﬁnitely many points whose pairwise…
and formal extensions of logic, while scruffy AI researchers use relatively simpler approach \cite{brownlee2011}. When creating Swarm Intelligence models and techniques researchers apply some principles of the natural swarm intelligence. From biology perspective, swarm behavior (fish schools, flocks of birds, herds of land animals, insects' communities, etc.) is based on the biological needs of individuals to stay and work together without any central control. In such a way, it is believed that…
MORAL DILEMMA Ant and Grasshopper Stephanie Gardner Should the ant give food to the grasshopper? Yes and no. Now I say both for a variety of different reasons. I have a feeling that the ant in this situation is not mean enough to just let the grasshopper go hungry. But is the grasshopper allowed to just get off without any punishment for not working hard? This is a classic argument of mercy verses justice. The ant can't show the grasshopper the mercy that he desires and at the same time have…
Divide and Conquer Strategies: Divide and conquer is an algorithm which design paradigm based on multi-branched recursion. This designed paradigm consists of following phases: 1) Break the problem (divide): Breaking the problem into several sub-problems that are smaller in size. 2) Solve the sub problem(conquer) : Solve the sub-problem recursively . 3) Combine the solutions (Merge): Combine solutions to subproblems to create a solution to the original problem. This technique is the basis of…
processing the cluster center to help compute your contours place while using the image the first contour is defined in the boundary of your image. To move the particular level set inwards, many people calculate the indoor sub region including zero level needs using 휙 > 0. This SDF satisfies your desirable property |∇퐼| = 1. The action functional (휙) hard disks the zero stage set toward finished boundaries [38-40]. Keeping 휙 pre-programmed and minimizing the force 퐸 regarding 푐1 and 푐2, it…
4 The Simplex Method As we have seen, a linear programming problem forms a convex polygon in the best possible scenario. It is imperative to obtain a process that would assist in determining the optimal solution without the need to examine the graphical representation. The need for an algorithm that would perform such process was essential in the early days of the formulations of linear programming problems. Although challenging, the task was accomplished by a mathematician of the twentieth…
provide details of the four modules of this invention. However, any one module of this invention can’t solve our problem alone. It is the interaction of all parts that allow the user to understand and improve the optimization models. We begin by defining the optimization problem. Our objective is to maximize or minimize the sum of objective terms by selecting optimal feasible levels of the independent variables. The set of process limits or constraints define the feasible region. For…