# Mathematical optimization

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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…

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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…

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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…

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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…

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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…

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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…

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Simulation In this study, optimisation of both parameters together with energy performance assessment of the mechanical ventilated PV façade system are conducted using TRNSYS. The schematic diagram of the components used to simulate the system is provided in Figure 2. The façade is part of a prototypical daylit cellular office building that is represented by Type 56 in Figure 2. This built form is chosen because it accounts for more than 67% of office buildings in England and Wales [25]. The…

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It is inserted into the equation simply to give a positive solution at the origin; we are artificially creating a solution: 2x1 + 4x2 - s1 + A1 = 16 2(0) + 4(0) - 0 + A1 = 16 A1 = 16 The artificial variable is somewhat analogous to a booster rocket—its purpose is to get us off the ground; but once we get started, it has no real use and thus is discarded. The artificial solution helps get the simplex process started, but we do not want it to end up in the optimal solution, because it has no real…

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Start, even as simply as writing an essay, but a good one, it requires a start and it requires the writer to start with his or her magic pen to let the article flow. Operation research is my new start. In the field of operation research, optimization attracts me with its unique beauty. Nonlinear optimization, linear optimization, integer optimization, decision diagram all these fields of study start letting me know what I’m good at and what I will devote my life in. Starting a PhD in operation…

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5. Hopf-Andronov-Poincare bifurcation In this section, we shall show that the system (2) undergoes a Hopf-Andronov-Poincare bifurcation by using as a bifurcation real parameter. Without loss of generality, suppose that is a function of and . Then system (2) becomes (29) with . System (29) can be written as (30) where , and is the bifurcation real parameter. The function is a on an open set in . Let be the set of equilibria of system…

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