# 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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CHAPTER 4 PSO AND GA TECHNIQUE 4.1 Moth Flame Optimization In the proposed MFO algorithm, I assumed that the candidate solutions are moths and the problem’s variables are the position of moths in the space. Therefore, the moths can fly in 1-D, 2-D, 3-D, or hyper dimensional space with changing their position vectors. Since the MFO algorithm is a population-based algorithm. It should be noted here that moths and flames are both solutions. The difference between them is the way we treat and…

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SOCIAL MEDIA OPTIMIZATION (SMO) Social media optimization (SMO) is the utilization of social media outlets include RSS feeds, news and bookmarking sites, social networking sites and video and blogging sites to publicize or create awareness regarding a commodity, brand or event. It works in achieving a potential for business for the product, as it attempts to letting as many people know about it as humanely possible. The age today is that of social networking, and staying in constant touch with…

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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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all the tours. * Temperature is cooled by the predetermined cooling factor in each iteration. * Once the process ends we have the best possible . C. Pseudo Code 1. Choose an initial tour S 2. Choose a temperature = > 0 3. Repeat : a.Choose a new tour S’ b. Let = , where is energy (length) of tour c. If , accept new tour i.e., d. Else if , accept new tour e. Else reject new tour f. Reduce temperature according to cooling factor 4. Until termination conditions are met 1.…

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is the discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization \cite{dorigo2007}. The name was firstly coined by Beni and Weng in the 1989 in order to present cellular robotic systems as capable of being intelligent \cite{beni1989}. Cellular Robotic Systems are collections of autonomous, non-synhronized, non-intelligent robots cooperating to achieve some given tasks \cite{beni1993}. In area of…

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2.3.2 PARTICLE SWARM OPTIMIZATION (PSO) Particle Swarm Optimization [27] is a population-based stochastic optimization developed by Dr. Ebehart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. In PSO, each single solution is a “bird” (particle) in the search space of food (the best solution). All particles have fitness values evaluated by the fitness function (the cost function for ELD problem), and have velocities that direct the “flying” (or evaluation)…

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What is the maximum value the queues attain? Can we control the distribution 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…

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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…

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Traveling Salesman Problem (TSP) is one of combinatorial optimization problems. X TSP is NP-hard problem which defined as a set of cities and each city should be visited once with minimum tour length. This paper solved this problem using Firefly Algorithm (FA) and k-means clustering by three steps: cluster the nodes, finding optimal path in each cluster and connect the clusters. The first step is to divide all nodes into sub-problems using k-means clustering, the second step is to use FA to find…

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