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…
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…
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.…
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)…
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…
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…
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…
Compared to the straight optimization of a non-transition state system to a ground state, transition states are more numerically sensitive and take more time to calculate. To achieve this level of accuracy, we continuously modified second derivative (force constants and frequencies) calculation criteria, which was either calculated initially by Gaussian and then approximated in further steps (Opt=CalcFC), or re-calculated at each step (Opt=CalcAll). Approximating the force constants was usually…
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…
In real life, Linear programming is part of a very crucial area of math called "optimization techniques". This field of study is used daily in the allocation and organization of resources. These "real life" systems can range from having dozens to hundreds of variables, or even way more. If you compare algebra to linear programming, in algebra you 'll only work with the very simple two-variable linear case. Linear programming is used largely by economists, business managers and public…