# Combinatorial optimization

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In this project, Vehicle Routing Problem (VRP) is studied. VRP is an NP-hard combinatorial optimization problem. It appears in a large number of real world situations, such as transportation of people and products, delivery services, garbage collection etc. It can be applied everywhere, for vehicles, trains, plains; that is why Vehicle Routing Problem is of great practical importance in real life. The Vehicle Routing Problems (VRPs) are the ones concerning the distribution of goods between depots and customers. In particular, the solution of VRP calls for the determination of a set of routes, each performed by a single vehicle that starts and ends at its own depot, such that all requirements of the customers are fulfilled, all operational constraints…

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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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2.RELATED WORK The artificial bee colony (ABC), an optimization technique is based upon the intelligent moving behavior of honey bee swarm was proposed by Karaboga in 2005. This kind of new Meta heuristic is inspired by the clever foraging behavior of honey bee swarm. The criteria presented in the work is for numerical function optimization. The advantage of ABC is that the global search ability in the algorithm is implemented by introducing neighborhood source production mechanism. Rao et al.…

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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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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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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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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…

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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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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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