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Vehicle Routing Problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. The objective of the VRP is to minimize the total route cost. In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy algorithm called the savings algorithm. Determining the optimal solution to VRP is NP-hard, so the size of problems that can be optimally solved using mathematical programming or combinatorial optimization may be limited. Therefore, commercial solvers tend to use he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Figure Illustrating The Vehicle Routing Problem
Figure may refer to: General *A shape, drawing, depiction, or geometric configuration *Figure (wood), wood appearance *Figure (music), distinguished from musical motif *Noise figure, in telecommunication *Dance figure, an elementary dance pattern *A person's figure, human physical appearance Arts *Figurine, a miniature statuette representation of a creature *Action figure, a posable jointed solid plastic character figurine *Figure painting, realistic representation, especially of the human form *Figure drawing *Model figure, a scale model of a creature Writing *figure, in writing, a type of floating block (text, table, or graphic separate from the main text) *Figure of speech, also called a rhetorical figure *Christ figure, a type of character * in typesetting, text figures and lining figures Accounting *Figure, a synonym for number *Significant figures in a decimal number Science *Figure of the Earth, the size and shape of the Earth in geodesy Sports *Figure (horse), a sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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LIFO (computing)
In computer science, a stack is an abstract data type that serves as a collection of elements, with two main operations: * Push, which adds an element to the collection, and * Pop, which removes the most recently added element that was not yet removed. Additionally, a peek operation can, without modifying the stack, return the value of the last element added. Calling this structure a ''stack'' is by analogy to a set of physical items stacked one atop another, such as a stack of plates. The order in which an element added to or removed from a stack is described as last in, first out, referred to by the acronym LIFO. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a datum deeper in the stack may require taking off multiple other items first. Considered as a linear data structure, or more abstractly a sequential collection, the push and pop operations occur only at one end of the structure, referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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List Of Graph Theory Topics
This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory terms for basic terminology Examples and types of graphs Graph coloring Paths and cycles Trees Terminology *Node ** Child node **Parent node ** Leaf node ** Root node ** Root (graph theory) Operations *Tree structure *Tree data structure *Cayley's formula * Kőnig's lemma * Tree (set theory) (need not be a tree in the graph-theory sense, because there may not be a unique path between two vertices) * Tree (descriptive set theory) * Euler tour technique Graph limits * Graphon Graphs in logic * Conceptual graph * Entitative graph * Existential graph * ''Laws of Form'' * Logical graph Mazes and labyrinths * Labyrinth * Maze * Maze generation algorithm Algorithms *Ant colony algorithm * Breadth-first search *Depth-first search * Depth-limited search *FKT algorithm * Flood fill *Graph exploration algorithm *Matching (graph theory) *Max flow min cut theorem * Maximum-cardinalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Arc Routing
Arc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a graph, respectively. The objective of arc routing problems involves minimizing the total distance and time, which often involves minimizing deadheading time, the time it takes to reach a destination. Arc routing problems can be applied to garbage collection, school bus route planning, package and newspaper delivery, deicing and snow removal with winter service vehicles that sprinkle salt on the road, mail delivery, network maintenance, street sweeping, police and security guard patrolling, and snow ploughing. Arc routings problems are NP hard, as opposed to route inspection problems that can be solved in polynomial-time. For a real-world example of arc routing problem solving, Cristina R. Delgado Serna & Joaquín Pacheco Bonrostro applied approximation algorithms to find the best ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Vehicle Rescheduling Problem
The vehicle rescheduling problem (VRSP) is a combinatorial optimization and integer programming problem seeking to service customers on a trip after change of schedule such as vehicle break down or major delay. Proposed by Li, Mirchandani and Borenstein in 2007, the VRSP is an important problem in the fields of transportation and logistics. Determining the optimal solution is an NP-complete problem in combinatorial optimization, so in practice heuristic and deterministic methods are used to find acceptably good solutions for the VRSP. Overview Several variations and specializations of the vehicle rescheduling problem exist: * Single Depot Vehicle Rescheduling Problem (SDVRSP): A number of trips need to be rescheduled due to delay, vehicle break down or for any other reason. The goal is to find optimal rescheduling of the existing fleet, using possibly extra vehicles from the depot, in order to minimise the delay and the operating costs. In the Single Depot variation, there is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Chinese Postman Problem
In graph theory, a branch of mathematics and computer science, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge of an (connected) undirected graph. When the graph has an Eulerian circuit (a closed walk that covers every edge once), that circuit is an optimal solution. Otherwise, the optimization problem is to find the smallest number of graph edges to duplicate (or the subset of edges with the minimum possible total weight) so that the resulting multigraph does have an Eulerian circuit. It can be solved in polynomial time. The problem was originally studied by the Chinese mathematician Kwan Mei-Ko in 1960, whose Chinese paper was translated into English in 1962. The original name "Chinese postman problem" was coined in his honor; different sources credit the coinage either to Alan J. Goldman or Jack Edmonds, both of whom were at the U.S. National Bureau of Standards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Simulated Annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound. The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy. Heating and cooling the material affects both the temperature and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tabu Search
Tabu search is a metaheuristic search method employing local search methods used for mathematical optimization. It was created by Fred W. Glover in 1986 and formalized in 1989. Local (neighborhood) searches take a potential solution to a problem and check its immediate neighbors (that is, solutions that are similar except for very few minor details) in the hope of finding an improved solution. Local search methods have a tendency to become stuck in suboptimal regions or on plateaus where many solutions are equally fit. Tabu search enhances the performance of local search by relaxing its basic rule. First, at each step ''worsening'' moves can be accepted if no improving move is available (like when the search is stuck at a strict local minimum). In addition, ''prohibitions'' (henceforth the term ''tabu'') are introduced to discourage the search from coming back to previously-visited solutions. The implementation of tabu search uses memory structures that describe the visited ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Genetic Algorithms
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Metaheuristic
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems. Compared to optimization algorithms and iterative methods, metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems. Many metaheuristics implement some form of stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, by searching over a large set of fea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Binary Data
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including ''bit'' (binary digit) in computer science, ''truth value'' in mathematical logic and related domains and ''binary variable'' in statistics. Mathematical and combinatoric foundations A discrete variable that can take only one state contains zero information, and is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three decimal dig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Job Shop Scheduling
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''job-shop scheduling'', each job consists of a set of ''operations'' ''O''1, ''O''2, ..., ''On'' which need to be processed in a specific order (known as ''precedence constraints''). Each operation has a ''specific machine'' that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |