The Vehicle routing problem (VRP) is one of the most challenging combinatorial optimization and nonlinear programming problems. The problem is to design a set of routes for a fleet of vehicles serving a number of customers or cities. The objective of the problem is to serve every customer with known demands at minimum vehicle routing cost. VRP arises in the fields of transportation, distribution and logistics planning; often in the context of delivering or picking up goods. The vehicle routing problem with time windows (VRPTW) is more specific than VRP such that the customers have time windows constraints within which the deliveries (or pickups) must be satisfied. Both VRP and VRPTW are integer programming problems categorized as NP-hard problems, in which the computational effort required to solve a problem increases exponentially with the problem size. With large size problems, the approximate solutions are obtained by numerical methods. Various heuristic methods have been proposed. These methods rely on the intrinsic nature of the problems. With advanced technologies, heuristic methods can be efficiently used to generate a promising solution.

Large-scale optimization

Optimization is a challenging problem that involves determination of the action parameters that best achieve a desired or overall goal or objective. The overall objective may consist of several objectives that have conflicts. In order to achieve the overall objective, some objectives may not be at the maximum or minimum. Otimization arises in decision problems in business or production activity planning. In a production problem, the objective may be to find the combination of input variables (resources) that minimizes the production costs or maximizes the profits. In a capital budgeting problem, the objective may be to select those projects that maximize the net present value of the investments. Usually, a large number of input parameters is involved in the problem and the exact solution may not be possible to obtain. Several heuristic methods such as Simulated Annealing, Genetic algorithm, etc. have been investigated and provide promising solutions. Each method may be suitable to certain types of problems.