Download
1 / 14
200 likes | 613 Views
VEHICLE ROUTING PROBLEM. אליאור זיברט דרור חבלין. Classical Vehicle Routing. n customers must be served from a single depot utilizing vehicle with capacity Q for delivering goods Each customer requires a quantity qi ≤ Q of goods Customer orders cannot be split. Depots
E N D
VEHICLE ROUTING PROBLEM אליאור זיברט דרור חבלין
Classical Vehicle Routing • n customers must be served from a single depot utilizing vehicle with capacity Q for delivering goods • Each customer requires a quantity qi ≤ Q of goods • Customer orders cannot be split
Depots Multiple locations Vehicles Multiple vehicle types and capacities Release, maximum and down times Customers Time windows (soft or hard) Accessibility restrictions Priority Pickup and delivery Routes Maximum time Link costs Objective Functions Minimize total traveled distance Minimize total traveled time Minimize number of vehicles Maximize quality of service Multiple objective functions Additional Features
Heuristics that Grow Fragments Nearest neighbor Double-ended nearest neighbor Multiple fragment heuristic Heuristics that Grow Tours Nearest addition Farthest addition Random addition Heuristics Based on Trees Minimum spanning tree Christofides heuristic Fast recursive partitioning How Can It Be Solved ??? AND MANY MORE
OUR CHOICE OF ALGORITHEM Ant Colony Optimization (ACO)
ACO Concepts • Ants (blind) navigate from nest to food source • Shortest path is discovered via pheromone trails • each ant moves at random • pheromone is deposited on path • ants detect lead ant’s path, inclined to follow • more pheromone on path increases probability of path being followed
ACO System • Virtual “trail” accumulated on path segments • Starting node selected at random • Path selected at random • based on amount of “trail” present on possible paths from starting node • higher probability for paths with more “trail” • Ant reaches next node, selects next path • Continues until reaches starting node • Finished “tour” is a solution
ACO System, cont. • A completed tour is analyzed for optimality • “Trail” amount adjusted to favor better solutions • better solutions receive more trail • worse solutions receive less trail • higher probability of ant selecting path that is part of a better-performing tour • New cycle is performed • Repeated until most ants select the same tour on every cycle (convergence to solution)
The Algorithm • At the beginning of the search process, a constant amount of pheromone is assigned to all arcs. When located at a node i an ant k uses the pheromone trail to compute the probability of choosing j as the next node: • α - is a weight function based on arc cost etc.. • β– is a weight function base on arc lengthi • When all ants have comleted a tour each ant compute the quantity per unit of length , the pheromone value changes as follows: • By using this rule, the probability increases that forthcoming ants will use this arc.
