Multiple Ant Colonies Presented by Brandon Borkholder Based on MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows

Problem Route a fleet of delivery vehicles Minimize cost and time Primary variable is cost/tours Most realistic as vehicles are variable cost

Solution Define two Ant Colony Systems (ACS) One for each parameter

Solution, cont. Cooperate by pheromone updating Pheromone levels indicate how desirable an arc is Opposing influences: exploration and exploitation Ants decide where to go (probabilistically) based on maximal pheromone levels As an ant passes over an arc, it decreases the pheromone

Implementation Procedure MACS-VRPTW() Repeat v ← #active_vehicles(ψ gb ) Activate ACS-VEI(v - 1) Activate ACS-TIME(v) While ACS-VEI and ACS-TIME are active Wait an improved solution ψ from ACS-VEI or ACS-TIME ψ gb ← ψ if #active_vehicles(ψ gb ) < v then kill ACS-TIME and ACS-VEI End While until a stopping criterion is met

Implementation, cont. Find an initial solution for given cost Improve on time until we can improve on cost Then improve on time with that parameter of cost

Implementation, cont. The ants for time might not find a complete solution Import the other edges in a greedy best-first manner

Alternative Methods Exact methods Tabu and large neighborhood searches Works well for constricted time windows Solution space is small

Results

Advantages/Disadvantages Very fast < 30 minutes for ~100 nodes All the advantages of swarm Adaptable, etc. Disadvantages Is a complex system with many concepts Really not optimizing both parameters simultaneously

Questions