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Ant Colony Optimization Chapter 5

Ant Colony Optimization Chapter 5. Ant Colony Optimization for NP-Hard Problems Ben Sauskojus. NP-Hard Problem Types. Routing Problems Assignment Problems Scheduling Problems. Routing Problems. Agents visiting locations Objective depends on order locations are visited. Routing Problems.

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Ant Colony Optimization Chapter 5

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  1. Ant Colony Optimization Chapter 5 Ant Colony Optimization for NP-Hard Problems Ben Sauskojus

  2. NP-Hard Problem Types • Routing Problems • Assignment Problems • Scheduling Problems

  3. Routing Problems • Agents visiting locations • Objective depends on order locations are visited

  4. Routing Problems • Sequential Ordering Problem (SOP) • Generalized asymmetric TSP • Has precedence constraints • Application: ACS based. Top performers use local search (3-opt)

  5. Routing Problems • Vehicle Routing Problem (VRP) • http://www.dna-evolutions.com/dnaappletsample.html • Capacitated (CVRP) • Each customer needs a specific amount of goods

  6. Vehicle Routing Problem • Objectives • Each customer is served by one vehicle • Vehicles start and end at Depot • Vehicles cannot deliver more than overall capacity • Subproblems • TSP • Bin packing problem

  7. Vehicle Routing Problem • Application: AS-rank based.

  8. Vehicle Routing Problem • Time Window (VRPTW) • Each customer has a time window in which they must be served • Objectives • Minimize the number of vehicles (routes) • Minimize travel time • Application • Multiple ACS (Two layered colonies)

  9. Assignment Problems • Assign a set of items to resources • Two assignment Types • Assignment order • Assignment to specific resources

  10. Quadratic Assignment (QAP) • Assigning facilities to locations • Objectives • Minimize the sum of the products between flows and distances

  11. Quadratic Assignment (QAP) • Example • Facilities are ‘Bathrooms’ • ‘Main work Area’ • ‘Parking Lot’

  12. General Assignment (GAP) • Tasks are assigned to Agents • Each Agent has limited capacity • Each Task consumes some of an Agent’s capacity • Assigning tasks incurs a cost • Objectives • Find a feasible task assignment of minimum cost

  13. General Assignment (GAP) • Application: MMAS-based • Only one ant • Only feasible solutions get pheromone • Pheromone has nothing to do with solution quality

  14. General Assignment (GAP)

  15. Scheduling Problems • Allocating scarce resources to tasks over time • Definition: An operation is a job that has to be processed on more than one machine. Example: building a car • Note: Processing time are fixed and job cannot be interrupted

  16. Single-Machine Total Weighted Tardiness (SMTWTP) • Jobs have to be processed sequentially on a single machine • Each job has: • Processing time • Weight • Due date

  17. Single-Machine Total Weighted Tardiness (SMTWTP)

  18. Single-Machine Total Weighted Tardiness (SMTWTP) • Pheromone trails refer to the desirability of scheduling a job to the i-th position • Application: ACS based and is one of the best algorithms for the problem

  19. Job Shop, Open Shop, Group Shop • Given: • A set of Operations • A set of Machines that can only do specific operations • A set of Jobs which consist of operations • Each operation has a processing time

  20. Job Shop, Open Shop, Group Shop • Job Shop (JSP) • Precedence constraints which induce a total ordering • Example: Robbing a bank • Open Shop (OSP) • No precedence constraints • Example: Employee scheduling,Cleaning house

  21. Job Shop, Open Shop, Group Shop • Group Shop (GSP) • Operations are arranged in group. • Groups must be completed in some order • Operations inside groups can be done in any order • Example: Commercial Cleaning

  22. Job Shop, Open Shop, Group Shop • Objectives • Minimize the completion time of the last task (Makespan) • Applications • AS based used for JSP (performs poorly) • AntQ based for OSP (performs poorly) • MMAS based for GSP (performs well)

  23. Job Shop, Open Shop, Group Shop • Pheromones • JSP and OSP pheromones refer to the desirability of scheduling operation j directly after i • GSP pheromones refer to the desirability of scheduling operation j sometime after i

  24. Resource-Constrained Project Scheduling (RCPSP) • Given • Activities with precedence constraints, processing times, and resource requirements • Non-reusable resources • Objectives • Assign to each activity a start time minimizing makespan

  25. Resource-Constrained Project Scheduling (RCPSP)

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