Combination of Ant Colony Optimisation and Exact Methods applied to Routing Problems Samuel Carvalho Ana Maria Rodrigues José Soeiro Ferreira Supported by FCT (PTDC/EGE GES/121406/2010)

Agenda 1. Introduction 2.Case Study 3.Models 4.ACO-LML 5.Computational Results 6.Conclusions and Future Work

1. Introduction Solid waste collection – a real problem.

Monção 33 boroughs 220 km 2 20,000 inhabitants 2. Case study

Depot Population Selective Containers Undifferentiated Containers Landfill Transfer Station 2. Case study

Capacity (m 3 ) Time to Collect (sec) T10,1230 T20,860 T30,0820 T43240 T55300 T60,055 T2 T1 T5 T3 T2 T4 T6 2. Case study Different Containers

T1 T2 T3 T4 T5 T6 Street Length (m) ID Container Borough (name) 2. Case study Data

Street Length (m) Deadheading (sec) Time Service (sec) Quantity to collect (m 3 ) Borough (name) 2. Case study More Data

Streets required and streets not required; One way streets; Capacity restrictions; Containers with different capacities; Landfills/transfer stations with limitations related to the number of daily discharges; Mixed Capacitated Arc Routing Problem with Limited Multi-Landfills MCARP-LML 2. Case study Problem Characteristics

Different types of vehicles 2. Case study MCARP – LML Heterogeneous fleet Truck limitations Dump cost MCARP-LML-HF Problem Characteristics

3. Models MCARP-LML ModelMCARP-LML-HF Model

Min Landfill’s restrictions: A. M. Rodrigues e J. Soeiro Ferreira: Recolha de Resíduos Sólidos Urbanos- otimização de rotas. Proceedings IO pp Models MCARP-LML Model

Q 1 e Q 2 - Capacities of vehicles 1 and 2 Required edges (E R ) : E R1 - Served by type 1; E R2 - Served by type 2; E R \ (E R1  E R2 ) - Served by both types; The same happens with the arcs: A R1, A R2 e A R \(A R1  A R2 ) 3. Models MCARP-LML-HF Model

Some new restrictions: 3. Models Min MCARP-LML-HF Model

4. ACO-LML Ant Colony Optimization

4. ACO-LML ACO - LML Initialization Initial population generation ACO algorithm

4. ACO-LML Initialization Read the Graph Initialize parameters # Ants # Elitist Ants Pheromone Evaporation parameter # Iterations Others Shortest Paths

4. ACO-LML Initial Population Generation Path Scanning with Random Criterion (PSRC) Greedy Criteria Giant Route Global and Local Search Division in feasible routes Verify Clones Initialize pheromones

4. ACO-LML ACO algorithm Solution Construction Choose the next link to the Giant Route 1.Desirability 2.More Pheromones 3.Random Probabilities based on Pheromone quantities Global and Local Search Division in feasible routes Elitist Ants

Pheromone Actualization Required edge - Required edge Required edge - Depot Proportional to the inverse value of the solution (among others) Pheromone Evaporation After x iterations without improvement Minimum τ 0 ACO algorithm 4. ACO-LML

Local and Global Search Global Search Local Search Start End Required Zone Not Required Zone Required Edge Optional Edge

4. ACO-LML Division in feasible routes Capacities of the vehicles Capacities of the Landfills

4. ACO-LML ACO - LML - HF Division Heuristic ACO - LML adaptation

5. Computational Results (In GDB Alto Minho Instances Tools CPLEX Microsoft Visual Basic 2010

5. Computational Results ACO-LML

5. Computational Results ACO-LML-HF

6. Conclusion and Future work Routing problems in connection with Solid Waste Collection Future work Combination with exact methods Sectoring Problem Consideration of two Optimization Models Development of a new ACO algorithm Solutions based on a real case