Authors:
Pablo Adasme
1
;
Janny Leung
2
and
Ismael Soto
1
Affiliations:
1
Universidad de Santiago de Chile, Chile
;
2
The Chinese University of Hong Kong (Shenzhen), China
Keyword(s):
Two-stage Stochastic Programming, Traveling Salesman Problem, Progressive Hedging Algorithm, Sample Average Approximation Method.
Related
Ontology
Subjects/Areas/Topics:
Agents
;
Artificial Intelligence
;
Bioinformatics
;
Biomedical Engineering
;
Enterprise Information Systems
;
Information Systems Analysis and Specification
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
Simulation
;
Stochastic Optimization
;
Symbolic Systems
Abstract:
In this paper, we propose an adapted version of the progressive hedging algorithm (PHA) (Rockafellar and
Wets, 1991; Lokketangen and Woodruff, 1996; Watson and Woodruff, 2011) for the two-stage stochastic
traveling salesman problem (STSP) introduced in (Adasme et al., 2016). Thus, we compute feasible solutions
for small, medium and large size instances of the problem. Additionally, we compare the PHA method with the
sample average approximation (SAA) method for all the randomly generated instances and compute statistical
lower and upper bounds. For this purpose, we use the compact polynomial formulation extended from (Miller
et al., 1960) in (Adasme et al., 2016) as it is the one that allows us to solve large size instances of the problem in
short CPU time with CPLEX. Our preliminary numerical results show that the results obtained with the PHA
algorithm are tight when compared to the optimal solutions of small and medium size instances. Moreover, we
obtain significantly better feasi
ble solutions than CPLEX for large size instances with up to 100 nodes and 10
scenarios in significantly low CPU time. Finally, the bounds obtained with SAA method provide an average
reference interval for the stochastic problem.
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