Quang Dung Pham

Constraint-Based local search for constrained optimum paths problems

Constrained Optimum Path (COP) problems arise in many real-life applications and are ubiquitous in communication networks. They have been traditionally approached by dedicated algorithms, which are often hard to extend with side constraints and to apply widely. This paper proposes a constraint-based local search (CBLS) framework for COP applications, bringing the compositionality, reuse, and extensibility at the core of CBLS and CP systems. The modeling contribution is the ability to express compositional models for various COP applications at a high level of abstraction, while cleanly separating the model and the search procedure. The main technical contribution is a connected neighborhood based on rooted spanning trees to find high-quality solutions to COP problems. The framework, implemented in COMET, is applied to Resource Constrained Shortest Path (RCSP) problems (with and without side constraints) and to the edge-disjoint paths problem (EDP). Computational results show the potential significance of the approach.

LS(Graph): a constraint-based local search for constraint optimization on trees and paths

Constrained optimum tree (COT) and constrained optimum path (COP) problems arise in many real-life applications and are ubiquitous in communication networks. They have been traditionally approached by dedicated algorithms, which are often hard to extend with side constraints and to apply widely. This paper proposes a constraint-based local search framework for COT/COP applications, bringing the compositionality, reuse, and extensibility at the core of constraint-based local search and constraint programming systems. The modeling contribution is the ability to express compositional models for various COT/COP applications at a high level of abstraction, while cleanly separating the model and the search procedure. The main technical contribution is a connected neighborhood based on rooted spanning trees to find high-quality solutions to COP problems. This framework is applied to some COT/COP problems, e.g., the quorumcast routing problem, the edge-disjoint paths problem, and the routing and wavelength assignment with delay side constraints problem. Computational results show the potential importance of the approach.

On the min-cost Traveling Salesman Problem with Drone

Abstract Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called “last-mile delivery”. In this novel approach, they are deployed alongside trucks to deliver goods to customers to improve the quality of service and reduce the transportation cost. This approach gives rise to a new variant of the traveling salesman problem (TSP), called TSP with drone (TSP-D). A variant of this problem that aims to minimize the time at which truck and drone finish the service (or, in other words, to maximize the quality of service) was studied in the work of Murray and Chu (2015). In contrast, this paper considers a new variant of TSP-D in which the objective is to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other. The problem is first formulated mathematically. Then, two algorithms are proposed for the solution. The first algorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu (2015), in which an optimal TSP solution is converted to a feasible TSP-D solution by local searches. The second algorithm, a Greedy Randomized Adaptive Search Procedure (GRASP), is based on a new split procedure that optimally splits any TSP tour into a TSP-D solution. After a TSP-D solution has been generated, it is then improved through local search operators. Numerical results obtained on various instances of both objective functions with different sizes and characteristics are presented. The results show that GRASP outperforms TSP-LS in terms of solution quality under an acceptable running time.

Exact methods for solving the elementary shortest and longest path problems

We consider in this paper the problems of finding the elementary shortest and longest paths on a graph containing negative and positive cycles. These problems are NP-hard. We propose exact algorithms based on mixed integer programming for their solution, employing different valid inequalities. Moreover, we propose decomposition techniques which are very efficient for cases with special structure. Experimental results show the efficiency of our algorithms compared with state of the art exact algorithms.

Solving the agricultural land allocation problem by constraint-based local search

Agricultural land allocation is a problem that exists in most provinces in Vietnam. Each household owns many disconnected parcels, which reduces agricultural development. The solution to the problem is to repartition this agricutural land among the households, while satisfying some criteria. Historically, this problem has been approached neither using optimization technology nor computer science. The present paper describes the formulation of the problem and proposes a constraint-based local search algorithm for solving it. Experimental results on real data in Dong Trung village show that the solution computed by our algorithm is better than traditional solutions.

Solving the quorumcast routing problem by constraint programming

The quorumcast routing problem is a generalization of multicasting which arises in many distributed applications. It consists of finding a minimum cost tree that spans the source node r and at least q out of m specified nodes on a given undirected weighted graph. This paper proposes a complete and an incomplete approach, both based on the same Constraint Programming (CP) model, but with two different specific search heuristics based on shortest paths. Experimental results show the efficiency of the two proposed approaches. Our complete approach (CP model + complete search) is better than the state of the art complete algorithm and our incomplete approach (CP model + incomplete search) is better than the state of the art incomplete algorithm. Moreover, the proposed complete search is better than the standard First-Fail search in the same CP model.

A Constraint-Based Local Search for Offline and Online General Vehicle Routing

Vehicle routing is a class of combinatorial optimization problems arising in the industry of transportation and logistics. The goal of these problems is to compute an optimal route plan for a set of vehicles for serving transport requests of customers. There are many variants of the vehicle routing problems: routing for delivering goods, routing for demand responsive transport (taxi, school bus, …). Each problem might have different constraints, objectives. In this paper, we introduce a Constraint-Based Local Search (CBLS) framework for general offline and online vehicle routing problems. We extend existing neighborhood structures in the literature by proposing new neighborhoods to facilitate the resolution of different class of vehicle routing problems in a unified platform. A novel feature of the framework is the available APIs for online vehicle routing problems where requests arrive online during the execution of the computed route plan. Experimental results on three vehicle routing problems (the min-...

Improving the connectivity of a bus system: a case study of Ho Chi Minh city

Public transportation modes like buses plays an important role in our real life. Designing a good bus system can bring advantages to both passengers and the society. One of key design criteria is the connectivity which can be measured by the minimum number of bus lines a passenger must take to travel from one station to another. This paper considers the bus system design problem with the objective of improving the connectivity of the system from the existing infrastructure. We defined the problem in the form of an optimization problem and propose an algorithm for the solution. Results obtained from the real instances derived from the bus system of Ho Chi Minh city are analysed and reported.

Solving the quorumcast routing problem as a mixed integer program

The quorumcast routing problem is a generalization of multicasting which arises in many distributed applications. It consists of finding a minimum cost tree that spans the source node and at least q out of m specified nodes on a given undirected weighted graph. In this paper, we solve this problem as a mixed integer program. The experimental results show that our four approaches outperform the state of the art. A sensitivity analysis is also performed on values of q and m.

Solving the longest simple path problem with constraint-based techniques

The longest simple path problem on graphs arises in a variety of context, e.g., information retrieval, VLSI design, robot patrolling. Given an undirected weighted graph G =(V ,E ), the problem consists of finding the longest simple path (i.e., no vertex occurs more than once) on G . We propose in this paper an exact and a tabu search algorithm for solving this problem. We show that our techniques give competitive results on different kinds of graphs, compared with recent genetic algorithms.