arXiv subjects

Minh Hoàng Hà

Publications and source records attributed to Minh Hoàng Hà.

10 recordsLinked to original sources

arXiv2021

An efficient branch-and-cut algorithm for the parallel drone scheduling traveling salesman problem

We propose an efficient branch-and-cut algorithm to exactly solve the parallel drone scheduling traveling salesman problem. Our algorithm can find optimal solutions for all but two existing instances with up to 229 customers in a reasonable running time. To make the problem more challenging for future methods, we introduce two new sets of 120 larger instances with the number of customers varying from 318 to 783 and test our algorithm and investigate the performance of state-of-the-art metaheuristics on these instances.

cs.DS↗

arXiv2021

Exact Algorithms for Scheduling Problems on Parallel Identical Machines with Conflict Jobs

Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which some jobs are conflict in the sense that they cannot be proceeded simultaneously on different machines. This conflict constraint naturally arises in several practical applications and has recently received considerable attentions in the research community. In fact, the problem is typically NP-hard (even for approximation) and most of algorithmic results achieved so far have heavily relied on special structures of the underlying graph used to model the conflict-job relation. Our focus is on three objective functions: minimizing the makespan, minimizing the weighted summation of the jobs' completion time, and maximizing the total weights of completed jobs; the first two of which have been intensively studied in the literature. For each objective function considered, we present several mixed integer linear programming models and a constraint programming model, from which we can solve the problems to optimality using dedicated solvers. Binary search-based algorithms are also proposed to solve the makespan problem. The results of numerical experiments performed on randomly generated data sets with up to 32 jobs and 6 machines are reported and analysed to verify the performance of the proposed methods.

cs.DS↗

arXiv2020

Arc Routing with Time-Dependent Travel Times and Paths

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, as well as heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules and completion bounds to find optimal solutions for problem counting up to 75 services. Based on these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.

cs.DS↗

arXiv2020

The two-echelon routing problem with truck and drones

In this paper, we study novel variants of the well-known two-echelon vehicle routing problem in which a truck works on the first echelon to transport parcels and a fleet of drones to intermediate depots while in the second echelon, the drones are used to deliver parcels from intermediate depots to customers. The objective is to minimize the completion time instead of the transportation cost as in classical 2-echelon vehicle routing problems. Depending on the context, a drone can be launched from the truck at an intermediate depot once (single trip drone) or several times (multiple trip drone). Mixed Integer Linear Programming (MILP) models are first proposed to formulate mathematically the problems and solve to optimality small-size instances. To handle larger instances, a metaheuristic based on the idea of Greedy Randomized Adaptive Search Procedure (GRASP) is introduced. Experimental results obtained on instances of different contexts are reported and analyzed.

cs.AI↗

arXiv2019

A new constraint programming model and a linear programming-based adaptive large neighborhood search for the vehicle routing problem with synchronization constraints

We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles' services, whose starting service times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on solving linear programming (LP) models to check the insertion feasibility. A number of acceleration techniques is also proposed to significantly reduce the computational time. The computational experiments show that our new CP model finds better solutions than an existing CP-based ANLS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the cp-ALNS, in terms of solution quality, when it provides solutions with better objective values, on average, for all instance classes. This demonstrates the advantage of using linear programming instead of constraint programming when dealing with a variant of vehicle routing problems with relatively tight constraints, which is often considered to be more favorable for CP-based methods.

cs.AI↗

arXiv2018

A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Drone

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.

cs.AI↗

arXiv2018

Solving the clustered traveling salesman problem with d-relaxed priority rule

The Clustered Traveling Salesman Problem with a Prespecified Order on the Clusters, a variant of the well-known traveling salesman problem is studied in literature. In this problem, delivery locations are divided into clusters with different urgency levels and more urgent locations must be visited before less urgent ones. However, this could lead to an inefficient route in terms of traveling cost. This priority-oriented constraint can be relaxed by a rule called d-relaxed priority that provides a trade-off between transportation cost and emergency level. Our research proposes two approaches to solve the problem with d-relaxed priority rule. We improve the mathematical formulation proposed in the literature to construct an exact solution method. A meta-heuristic method based on the framework of Iterated Local Search with problem-tailored operators is also introduced to find approximate solutions. Experimental results show the effectiveness of our methods.

cs.AI↗

arXiv2018

On three soft rectangle packing problems with guillotine constraints

We investigate how to partition a rectangular region of length $L_1$ and height $L_2$ into $n$ rectangles of given areas $(a_1, \dots, a_n)$ using two-stage guillotine cuts, so as to minimize either (i) the sum of the perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of the rectangles. These problems play an important role in the ongoing Vietnamese land-allocation reform, as well as in the optimization of matrix multiplication algorithms. We show that the first problem can be solved to optimality in $\mathcal{O}(n \log n)$, while the two others are NP-hard. We propose mixed integer programming (MIP) formulations and a binary search-based approach for solving the NP-hard problems. Experimental analyses are conducted to compare the solution approaches in terms of computational efficiency and solution quality, for different objectives.

math.OC↗

arXiv2017

On the Min-cost Traveling Salesman Problem with Drone

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.

cs.AI↗

arXiv2017

The Vehicle Routing Problem with Service Level Constraints

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems.

math.OC↗