Iterative Column Generation Algorithm for Generalized Multi-Vehicle Covering Tour Problem

2018 ◽  
Vol 35 (04) ◽  
pp. 1850021 ◽  
Author(s):  
Keisuke Murakami
Keyword(s):  
Column Generation ◽  
Minimum Cost ◽  
Computational Experiments ◽  
Generation Algorithm ◽  
Covering Tour Problem ◽  
Original Formula

The multi-vehicle covering tour problem ([Formula: see text]-CTP) is defined on a graph [Formula: see text], where [Formula: see text] is a set of vertices that can be visited and [Formula: see text] is a set of vertices that must be covered but cannot be visited. The objective of the [Formula: see text]-CTP is to obtain a set of total minimum cost tours on subset of [Formula: see text], while covering all [Formula: see text] by up to [Formula: see text] vehicles. In this paper, we first generalize the original [Formula: see text]-CTP by adding a realistic constraint, and then propose an algorithm for the generalized [Formula: see text]-CTP using a column generation approach. Computational experiments show that our algorithm performs well and outperforms the existing algorithms.

A generalized model and a heuristic algorithm for the large-scale covering tour problem

2018 ◽  
Vol 52 (2) ◽  
pp. 577-594
Author(s):  
Keisuke Murakami
Keyword(s):  
Local Search ◽  
Heuristic Algorithm ◽  
Large Scale ◽  
Minimum Cost ◽  
The Other ◽  
Computational Experiments ◽  
Generalized Model ◽  
Search Techniques ◽  
Covering Tour Problem

The covering tour problem (CTP) is defined on a graph, where there exist two types of vertices. One is called visited vertex, which can be visited. The other is called covered vertex, which must be covered but cannot be visited. Each visited vertex covers a subset of covered vertices, and the costs of edges between visited vertices are given. The objective of the CTP is to obtain a minimum cost tour on a subset of visited vertices while covering all covered vertices. In this paper, we deal with the large-scale CTPs, which are composed of tens of thousands of vertices; in the previous studies, the scales of the instances in the experiments are at most a few hundred vertices. We propose a heuristic algorithm using local search techniques for the large-scale CTP. With computational experiments, we show that our algorithm outperforms the existing methods.

An Improved Integral Column Generation Algorithm Using Machine Learning for Aircrew Pairing

2021 ◽  
Author(s):  
Adil Tahir ◽  
Frédéric Quesnel ◽  
Guy Desaulniers ◽  
Issmail El Hallaoui ◽  
Yassine Yaakoubi
Keyword(s):  
Neural Network ◽  
Column Generation ◽  
Real Life ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Generation Algorithm ◽  
Planning Software ◽  
The Neural Network ◽  
Commercial Airline ◽  
Crew Pairing

The crew-pairing problem (CPP) is solved in the first step of the crew-scheduling process. It consists of creating a set of pairings (sequence of flights, connections, and rests forming one or multiple days of work for an anonymous crew member) that covers a given set of flights at minimum cost. Those pairings are assigned to crew members in a subsequent crew-rostering step. In this paper, we propose a new integral column-generation algorithm for the CPP, called improved integral column generation with prediction ([Formula: see text]), which leaps from one integer solution to another until a near-optimal solution is found. Our algorithm improves on previous integral column-generation algorithms by introducing a set of reduced subproblems. Those subproblems only contain flight connections that have a high probability of being selected in a near-optimal solution and are, therefore, solved faster. We predict flight-connection probabilities using a deep neural network trained in a supervised framework. We test [Formula: see text] on several real-life instances and show that it outperforms a state-of-the-art integral column-generation algorithm as well as a branch-and-price heuristic commonly used in commercial airline planning software, in terms of both solution costs and computing times. We highlight the contributions of the neural network to [Formula: see text].

scholarly journals A HYBRID COLUMN GENERATION ALGORITHM BASED ON METAHEURISTIC OPTIMIZATION

Transport ◽  
2013 ◽  
Vol 31 (4) ◽  
pp. 389-407 ◽  
Author(s):  
Wenbin Hu ◽  
Bo Du ◽  
Ye Wu ◽  
Huangle Liang ◽  
Chao Peng ◽  
...  
Keyword(s):  
Column Generation ◽  
Time Windows ◽  
Path Selection ◽  
Optimization Strategy ◽  
Heuristic Solution ◽  
Generation Algorithm ◽  
Metaheuristic Optimization ◽  
Selection Strategies ◽  
Dual Variables ◽  
Labelling Algorithm

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid Column Generation Algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling Algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two pathkeeping conditions in the main problem.

scholarly journals Two meta-heuristics for solving the multi-vehicle multi-covering tour problem with a constraint on the number of vertices

2020 ◽  
pp. 14-14
Author(s):  
Manel Kammoun ◽  
Houda Derbel ◽  
Bassem Jarboui
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Variable Neighborhood Search ◽  
Search Algorithm ◽  
Descent Method ◽  
Computational Experiments ◽  
Neighborhood Search ◽  
Variable Neighborhood Descent ◽  
Covering Tour Problem ◽  
Neighborhood Search Algorithm

In this work we deal with a generalized variant of the multi-vehicle covering tour problem (m-CTP). The m-CTP consists of minimizing the total routing cost and satisfying the entire demand of all customers, without the restriction of visiting them all, so that each customer not included in any route is covered. In the m-CTP, only a subset of customers is visited to fulfill the total demand, but a restriction is put on the length of each route and the number of vertices that it contains. This paper tackles a generalized variant of the m-CTP, called the multi-vehicle multi-covering Tour Problem (mm-CTP), where a vertex must be covered several times instead of once. We study a particular case of the mm-CTP considering only the restriction on the number of vertices in each route and relaxing the constraint on the length (mm-CTP-p). A hybrid metaheuristic is developet by combining Genetic Algorithm (GA), Variable Neighborhood Descent method (VND), and a General Variable Neighborhood Search algorithm (GVNS) to solve the problem. Computational experiments show that our approaches are competitive with the Evolutionary Local Search (ELS) and Genetic Algorithm (GA), the methods proposed in the literature.

A Note on “The Facility Location Problem with Limited Distances”

2020 ◽  
Vol 54 (6) ◽  
pp. 1439-1445
Author(s):  
Prahalad Venkateshan
Keyword(s):  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Facility Location Problem ◽  
Sum Of Squares ◽  
Generation Algorithm ◽  
Math Programming ◽  
Modified Algorithm

In this paper, it is shown that the polynomially bounded enumerative procedure to solve the facility location problem with limited distances, originally described by Drezner, Mehrez, and Wesolowsky [Drezner Z, Mehrez A, Wesolowsky GO (1991) The facility location problem with limited distances. Transportation Sci. 25(3):183–187.], and subsequently corrected by Aloise, Hansen, and Liberti [Aloise D, Hansen P, Liberti L (2012) An improved column generation algorithm for minimum sum-of-squares clustering. Math. Programming 131(1–2):195–220.], can still fail to optimally solve the problem. Conditions under which the procedures succeed are identified. A new modified algorithm is presented that solves the facility location problem with limited distances. It is further shown that the proposed correction is complete in that it does not require further corrections.

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