The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company

2021 ◽  
Vol 55 (2) ◽  
pp. 510-531
Author(s):  
Camilo Ortiz-Astorquiza ◽  
Jean-François Cordeau ◽  
Emma Frejinger
Keyword(s):  
Assignment Problem ◽  
Benders Decomposition ◽  
Optimization Problems ◽  
Computational Study ◽  
Computational Time ◽  
Fixed Cost ◽  
Modeling Framework ◽  
Distributed Power ◽  
Railway Company ◽  
Locomotive Assignment

Some of the most important optimization problems faced by railway operators arise from the management of their locomotive fleet. In this paper, we study a general version of the locomotive assignment problem encountered at the tactical level by one of the largest railroads in North America: the Canadian National (CN) Railway Company. We present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing decisions on each train’s operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it winto smaller time windows. Given the difficulty in solving the problem, one of the formulations is enhanced through various refinements, such as constraint relaxations, preprocessing, and fixed cost approximations. We thus achieve a significant reduction in the required computational time to solve instances of realistic size. We also present two versions of a Benders decomposition–based algorithm to obtain feasible solutions. On average, it allows a reduction of the associated computational time by two hours. Results from an extensive computational study and a case study with data provided by CN confirm the potential benefits of the model and solution approach.

A Nelder and Mead Methodology for Solving Small Fixed-Charge Transportation Problems

2011 ◽  
pp. 345-356
Author(s):  
G. Kannan ◽  
P. Senthil ◽  
P. Sasikumar ◽  
V. P. Vinay
Keyword(s):  
Supply Chain ◽  
Transportation Problem ◽  
Optimization Problems ◽  
Fixed Charge ◽  
Computational Time ◽  
Variable Cost ◽  
Fixed Cost ◽  
Supply Chain Optimization ◽  
Business World ◽  
Fixed Charge Transportation Problem

The term ‘supply chain management’ has become common in the business world, which can be understood from the positive results of research in the area, particularly in supply chain optimization. Transportation is a frontier in achieving the objectives of the supply chain. Thrust is also given to optimization problems in transportation. The fixed-charge transportation problem is an extension of the transportation problem that includes a fixed cost, along with a variable cost that is proportional to the amount shipped. This article approaches the problem with another meta-heuristics known as the Nelder and Mead methodology to save the computational time with little iteration and obtain better results with the help of a program in C++.

scholarly journals Discrete self-organizing migration algorithm and p-location problems

2020 ◽  
Vol 11 (2) ◽  
pp. 241-248
Author(s):  
Jaroslav Janacek ◽  
Marek Kvet
Keyword(s):  
Optimization Problems ◽  
Computational Study ◽  
Human Life ◽  
Optimal Solution ◽  
Location Problems ◽  
Computational Time ◽  
Exact Methods ◽  
Practical Applications ◽  
Special Adaptation ◽  
Self Organizing

Mathematical modelling, and integer programming generally, has many practical applications in different areas of human life. Effective and fast solving approaches for various optimization problems play an important role in the decision-making process and therefore, big attention is paid to the development of many exact and approximate algorithms. This paper deals only with a special class of location problems in which given number of facilities are to be chosen to minimize the objective function value. Since the exact methods are not suitable for their unpredictable computational time or memory demands, we focus here on possible usage of a special type of a particle swarm optimization algorithm transformed by discretization and meme usage into so-called discrete self-organizing migrating algorithm. In the paper, there is confirmed that it is possible to suggest a sophisticated heuristic for zero-one programming problem, which can produce near-to-optimal solution in much smaller time than the time demanded by exact methods. We introduce a special adaptation of the discrete self-organizing migration algorithm to the $p$-location problem making use of the path-relinking method. In the theoretical part of this paper, we introduce several strategies of the migration process. To verify their features and effectiveness, a computational study with real-sized benchmarks was performed. The main goal of the experiments was to find the most efficient version of the suggested solving tool.

Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets

2021 ◽  
Author(s):  
Juan S. Borrero ◽  
Leonardo Lozano
Keyword(s):  
Robust Optimization ◽  
Convex Sets ◽  
Optimization Problems ◽  
Computational Study ◽  
Mixed Integer ◽  
Computational Time ◽  
Point Problem ◽  
Solution Algorithms ◽  
Uncertainty Sets ◽  
Uncertainty Set

We study a class of sequential defender-attacker optimization problems where the defender’s objective is uncertain and depends on the operations of the attacker, which are represented by a mixed-integer uncertainty set. The defender seeks to hedge against the worst possible data realization, resulting in a robust optimization problem with a mixed-integer uncertainty set, which requires the solution of a challenging mixed-integer problem, which can be seen as a saddle-point problem over a nonconvex domain. We study two exact solution algorithms and present two feature applications for which the uncertainty is naturally modeled as a mixed-integer set. Our computational experiments show that the considered algorithms greatly outperform standard algorithms both in terms of computational time and solution quality. Moreover, our results show that modeling uncertainty with mixed-integer sets, instead of approximating the data using convex sets, results in less conservative solutions, which translates to a lower cost for the defender to protect from uncertainty. Summary of Contribution: We consider a class of defender-attacker problems where the defender has to make operational decisions that depend on uncertain actions from an adversarial attacker. Due to the type of information available to the defender, neither probabilistic modeling, nor robust optimization methods with convex uncertainty sets, are well suited to address the defender’s decision-making problem. Consequently, we frame the defender’s problem as a class of robust optimization problems with a mixed-integer uncertainty sets, and devise two exact algorithms that solve this class of problems. A comprehensive computational study shows that for the considered applications, our algorithms improves the performance of existing robust optimization approaches that can be adapted to solve this class of problems. Moreover, we show how mixed-integer uncertainty sets can reduce the level of over-conservatism that is a known issue of robust optimization approaches.

scholarly journals A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen
Keyword(s):  
Stochastic Programming ◽  
Benders Decomposition ◽  
Equivalent Model ◽  
Computational Time ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Equivalent ◽  
Location Routing ◽  
Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

scholarly journals Ions motion optimization algorithm for multiobjective optimization problems

2021 ◽  
pp. 93-110 ◽  
Author(s):  
Hitarth Buch ◽  
Indrajit Trivedi
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Computational Time ◽  
Selection Strategy ◽  
Pareto Optimum ◽  
Optimal Solutions ◽  
Good Convergence ◽  
Motion Optimization ◽  
Multiobjective Approach ◽  
Benchmark Test Functions

This paper offers a novel multiobjective approach – Multiobjective Ions Motion Optimization (MOIMO) algorithm stimulated by the movements of ions in nature. The main inspiration behind this approach is the force of attraction and repulsion between anions and cations. A storage and leader selection strategy is combined with the single objective Ions Motion Optimization (IMO) approach to estimate the Pareto optimum front for multiobjective optimization. The proposed method is applied to 18 different benchmark test functions to confirm its efficiency in finding optimal solutions. The outcomes are compared with three novel and well-accepted techniques in the literature using five performance parameters quantitatively and obtained Pareto fronts qualitatively. The comparison proves that MOIMO can approximate Pareto optimal solutions with good convergence and coverage with minimum computational time.

The Application of Fuzzification for Solving Quadratic Functions

2021 ◽  
Author(s):  
Lunshan Gao
Keyword(s):  
Approximate Solution ◽  
Approximation Algorithm ◽  
Critical Point ◽  
Numerical Experiments ◽  
Optimization Problems ◽  
Local Minimizer ◽  
Quadratic Functions ◽  
Computational Time ◽  
Computational Results ◽  
Average Computational Time

Abstract This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

scholarly journals Location Decision Making and Transportation Route Planning Considering Fuel Consumption

2019 ◽  
Vol 5 (2) ◽  
pp. 27 ◽  
Author(s):  
Chalermchat Theeraviriya ◽  
Rapeepan Pitakaso ◽  
Kittima Sillapasa ◽  
Sasitorn Kaewman
Keyword(s):  
Fuel Consumption ◽  
Palm Oil ◽  
Processing Time ◽  
Computational Study ◽  
Exact Method ◽  
Neighborhood Search ◽  
Fixed Cost ◽  
Location Routing ◽  
Consumption Cost

This study presents the Location Routing Problem (LRP) for which we have created a model for the integration of locating facilities and vehicle routing decisions to solve the problem. The case study is the Palm Oil Collection Center, which is also important for the supply chain system. A mathematical model was made to minimize the total cost of a facility-opening cost, fixed cost of vehicle uses and fuel consumption cost. The fuel consumption cost relies on the distance and road conditions, in case of poor physical condition of a road, and its width, which can be affected the speed of the vehicle as well as the used fuel. Thus, we propose an Adaptive Large Neighborhood Search (ALNS) based on heuristic for solving the LRP. The ALNS method was tested with three datasets of samples divided into small, medium and large problems. Then, the results were compared with the results from the exact method by the Lingo program. The computational study indicated that the ALNS algorithm was competitive to the results of the Lingo for all instance sizes. Moreover, the ALNS was more effective than the exact method; approximately 99% in terms of processing time. We extended this approach to solve the case study, which was considered to be the largest problem, and the ALNS algorithm was efficient with acceptable solutions and short processing time. Therefore, the proposed method provided an effective solution to manage location routing decision of the palm oil collection center.

An Assessment of Computational Fluid Dynamics Cavitation Models Using Bubble Growth Theory and Bubble Transport Modeling

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Michael P. Kinzel ◽  
Jules W. Lindau ◽  
Robert F. Kunz
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Analytic Solutions ◽  
Cfd Modeling ◽  
Computational Time ◽  
Cavitation Model ◽  
Modeling Framework ◽  
Homogeneous Models ◽  
Bubble Transport ◽  
Computational Fluid Dynamics Cfd

This effort investigates advancing cavitation modeling relevant to computational fluid dynamics (CFD) through two strategies. The first aims to reformulate the cavitation models and the second explores adding liquid–vapor slippage effects. The first aspect of the paper revisits cavitation model formulations with respect to the Rayleigh–Plesset equation (RPE). The present approach reformulates the cavitation model using analytic solutions to the RPE. The benefit of this reformulation is displayed by maintaining model sensitivities similar to RPE, whereas the standard models fail these tests. In addition, the model approach is extended beyond standard homogeneous models, to a two-fluid modeling framework that explicitly models the slippage between cavitation bubbles and the liquid. The results indicate a significant impact of slip on the predicted cavitation solution, suggesting that the inclusion of such modeling can potentially improve CFD cavitation models. Overall, the results of this effort point to various aspects that may be considered in future CFD-modeling efforts with the goal of improving the model accuracy and reducing computational time.

A Linear Optimization Approach for Increasing Sustainability in Vegetable Crop Production

2011 ◽  
pp. 234-265 ◽  
Author(s):  
Lana dos Santos ◽  
Marcos Arenales ◽  
Alysson Costa ◽  
Ricardo Santos
Keyword(s):  
Crop Rotation ◽  
Crop Production ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Future Research ◽  
Optimization Approach ◽  
Vegetable Crops ◽  
Vegetable Crop ◽  
Modeling Framework ◽  
Ecological Criteria

This chapter is concerned with a set of optimization problems associated to crop rotation scheduling in the context of vegetable crop production according to some ecological criteria: no crop of the same botanic family is planted in sequence, green manure and fallow periods must be present in any schedule. A core mathematical model called the crop rotation scheduling model is proposed to represent these ecological criteria together with specific technical constraints associated to the growing of vegetable crops. Three optimization problems based on crop rotation schedules are written in detail in this chapter. For each problem, the authors present a general modeling framework and a solution methodology based on a technique known as column generation, which iteratively builds crop rotation plans for a number of plots. Some extensions are also presented, with the aim of incorporating additional characteristics found in production field conditions. This chapter ends with a brief discussion on a set of computational experiments and some suggestions for future research.

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