scholarly journals Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

2020 ◽  
pp. ijoo.2019.0040
Author(s):  
Hasan Manzour ◽  
Simge Küçükyavuz ◽  
Hao-Hsiang Wu ◽  
Ali Shojaie
Keyword(s):  
Programming Model ◽  
Score Function ◽  
Directed Acyclic Graphs ◽  
Mixed Integer ◽  
Computational Time ◽  
Quadratic Program ◽  
Acyclic Graphs ◽  
Continuous Relaxation ◽  
Integer Quadratic Program ◽  
Better Than

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model that can naturally incorporate a superstructure to reduce the set of possible candidate DAGs. We use a negative log-likelihood score function with both l0 and l1 penalties and propose a new mixed-integer quadratic program, referred to as a layered network (LN) formulation. The LN formulation is a compact model that enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only l1 regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse superstructure.

Predictively Coordinated Vehicle Acceleration and Lane Selection Using Mixed Integer Programming

2018 ◽  
Author(s):  
R. Austin Dollar ◽  
Ardalan Vahidi
Keyword(s):  
Autonomous Vehicle ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Vehicle To Vehicle ◽  
Trip Time ◽  
Induced Travel ◽  
Vehicle Acceleration ◽  
Vehicle Technology ◽  
Rule Based Approach ◽  
Integer Quadratic Program

Autonomous vehicle technology provides the means to optimize motion planning beyond human capacity. In particular, the problem of navigating multi-lane traffic optimally for trip time, energy efficiency, and collision avoidance presents challenges beyond those of single-lane roadways. For example, the host vehicle must simultaneously track multiple obstacles, the drivable region is non-convex, and automated vehicles must obey social expectations. Furthermore, reactive decision-making may result in becoming stuck in an undesirable traffic position. This paper presents a fundamental approach to these problems using model predictive control with a mixed integer quadratic program at its core. Lateral and longitudinal movements are coordinated to avoid collisions, track a velocity and lane, and minimize acceleration. Vehicle-to-vehicle connectivity provides a preview of surrounding vehicles’ motion. Simulation results show a 79% reduction in congestion-induced travel time and an 80% decrease in congestion-induced fuel consumption compared to a rule-based approach.

scholarly journals Multi-Objective Sustainable Truck Scheduling in a Rail–Road Physical Internet Cross-Docking Hub Considering Energy Consumption

2019 ◽  
Vol 11 (11) ◽  
pp. 3127 ◽  
Author(s):  
Tarik Chargui ◽  
Abdelghani Bekrar ◽  
Mohamed Reghioui ◽  
Damien Trentesaux
Keyword(s):  
Energy Consumption ◽  
Programming Model ◽  
Mixed Integer ◽  
Computational Time ◽  
Neighborhood Search ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Sustainable Logistics ◽  
Cross Docking ◽  
Physical Internet

In the context of supply chain sustainability, Physical Internet (PI or π ) was presented as an innovative concept to create a global sustainable logistics system. One of the main components of the Physical Internet paradigm consists in encapsulating products in modular and standardized PI-containers able to move via PI-nodes (such as PI-hubs) using collaborative routing protocols. This study focuses on optimizing operations occurring in a Rail–Road PI-Hub cross-docking terminal. The problem consists of scheduling outbound trucks at the docks and the routing of PI-containers in the PI-sorter zone of the Rail–Road PI-Hub cross-docking terminal. The first objective is to minimize the energy consumption of the PI-conveyors used to transfer PI-containers from the train to the outbound trucks. The second objective is to minimize the cost of using outbound trucks for different destinations. The problem is formulated as a Multi-Objective Mixed-Integer Programming model (MO-MIP) and solved with CPLEX solver using Lexicographic Goal Programming. Then, two multi-objective hybrid meta-heuristics are proposed to enhance the computational time as CPLEX was time consuming, especially for large size instances: Multi-Objective Variable Neighborhood Search hybridized with Simulated Annealing (MO-VNSSA) and with a Tabu Search (MO-VNSTS). The two meta-heuristics are tested on 32 instances (27 small instances and 5 large instances). CPLEX found the optimal solutions for only 23 instances. Results show that the proposed MO-VNSSA and MO-VNSTS are able to find optimal and near optimal solutions within a reasonable computational time. The two meta-heuristics found optimal solutions for the first objective in all the instances. For the second objective, MO-VNSSA and MO-VNSTS found optimal solutions for 7 instances. In order to evaluate the results for the second objective, a one way analysis of variance ANOVA was performed.

scholarly journals Application of mixed integer quadratic program to shortest vector problems

JSIAM Letters ◽  
2017 ◽  
Vol 9 (0) ◽  
pp. 65-68
Author(s):  
Keiji Kimura ◽  
Hayato Waki ◽  
Masaya Yasuda
Keyword(s):  
Mixed Integer ◽  
Quadratic Program ◽  
Integer Quadratic Program

scholarly journals Variable Neighborhood Search for Parallel Machines Scheduling Problem with Step Deteriorating Jobs

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Wenming Cheng ◽  
Peng Guo ◽  
Zeqiang Zhang ◽  
Ming Zeng ◽  
Jian Liang
Keyword(s):  
Variable Neighborhood Search ◽  
Parallel Machines ◽  
Programming Model ◽  
Search Algorithm ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Mixed Integer ◽  
Computational Time ◽  
Neighborhood Search ◽  
Scheduling Problem

In many real scheduling environments, a job processed later needs longer time than the same job when it starts earlier. This phenomenon is known as scheduling with deteriorating jobs to many industrial applications. In this paper, we study a scheduling problem of minimizing the total completion time on identical parallel machines where the processing time of a job is a step function of its starting time and a deteriorating date that is individual to all jobs. Firstly, a mixed integer programming model is presented for the problem. And then, a modified weight-combination search algorithm and a variable neighborhood search are employed to yield optimal or near-optimal schedule. To evaluate the performance of the proposed algorithms, computational experiments are performed on randomly generated test instances. Finally, computational results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time even for large-sized problems.

scholarly journals Model and Hybrid Algorithm of Collaborative Distribution System with Multiple Drones and a Truck

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Min Lin ◽  
Jun-Yan Lyu ◽  
Jia-Jing Gao ◽  
Ling-Yu Li
Keyword(s):  
Distribution System ◽  
Road Network ◽  
Programming Model ◽  
Hybrid Genetic Algorithm ◽  
Mixed Integer ◽  
Particle Swarm Algorithm ◽  
Routing Problem ◽  
Urban Road ◽  
Distribution Centre ◽  
Better Than

This paper studies a coordinated system for multidrone single-truck distribution, where a truck delivers goods to a group of customers along a closed ground path with the help of a number of drones. For each delivery, the truck departs from the distribution centre with drones and all goods needed and returns back to the centre after fulfilling the delivery tasks. That is, the truck assigns these delivery tasks to several of its drones, each of which is responsible for sending goods to a different subgroup of customers in the empty air space. This study provides a new mixed-integer programming model of the routing problem with this distribution system based on urban road network. Meanwhile, a hybrid genetic algorithm and a hybrid particle swarm algorithm are designed. Experimental results show that the performance of the hybrid algorithms is better than that of the corresponding basic algorithms.

Domiciling Truck Drivers More Strategically in a Transportation Network

2018 ◽  
pp. 846-865
Author(s):  
Kerry Melton ◽  
Sandeep Parepally
Keyword(s):  
Numerical Experiment ◽  
Transportation Network ◽  
Truck Drivers ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Routing Problem ◽  
New Approach ◽  
Driving Time ◽  
Highway Transportation ◽  
Integer Quadratic Program

The authors propose a method to better domicile truck drivers in a relay-point highway transportation network to obtain better solutions for the truck driver domiciling and sourcing problem. The authors exploit characteristics of the truckload driver routing problem over a transportation network and introduce a new approach to domicile, source, and route truck drivers while more inclusively considering performance and cost measures related to the driver, transportation carrier, and customer. Driver domicile and relay-point locations are exploited to balance driver pay and recruiting costs and driving time. A mixed integer quadratic program will determine where driver domiciles are located to base drivers, source drivers, route drivers, etc. while considering key costs related to transporting truckload freight over long distances. A method to improve driver domicile locations is introduced to enhance driving jobs and driver sourcing, but not at the expense of the transportation carrier and customer. A numerical experiment will be conducted.

A detailed mathematical programming model for the optimal daily planning of sawmills

2019 ◽  
Vol 49 (11) ◽  
pp. 1400-1411 ◽  
Author(s):  
Nicolás Vanzetti ◽  
Diego Broz ◽  
Gabriela Corsano ◽  
Jorge M. Montagna
Keyword(s):  
Production Planning ◽  
Programming Model ◽  
Optimal Number ◽  
Mixed Integer ◽  
Computational Time ◽  
Efficient Production ◽  
Daily Production ◽  
Demand Fulfillment ◽  
Key Factor ◽  
Suitable Technique

The daily production planning of sawmills is a critical task in pursuing the optimal exploitation of forest resources. Production planning determines which logs are to be processed, taking into account their characteristics with the aim of satisfying the demand for final products. Logs are turned into lumber when they are cut according to a set of available cutting patterns (CPs). The development of efficient production planning is a key factor in improving the productivity of sawmills, and mathematical modeling is a suitable technique to achieve this objective. In this paper, a mixed integer linear programming (MILP) model for optimal daily production planning in sawmills is proposed. The model involves a set of CPs for each type of log, which is obtained through an exhaustive algorithm, attaining all possible feasible CPs. The proposed approach determines the optimal number of logs of each type to be cut, the selected CPs to be used, material inventory, demand fulfillment, and other industrial and commercial issues with the objective of maximizing the firm’s benefit, in reasonable computational time, considering the size of the problem.

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