scholarly journals Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

2021 ◽  
Author(s):  
Zahed Shahmoradi ◽  
Taewoo Lee
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Robust Regression ◽  
Model Fitting ◽  
Exact Algorithm ◽  
Integer Program ◽  
Inverse Optimization ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
The Impact

Although inverse linear programming (LP) has received increasing attention as a technique to identify an LP that can reproduce observed decisions that are originally from a complex system, the performance of the linear objective function inferred by existing inverse LP methods is often highly sensitive to noise, errors, and uncertainty in the underlying decision data. Inspired by robust regression techniques that mitigate the impact of noisy data on the model fitting, in “Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming,” Shahmoradi and Lee propose a notion of stability in inverse LP and develop an inverse optimization model that identities objective functions that are stable against data imperfection. Although such a stability consideration renders the inverse model a large-scale mixed-integer program, the authors analyze the connection between the model and well-known biclique problems and propose an efficient exact algorithm as well as heuristics.

scholarly journals A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6610
Author(s):  
Raka Jovanovic ◽  
Islam Safak Bayram ◽  
Sertac Bayhan ◽  
Stefan Voß
Keyword(s):  
Public Transport ◽  
High Speed ◽  
Large Scale ◽  
Integer Program ◽  
Mixed Integer ◽  
Transport Systems ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Electric Bus ◽  
Battery Capacity

Electrifying public bus transportation is a critical step in reaching net-zero goals. In this paper, the focus is on the problem of optimal scheduling of an electric bus (EB) fleet to cover a public transport timetable. The problem is modelled using a mixed integer program (MIP) in which the charging time of an EB is pertinent to the battery’s state-of-charge level. To be able to solve large problem instances corresponding to real-world applications of the model, a metaheuristic approach is investigated. To be more precise, a greedy randomized adaptive search procedure (GRASP) algorithm is developed and its performance is evaluated against optimal solutions acquired using the MIP. The GRASP algorithm is used for case studies on several public transport systems having various properties and sizes. The analysis focuses on the relation between EB ranges (battery capacity) and required charging rates (in kW) on the size of the fleet needed to cover a public transport timetable. The results of the conducted computational experiments indicate that an increase in infrastructure investment through high speed chargers can significantly decrease the size of the necessary fleets. The results also show that high speed chargers have a more significant impact than an increase in battery sizes of the EBs.

scholarly journals Supply Chain Optimization by Mixed Integer Program for Manufacturer and Retailer System of Poultry firm in Bangladesh

2016 ◽  
Vol 34 ◽  
pp. 75-87
Author(s):  
Mohammad Khairul Islam ◽  
Mohammed Forhad Uddin ◽  
Md M Alam
Keyword(s):  
Large Scale ◽  
Raw Materials ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Selling Price ◽  
Supply Chain Optimization ◽  
Self Employment ◽  
Gdp Growth Rate ◽  
The Cost

In this study, we formulate mixed integer program for manufacturer and retailer system of poultry firm in Bangladesh that is one of the most promising sectors to increase Gross Domestic Product (GDP) growth rate plus equitable distribution through arranging food security as well as ensuring self-employment, creating purchasing power and reducing poverty at a large scale. From the survey, it has observed that the selling price of eggs and chicken fluctuate depending on the natural calamities. We have made a question survey on some poultry firm in the district of Mymensingh and Gazipur. This paper maximized the profit and minimizes the cost. The formulated mixed integer program has solved by branch and bound algorithm using A Mathematical Programming Language (AMPL). It has observed that the profit and selling price have very good relationship with production cost and raw materials cost but no significant relation with fixed cost.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 75-87

scholarly journals Inverting the Multiple-Assisting Tool Network Problem to Solve for Optimality

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Robert Rich
Keyword(s):  
Material Handling ◽  
Main Tool ◽  
Network Routing ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Routing Problem ◽  
Network Problems ◽  
Tool Set ◽  
The Impact

Many network problems deal with the routing of a main tool comprised of several parallel assisting tools. These problems can be found with multi-tool-head routing of CNC machines, waterjets, plasma sprayers, and cutting machines. Other applications involve logistics, distribution, and material handling that require a main tool with assisting tools. Currently no studies exist that optimally route a main tool comprised of and fitted with multiple tools, nor do any studies evaluate the impact of adding additional capabilities to the tool set. Herein we define the network routing problem for a main tool comprised of multiple secondary tools. We introduce first principles to properly configure the main tool with the appropriate number of supporting tools such that that system is not overstatured. We invert the network geometry to extract the “best case” configuration for toolset configuration to include speed, range, and number of such that the system is lean. Our computational studies reveal that the theorems introduced herein greatly improve the overall system performance without oversaturating it with unused resources. In order to validate experiments, we define a mixed integer program and compare it to our metaheuristics developed for experimentation. Both the MIP and the metaheuristics herein optimally route a main tool with multiple assisting tools as well as the routing of a parcel delivery truck comprised of many drones.

3D deployment of UAVs in wireless networks for traffic offloading and edge computing

2019 ◽  
Author(s):  
◽  
Rania Islambouli
Keyword(s):  
Wireless Networks ◽  
Large Scale ◽  
Scale Up ◽  
Integer Program ◽  
Use Cases ◽  
Base Stations ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
5G Networks ◽  
Iot Devices

Unmanned aerial vehicles (UAVs) have recently emerged as enablers for mul- titude use cases in 5G networks leading to interesting industrial and business applications. 5G networks envision a multi-service network promoting various applications with a distinct set of performance and service demands. In this the- sis, we leverage the high exibility, low-cost, and mobility of UAVs to scale up and improve the e ciency of IoT and mobile networks. We study the utilization of UAVs to increase the capacity and coverage in wireless networks on one side and to extend low computational capabilities and mitigate battery limitations in constrained devices on another side. However, to unlock these promising use cases of UAVs, we address the challenges coupled with UAV utilization mainly 3D deployment and device association. First, we address the problem of deploying multiple UAVs to act as aerial base stations (ABS) in 3D space while autonomously adapting their positions as users move around within the network. We formulate the problem as a mixed integer program and then propose a novel autonomous positioning approach that can e ciently gear the UAV positions in a way to maintain target quality re- quirements. Next, we leverage the mobility and agility of UAVs and use them as mo- bile edge servers or cloudlets to o er computation o oading opportunities to IoT devices. This being said, computation tasks generated by IoT devices can be pro- cessed in less latency and with much lower energy consumption at the devices. To optimally deploy UAVs as mounted cloudlets, we formulate our problem as mixed integer program and then use an e cient meta-heuristic algorithm to generate optimized results for large scale IoT networks. The simulation results presented in this thesis demonstrate the e ectiveness of the proposed solutions and algo- rithms compared to the optimal solutions and related work in the literature for various network scenario

scholarly journals Inverting the Truck-Drone Network Problem to Find Best Case Configuration

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Robert Rich
Keyword(s):  
Linear Programming ◽  
Delivery System ◽  
Network Routing ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Routing Problem ◽  
Network Problem ◽  
Last Mile ◽  
Last Mile Delivery

Many industries are looking for ways to economically use truck/rail/ship fitted with drone technologies to augment the “last mile” delivery effort. While drone technologies abound, few, if any studies look at the proper configuration of the drone based on significant features of the problem: delivery density, operating area, drone range, and speed. Here, we first present the truck-drone problem and then invert the network routing problem such that the best case drone speed and range are fitted to the truck for a given scenario based on the network delivery density. By inverting the problem, a business can quickly determine the drone configuration (proper drone range and speed) necessary to optimize the delivery system. Additionally, we provide a more usable version of the truck-drone routing problem as a mixed integer program that can be easily adopted with standardized software used to solve linear programming. Furthermore, our computational metaheuristics and experiments conducted in support of this work are available for download. The metaheuristics used herein surpass current best-in-class algorithms found in literature.

Biased Random-Key Genetic Algorithms for the Winner Determination Problem in Combinatorial Auctions

2015 ◽  
Vol 23 (2) ◽  
pp. 279-307 ◽  
Author(s):  
Carlos Eduardo de Andrade ◽  
Rodrigo Franco Toso ◽  
Mauricio G. C. Resende ◽  
Flávio Keidi Miyazawa
Keyword(s):  
Genetic Algorithms ◽  
Linear Programming ◽  
Large Scale ◽  
Programming Model ◽  
Exact Algorithm ◽  
Mixed Integer ◽  
Winner Determination Problem ◽  
Winner Determination ◽  
Linear Integer Programming ◽  
Linear Programming Relaxations

In this paper we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

2016 ◽  
Vol 46 (2) ◽  
pp. 234-248 ◽  
Author(s):  
Erin J. Belval ◽  
Yu Wei ◽  
Michael Bevers
Keyword(s):  
Wildland Fire ◽  
Fire Behavior ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Weather Forecasts ◽  
Placement Decisions ◽  
Weather Events ◽  
Weather Changes ◽  
Nonanticipativity Constraints

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of “suppression nodes”, which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. Multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

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