scholarly journals A Spatial Optimization Approach for Simultaneously Districting Precincts and Locating Polling Places

2020 ◽  
Vol 9 (5) ◽  
pp. 301
Author(s):  
Kamyoung Kim
Keyword(s):  
Spatial Optimization ◽  
Search Costs ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Basic Form ◽  
Median Problem ◽  
Spatial Continuity ◽  
Strategic Approach ◽  
Spatial Decision Making ◽  
Population Sizes

Voting is the most basic form of political participation. The agencies that are responsible for voting must delineate precincts and designate a polling place for each precinct. This spatial decision-making requires a strategic approach for several reasons. First, changes in the location of polling places induce transportation and search costs from the perspective of voters. Second, improving accessibility to polling places can increase turnout. Third, differences in the population sizes of precincts may produce biased voting results. Spatial optimization approaches can be a strategic method for delimiting precincts and siting polling places. The purpose of this paper is to develop a spatial optimization model, namely, the capacitated double p-median problem with preference (CDPMP-P), which simultaneously delimits boundaries of precincts and selects potential facilities in terms of mixed integer programming (MIP). The CDPMP-P explicitly includes realistic requirements, such as population balance, the spatial continuity of precincts, the preferences of potential facilities where polling places can be installed, and the possibility of allocating multiple polling places in one facility.

A mixed-integer optimization approach for homogeneous magnet design

TECHNOLOGY ◽  
2018 ◽  
Vol 06 (02) ◽  
pp. 49-58
Author(s):  
Iman Dayarian ◽  
Timothy C.Y. Chan ◽  
David Jaffray ◽  
Teo Stanescu
Keyword(s):  
Imaging Modality ◽  
Spatial Location ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Integer Optimization ◽  
Magnet Design ◽  
Field Homogeneity ◽  
Feasibility Constraints ◽  
Design Generation ◽  
Magnetic Resonance Imaging Mri

Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medical linear accelerator to form novel cancer therapy systems (MR-linac), but the design of these systems to date relies on heuristic procedures. This paper develops an exact, optimization-based approach for magnet design that 1) incorporates the most accurate physics calculations to date, 2) determines precisely the relative spatial location, size, and current magnitude of the magnetic coils, 3) guarantees field homogeneity inside the imaging volume, 4) produces configurations that satisfy, for the first time, small-footprint feasibility constraints required for MR-linacs. Our approach leverages modern mixed-integer programming (MIP), enabling significant flexibility in magnet design generation, e.g., controlling the number of coils and enforcing symmetry between magnet poles. Our numerical results demonstrate the superiority of our method versus current mainstream methods.

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

A Novel Approach for Two-Stage UAV Path Planning in Pipeline Network Inspection

2020 ◽  
Author(s):  
Rui Qiu ◽  
Yongtu Liang
Keyword(s):  
Path Planning ◽  
Large Scale ◽  
Flight Path ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Two Stage ◽  
Calculation Time ◽  
Pipeline Network ◽  
Second Stage ◽  
Computational Performance

Abstract Currently, unmanned aerial vehicle (UAV) provides the possibility of comprehensive coverage and multi-dimensional visualization of pipeline monitoring. Encouraged by industry policy, research on UAV path planning in pipeline network inspection has emerged. The difficulties of this issue lie in strict operational requirements, variable flight missions, as well as unified optimization for UAV deployment and real-time path planning. Meanwhile, the intricate structure and large scale of the pipeline network further complicate this issue. At present, there is still room to improve the practicality and applicability of the mathematical model and solution strategy. Aiming at this problem, this paper proposes a novel two-stage optimization approach for UAV path planning in pipeline network inspection. The first stage is conventional pre-flight planning, where the requirement for optimality is higher than calculation time. Therefore, a mixed integer linear programming (MILP) model is established and solved by the commercial solver to obtain the optimal UAV number, take-off location and detailed flight path. The second stage is re-planning during the flight, taking into account frequent pipeline accidents (e.g. leaks and cracks). In this stage, the flight path must be timely rescheduled to identify specific hazardous locations. Thus, the requirement for calculation time is higher than optimality and the genetic algorithm is used for solution to satisfy the timeliness of decision-making. Finally, the proposed method is applied to the UAV inspection of a branched oil and gas transmission pipeline network with 36 nodes and the results are analyzed in detail in terms of computational performance. In the first stage, compared to manpower inspection, the total cost and time of UAV inspection is decreased by 54% and 56% respectively. In the second stage, it takes less than 1 minute to obtain a suboptimal solution, verifying the applicability and superiority of the method.

scholarly journals Comparative Assessment of Priority Listing and Mixed Integer Linear Programming Unit Commitment Methods for Non-Interconnected Island Systems

Energies ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 657 ◽  
Author(s):  
Georgios Psarros ◽  
Stavros Papathanassiou
Keyword(s):  
Linear Programming ◽  
Power Systems ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Unit Commitment ◽  
Renewable Energy Sources ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Droop Characteristic

The generation management concept for non-interconnected island (NII) systems is traditionally based on simple, semi-empirical operating rules dating back to the era before the massive deployment of renewable energy sources (RES), which do not achieve maximum RES penetration, optimal dispatch of thermal units and satisfaction of system security criteria. Nowadays, more advanced unit commitment (UC) and economic-dispatch (ED) approaches based on optimization techniques are gradually introduced to safeguard system operation against severe disturbances, to prioritize RES participation and to optimize dispatch of the thermal generation fleet. The main objective of this paper is to comparatively assess the traditionally applied priority listing (PL) UC method and a more sophisticated mixed integer linear programming (MILP) UC optimization approach, dedicated to NII power systems. Additionally, to facilitate the comparison of the UC approaches and quantify their impact on systems security, a first attempt is made to relate the primary reserves capability of each unit to the maximum acceptable frequency deviation at steady state conditions after a severe disturbance and the droop characteristic of the unit’s speed governor. The fundamental differences between the two approaches are presented and discussed, while daily and annual simulations are performed and the results obtained are further analyzed.

Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm

2021 ◽  
Vol 11 (23) ◽  
pp. 11525
Author(s):  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Lázaro Alvarado-Barrios ◽  
Andres Arias-Londoño ◽  
Cesar Álvarez-Arroyo
Keyword(s):  
Power Flow ◽  
Fitness Function ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Solar Pv ◽  
Flow Method ◽  
Power Flow Method

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution (xit) and the best current solution (xbest), where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of 26.89% and 27.60% for each test feeder with respect to the benchmark cases.

scholarly journals Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach

2020 ◽  
Vol 12 (2) ◽  
pp. 581 ◽  
Author(s):  
Yiyong Xiao ◽  
Pei Yang ◽  
Siyue Zhang ◽  
Shenghan Zhou ◽  
Wenbing Chang ◽  
...  
Keyword(s):  
Large Scale ◽  
Dynamic Equilibrium ◽  
Cost Effective ◽  
Mixed Integer ◽  
Single Pair ◽  
Median Problem ◽  
Solution Approach ◽  
Maximum Loss ◽  
Large Scale Problems ◽  
Objective Model

This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems.

Flexible Synthesis of Heat Exchanger Network with Particle Swarm Optimization Algorithm

2011 ◽  
Vol 214 ◽  
pp. 569-572 ◽  
Author(s):  
Xio Ling Zhang ◽  
Hong Chao Yin ◽  
Zhao Yi Huo
Keyword(s):  
Particle Swarm Optimization ◽  
Heat Exchanger ◽  
Operating Cost ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Nonlinear Program ◽  
Heat Exchanger Network ◽  
Swarm Optimization

In this paper, the flexible synthesis problem for heat exchanger network(HEN) is formulated to a mixed integer nonlinear program(MINLP) model. The objection function of the model consists of two components: First, a candidate HEN structure has to satisfy flexible criterion during input span. Second, a minimized annual cost consisting of investment cost and operating cost is investigated. The solution strategy based on particle swarm optimization(PSO) algorithm is proposed to obtain the optimal solution of the presented model. Finally, a four streams example is investigated to show the advantage of the whole proposed optimization approach.

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