Speeding up Energy System Models - a Best Practice Guide

Background Energy system models (ESM) are widely used in research and industry to analyze todays and future energy systems and potential pathways for the European energy transition. Current studies address future policy design, analysis of technology pathways and of future energy systems. To address these questions and support the transformation of today’s energy systems, ESM have to increase in complexity to provide valuable quantitative insights for policy makers and industry. Especially when dealing with uncertainty and in integrating large shares of renewable energies, ESM require a detailed implementation of the underlying electricity system. The increased complexity of the models makes the application of ESM more and more difficult, as the models are limited by the available computational power of today’s decentralized workstations. Severe simplifications of the models are common strategies to solve problems in a reasonable amount of time – naturally significantly influencing the validity of results and reliability of the models in general. Solutions for Energy-System Modelling Within BEAM-ME a consortium of researchers from different research fields (system analysis, mathematics, operations research and informatics) develop new strategies to increase the computational performance of energy system models and to transform energy system models for usage on high performance computing clusters. Within the project, an ESM will be applied on two of Germany’s fastest supercomputers. To further demonstrate the general application of named techniques on ESM, a model experiment is implemented as part of the project. Within this experiment up to six energy system models will jointly develop, implement and benchmark speed-up methods. Finally, continually collecting all experiences from the project and the experiment, identified efficient strategies will be documented and general standards for increasing computational performance and for applying ESM to high performance computing will be documented in a best-practice guide

Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

Generic Connectivity-Based CGRA Mapping via Integer Linear Programming

Coarse-grained reconfigurable architectures (CGRAs) are programmable logic devices with large coarse-grained ALU-like logic blocks, and multi-bit datapath-style routing. CGRAs often have relatively restricted data routing networks, so they attract CAD mapping tools that use exact methods, such as Integer Linear Programming (ILP). However, tools that target general architectures must use large constraint systems to fully describe an architecture's flexibility, resulting in lengthy run-times. In this paper, we propose to derive connectivity information from an otherwise generic device model, and use this to create simpler ILPs, which we combine in an iterative schedule and retain most of the exactness of a fully-generic ILP approach. This new approach has a speed-up geometric mean of 5.88x when considering benchmarks that do not hit a time-limit of 7.5 hours on the fully-generic ILP, and 37.6x otherwise. This was measured using the set of benchmarks used to originally evaluate the fully-generic approach and several more benchmarks representing computation tasks, over three different CGRA architectures. All run-times of the new approach are less than 20 minutes, with 90th percentile time of 410 seconds. The proposed mapping techniques are integrated into, and evaluated using the open-source CGRA-ME architecture modelling and exploration framework.Comment: 8 pages of content; 8 figures; 3 tables; to appear in FCCM 2019; Uses the CGRA-ME framework at http://cgra-me.ece.utoronto.ca

Continuous Modeling and Optimization Approaches for Manufacturing Systems

This thesis is concerned with two macroscopic models that are based on hyper- bolic partial differential equations (PDE) with discontinuous flux functions. The first model describes the material flow of an entire production line with finite buffers. We consider different solutions of the model, present the novel DFG- method (Discontinuous Flux Godunov), and compare the results with other established numerical methods. Additionally, we investigate a restricted optimization problem with respect to partial differential equations with discontinuous flux functions and consider two different solution approaches that are based on the adjoint method and the mixed integer problem (MIP). Further, we extend the model and its optimization problem to network structures. The second model describe the material flow on conveyor belts with obstacle interactions. We introduce a novel two dimensional model with a discontinuous and a non-local flux function. We consider a finite volume method and the discon- tinuous Galerkin method for solving this model. Finally, we validate the model with real data and present a numerical study with respect to the introduced solution methods

Optimization techniques for task allocation and scheduling in distributed multi-agent operations

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 105-107).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.This thesis examines scenarios where multiple autonomous agents collaborate in order to accomplish a global objective. In the environment that we consider, there is a network of agents, each of which offers different sets of capabilities or services that can be used to perform various tasks. In this environment, an agent formulates a problem, divides it into a precedence-constrained set of sub-problems, and determines the optimal allocation of these sub-problems/tasks to other agents so that they are completed in the shortest amount of time. The resulting schedule is constrained by the execution delay of each service, job release times and precedence relations, as well as communication delays between agents. A Mixed Integer-Linear Programming (MILP) approach is presented in the context of a multi-agent problem-solving framework that enables optimal makespans to be computed for complex classifications of scheduling problems that take many different parameters into account. While the algorithm presented takes exponential time to solve and thus is only feasible to use for limited numbers of agents and jobs, it provides a flexible alternative to existing heuristics that model only limited sets of parameters, or settle for approximations of the optimal solution. Complexity results of the algorithm are studied for various scenarios and inputs, as well as recursive applications of the algorithm for hierarchical decompositions of large problems, and optimization of multiple objective functions using Multiple Objective Linear Programming (MOLP) techniques.by Mark F. Tompkins.M.Eng

Automatically improving SAT encoding of constraint problems through common subexpression elimination in Savile Row

The formulation of a Propositional Satisfiability (SAT) problem instance is vital to efficient solving. This has motivated research on preprocessing, and inprocessing techniques where reformulation of a SAT instance is interleaved with solving. Preprocessing and inprocessing are highly effective in extending the reach of SAT solvers, however they necessarily operate on the lowest level representation of the problem, the raw SAT clauses, where higher-level patterns are difficult and/or costly to identify. Our approach is different: rather than reformulate the SAT representation directly, we apply automated reformulations to a higher level representation (a constraint model) of the original problem. Common Subexpression Elimination (CSE) is a family of techniques to improve automatically the formulation of constraint satisfaction problems, which are often highly beneficial when using a conventional constraint solver. In this work we demonstrate that CSE has similar benefits when the reformulated constraint model is encoded to SAT and solved using a state-of-the-art SAT solver. In some cases we observe speed improvements of over 100 times

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds

Mathematical Model and Framework for Multi-Phase Project Optimization

This research aims to assist investors of “real” tangible assets such as construction projects in making an optimal portfolio of phased and regular projects which will yield the best financial outcome calculated in terms of discounted cash flow of future anticipated revenues and costs. We use optimization techniques to find the optimal timing and phasing of a single project that has the potential of being decomposed into smaller sequential phases. Existence of uncertainties is inevitable especially in cases in which we are planning for long durations. In the presence of these uncertainties, full upfront commitment to large projects may jeopardize the rationality of investments and cause substantial economic risks. Breaking a big project into smaller stages (phases) and implementing a staged development is a potential mechanism to hedge the risk. Under this approach, by adding managerial flexibilities, we may choose to abandon a project at any time once the uncertain outcomes are not favorable. In addition to the benefits resulting from hedging unfavorable risks, phasing a project can transform a financially infeasible project into a feasible one due to less load on capital budgets during each time. Once some phases of a project are delayed and planned to be implemented sequentially, it is important to prepare the infrastructure required for their future development. Initially, we present a Mixed Integer Programming (MIP) model for the deterministic case with no uncertainties that considers interrelationships between phases of projects such as scheduling and costs (economy of scales) in addition to the initial infrastructural investment required for implementation of future phases. Pairing possible phases of a project and doing them in parallel is beneficial due to positive synergies between phases but on the downside requires larger capital investments. Unavailability of enough budgets to fully develop a profitable project will cause the investment to be carried out in different phases e.g. during times when the required capital for developing the next phase (or group of phases) is available. After, presenting the model for the deterministic case, we present a scenario-based multi-stage MIP model for the stochastic case. The source of uncertainty considered is future demand that is modeled using a trinomial lattice. We then present two methods for solving the stochastic problem and finding the value of the here and now decision variable (the size of the infrastructure/foundation). Finding the value of the here and now decision variable for all scenarios using a novel technique that does not require solving all the scenarios is the first method. The second method combines simulation and optimization to find good solutions for the here and now decision variable. Lastly, we present a MIP for the deterministic multi-project case. In this setting, projects could have multiple phases. The MIP will help the managers in making the project selection and scheduling decision simultaneously. It will also assist the managers in making appropriate decisions for the size of the infrastructure and the implementation schedule of the phases of each project. To solve this complex model, we present a pre-processing step that helps reduce the size of the problem and a heuristic that finds good solutions very fast

Cardinal Optimizer (COPT) User Guide

Cardinal Optimizer is a high-performance mathematical programming solver for efficiently solving largescale optimization problem. This documentation provides basic introduction to the Cardinal Optimizer

동력원을 고려한 교통망에서 에너지 최적화를 위한 링크 시계열로 이산화 된 동적 교통 배정 연구

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 차석원.Vehicle that provides convenience for mobility has been studied for more than 100 years. Recently, there has been a lot of research on the performance of a single-vehicle and interaction between other cars. For example, research on technologies such as vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and autonomous driver assistant system (ADAS) is actively studied. This change also extends the scope of the study, from a single vehicle to a vehicle fleet, and from micro-traffic to macro-traffic. In the case of vehicles subject to the main experiment, it is classified into internal combustion engine vehicle (ICEV), hybrid electric vehicle (HEV), electric vehicle (EV), and fuel-cell electric vehicle (FCEV) according to the electrification of the powertrain. Also, it can be divided into different categories depending on whether autonomous driving and communication are possible. This study focused on expanding the fuel consumption of vehicles, which has affected environmental pollution for a long time, to the transportation network level. Of course, these researches have been studied for more than a decade, but recent optimization studies using various powertrains have been hard to find. In particular, I decided to build a system that reflects the energy superiority of each road, based on the tendency to consume fuel by road type according to the powertrain. For several decades, the study of arranging the traffic situation of vehicles and determining the route of each vehicle has been mainly applied to traffic allocation for road planning, such as road construction. Therefore, the main content was to predict users' choices and to study from a macro perspective in hours or days. However, in the near future, it is expected to be able to control the route of vehicles in a specific unit of a transportation network, so based on these assumptions, researchers conducted many researches to optimize energy in the transportation network. Many studies on fuel consumption have advanced, but it is hard to find a study of many vehicles consisting of various powertrains. The main reason is that the fuel consumption itself is difficult to predict and calculate, and there is a significant variation for each vehicle. In this study, the average value of each variable for energy consumption was predicted using Vehicle Specific Power (VSP). It used to calculate the fuel consumption that matches the powertrain by each vehicle. Data on fuel consumption were taken from Autonomie, a forward simulator provided by Argonne National Laboratory in the United States. Based on the relationship between the simulated fuel consumption and the VSP as a variable, the deviation was optimized with Newton's method. However, after energy optimization, different vehicles have different travel times, resulting in wasted time due to relative superiority about the fuel consumption, which is a problem in terms of fairness for drivers. Therefore, based on the traffic time of each road, the first principle of Wardrop was applied to optimize the allocation of traffic. The first principle of Wardrop is Wardrop's User Equilibrium (UE) which means an optimal state with same travel cost in the same origin-destination. Based on UE, it was replaced by the question of distributing the allocated traffic flow depends on vehicle type. To this end, it is necessary to apply the traffic assignment based on the route, not the link unit, so that each vehicle can be distributed to the route. This distribution is also an optimization problem, which is a Linear Programming (LP) problem with equality constraint and inequality constraint with the fuel consumption per vehicle derived for each route as a factor. This problem can be resolved through the process of replacing the constraints with the Lagrange multiplier, and the simple conditions for optimization are met. In conclusion, the goal of this study is to allocate a path-based dynamic traffic assignment (DTA) so that it can be applied in real-time with minimal computation and to distribute them by vehicle type. First, under the current road conditions, each vehicle moves toward the intersection. The intersection at the end of the road that is currently running by time unit was organized by Origin-Destination (O-D). In DTA studies, intricate and detailed model like the cell transmission model (CTM) is used for modeling. The traffic flow is calculated as a fluid, which needs high calculating costs and many complex constraints to optimization. Therefore, link time-series was suggested to be modeled for each link and applied as a kind of historical information. This approach can be regarded as Discretized-DTA based on link time-series. It is possible to apply the time axis to the traffic network with a small computing cost and to allocate O-D traffic that changes with time. This optimization problem can be resolved by the Gradient Projection algorithm, which was widely used in path-based traffic allocation. Different delay equations were applied for the intersections by traffic lights for the modeling of the time delay. The actual transportation network flow was predicted as much as possible by the Discretized-DTA algorithm. The allocated traffic was divided by the route, and the fuel consumption per vehicle was derived for each route. In the Sioux Falls Network, the most commonly used example of a traffic allocation simulation, the total energy cost was reduced by about 2% when applying the vehicle distribution used in this study after static traffic assignment. This performance is the result of no time loss between the vehicles, as it is in a UE state. And if traffic simulation case is limited to O-D allocated on multiple paths, it is an effect of more than 3%. This improvement could be replaced by a reduction in fuel cost of about 20 million won for 360,600 vehicles daily. For evaluation of the performance as a navigating system, four navigating systems, as a comparison group, are modeled with algorithms that recommend the optimal route in real-time. The system proposed in this study was able to improve 20% in total traffic time and 15% in the energy aspect compared to the comparison group. It was also applied to Gangdong-gu, Seoul, to simulate a somewhat congested transportation network. At this time, the performance improvement was reduced by 10% in traffic time and 5% in the energy aspect. In the case of the navigating system, indeed, the effect of energy optimization for distributing by vehicle type is not substantial because allocation for each vehicle causes rarely distributed path. However, this improvement can be a significant impact if the effects are accumulated in the transportation network. In this study, energy optimization in the transportation network was achieved based on fuel consumption tendency by vehicle type, and the navigation system was developed for this. Nowadays, with the development of various communication and control technologies, the navigation system based on them can contribute to reducing the cost of transportation, both personally and socially.사람들의 이동에 편의성을 제공하는 자동차는 100년 넘는 긴 시간 동안 연구되어왔다. 최근에는 단일 자동차의 성능에 대한 연구에 더불어 다른 자동차와의 상호 작용에 대한 연구가 많이 이루어지고 있다. 예로 차량 간 (vehicle-to-vehicle: V2V) 통신, 차량 인프라 간(vehicle-to-infrastructure: V2I) 통신, 지능형 운전자 보조 시스템(advanced driver assistance system: ADAS) 등의 기술에 대한 연구를 들 수 있다. 이 같은 변화는 연구 대상의 범위도 단일 차량에서 차량 fleet, 그리고 micro-traffic부터 macro-traffic까지 넓어지게 하고 있다. 주 실험 대상인 자동차의 경우에도 동력전달계의 전기화에 따라 내연기관자동차, 하이브리드자동차, 전기자동차, 연료전지자동차등으로 분류되며, 자율주행과 통신 가능 여부에 따라 또 다른 분류로 나뉠 수 있다. 본 연구는 오랫동안 환경에 큰 영향을 끼치는 자동차의 연료소모량을 교통망 차원으로 넓히는 것에 착안하였다. 물론 이러한 연구는 십년 넘게 이루어져왔지만, 최근 다양해진 동력전달계에 따른 최적화 연구는 찾기 힘들었다. 특히 동력전달계에 따라 도로 별 연료소모 경향이 달라지는 것에 착안하여, 도로 별 에너지적 우위를 반영한 시스템을 구축하기로 하였다. 수 십년 동안 차량들의 교통 상황을 정리하여 각 차량들의 루트를 정하는 연구는, 도로 건설 등의 도로 계획을 위한 통행 배정에 주로 적용되어왔다. 따라서 이용자들의 선택을 예측하고, 시간 단위 또는 일 단위의 거시적인 관점에서의 연구가 주 내용이었다. 하지만 근 시일 내에 일정 단위의 교통망에서는 차량들의 루트를 컨트롤할 수 있을 것이라 예상되기에 이러한 가정을 기반으로 교통망 내의 에너지를 최적화 하는 연구를 진행하였다. 연료소모량에 대한 연구는 많이 진행되었지만, 다양한 파워트레인으로 구성된 다수의 차량들에 대한 연구는 찾아보기 힘들다. 그 대표적인 이유는 연료소모량자체가 예측 및 계산하기 힘들고, 차량마다 그 편차가 크기 때문이다. 본 연구에서는 차량 비출력(Vehicle specific power: VSP)를 이용하여 각 변수들의 평균치로 예측한 후에, 이를 이용하여 차종 별 동력전달계에 맞는 연료소모량을 계산하는 방법을 활용하였다. 연료소모량에 대한 데이터는 미국의 Argonne national laboratory에서 공급하는 전방향 시뮬레이터인 Autonomie에서 가져왔다. 시뮬레이션 된 연료소모량과 VSP와의 관계를 변수로 하여 뉴턴법(Newtons method)로 편차를 최소화하도록 최적화하였다. 하지만 교통망 내에서 에너지 최적화 후, 차종에 따라 통행 시간이 달라져서 상대적 우위에 따른 시간 낭비가 생기면 운전자의 공정성 측면에서 문제가 된다. 따라서 각 도로의 통행시간을 기준으로 Wardrop의 첫번째 원칙을 적용한 최적 통행 배정을 수행하였다. 그리고 이를 기준으로 배정된 통행의 차량 흐름을 차종 별로 분배하는 문제로 치환하였다. 이를 위해서는 통행 배정을 링크 단위가 아니라 경로를 기반으로 적용하여야 각 차종을 경로에 분배할 수 있다. 이러한 분배 또한 최적화 문제로, 이는 각 경로에 대해 도출된 차량당 연료소모량을 계수로 하고, 등식 제한 조건과 부등식 제한 조건을 가지는 선형계획법(Linear Programming: LP)문제이다. 이는 제한조건을 라그랑주 상수(Lagrange Multiplier)로 치환하는 과정을 통해, 해결할 수 있으며 조건이 단순하기 때문에, 최적화를 위한 조건을 만족시킨다. 또한 본 연구에서는 실시간으로 루트를 정해주는 일종의 네비게이션을 목표로 하였기 때문에, Wardrop의 이용자 평형(User Equilibrium: UE)상태를 시간에 따라 변하는 동적 상태로 적용해야 했다. 결론적으로, 경로 기반의 동적 통행 배정(Dynamic Traffic Assignment: DTA)을 연산을 최소화하여 실시간으로 적용할 수 있도록 배정을 하고, 차종 별로 분배를 하는 것이 본 연구의 목표이다. 먼저 현재 차량 상황에서 각 도로는 교차로를 향해서 이동하기 때문에, 시간 단위 별로 현재 달리고 있는 도로의 끝의 교차로를 기점으로 하고 원래 가고자 하는 목적지를 종점으로 가지는 기 종점을 구성하였다. 동적 통행 배정의 연구에서는 세포 전이 모델(Cell Transmission Model: CTM) 등을 이용하여, 교통 흐름을 유체처럼 계산하여 시간 소모가 많다. 따라서 도로에 진입하는 각 통행 흐름을 도로의 시계열에 저장하는 이산화 된 동적 통행 배정(Discretized-DTA)방법을 고안하였다. 이는 적은 계산 비용으로 심플하게 시간 축을 교통망에 부여하였고, 이를 통해 시간에 따라 변화하는 기 종점을 통행을 배정할 수 있게 되었다. 이 최적화 문제는 경로 기반 통행배정에서 많이 사용된 경사 투영법(Gradient Projection) 알고리즘을 적용하였다. 각 도로의 교통 흐름에 따른 시간 지체도 신호등이 있는 교차로의 단속류와 신호등이 없는 도로의 연속류에 따라 다른 지체 식을 적용하여 실제 현실의 교통망의 흐름을 최대한 예측하였다. 이렇게 배정된 통행량을 경로 별로 나누어, 각 경로에 대한 차량당 연료소모량을 도출하였다. 통행 배정 시뮬레이션에서 가장 많이 사용하는 예제인 Sioux Falls 네트워크에서는 정적 통행 배정 이후 본 연구에 사용된 차종 분배를 적용할 경우에, 전체 에너지 코스트가 약 2% 감소하였다. 이는 Wardrop의 이용자 평형 상태이기 때문에, 차량들 간의 어떤 시간 손해도 없는 결과이다. 그리고 만약 통행량이 복수의 경로로 배정된 O-D에 한정할 경우에, 약 3%가 넘는 효과라고 할 수 있다. 이는 하루 기준으로, 360,600대의 차량에 대해 2000만원 정도의 연료비 감소로 치환할 수 있었다. 네비게이팅 시스템의 경우에는, 현재 도로의 상태를 4가지 정도로 나누어서 실시간 최적 경로로 추천하는 경우를 비교군으로 정하였다. 비교군에 비해 본 연구에서 제안하는 시스템은 전체 통행시간과 에너지적 측면을 개선할 수 있었다. 또한 이를 서울시 강동구에 적용하여 어느 정도 혼잡한 교통망을 모사하였다. 이 때 시뮬레이션 결과와 기존의 최소 시간 알고리즘을 적용하는 상용 네비게이션 시스템 결과를 비교하였다. 결과적으로 약 8000대의 차량이 주행하는 시나리오 1의 교통망을 기준으로 전체 통행시간은 66%, 에너지 소모 비용은 34%를 줄일 수 있었다. 이는 일정 혼잡도까지는 효과가 커졌지만, 어느 이상에서는 효과가 감소하기도 하였다. 물론 이산화 된 동적 교통 분배를 기반으로하기 때문에, 일정 시간 단위의 차량들을 편대로 묶어 통행을 배정하고, 그 결과 경로가 분산되는 경우 자체가 적기 때문에 분산된 경로에 차종 별로 분배하는 에너지 최적화의 효과는 크지 않은 것이 사실이다. 하지만 이 또한 교통망 내에서 그 효과를 누적하면 영향이 크다고 할 수 있다. 본 연구에서는 결과적으로 차종 별 연료 소모 경향에 근거하여 교통망 내 통행 시간 감소에 더불어 에너지 최적화를 이루었고, 이를 위한 네비게이팅 시스템을 개발했다. 각종 통신과 제어 기술이 발전한 요즘, 그에 기반한 네비게이팅 시스템은 개인적, 사회적으로 교통에서 발생하는 비용을 줄이는 데 기여할 수 있다.Chapter 1. Introduction 1 1.1. Background 1 1.2. Research Scope and Contents 7 Chapter 2. Theory and Literature Review 11 2.1. Traffic Assignment Problem 11 2.1.1. Wardrops Principle 11 2.1.2. Dynamic Traffic Assignment (DTA) 16 2.1.3. Volume-Delay Function (VDF) 18 2.2. Vehicle Fuel Consumption 20 2.2.1. Tendency Based on Driving Cycle 21 2.2.2. Tendency Based on Powertrain 22 2.3. Vehicle Specific Power (VSP) 24 2.4. Route Guidance System 26 2.4.1. Optimal Routing System Based on Fuel Economy 27 Chapter 3. Target Model Development 29 3.1. Vehicle Model Development 29 3.2. Fuel Consumption Trend Depends on Vehicle Model 32 3.3. Introduction of Vehicle Specific Power 35 3.4. Calibration of VSP Parameters 36 3.5. Regression of VSP Variables 38 3.5.1.. VSP Variables from General Vehicles 39 3.5.2. Regression of VSP Variables by Travel Time 40 Chapter 4. Traffic Assignment based on Energy Consumption 46 4.1. Model for Static Traffic Assignment 46 4.1.1. Sioux Falls Network 46 4.2. Gradient Projection (GP) Algorithm 48 4.3. Distribution of Vehicles to Energy Optimization 51 4.3.1. Problem Formulation for Vehicle Distribution 51 4.3.2. Linear Programming 53 4.4. Simulation Result in Test Network 54 Chapter 5. Navigating System using Discretized Dynamic Traffic Assignment 57 5.1. Modeling of Discretized Dynamic Traffic Assignment 57 5.1.1. Discretized-DTA with Vehicle Fleets 57 5.1.2. Discretized-DTA with Link Time-Series 60 5.1.3. Target Network 62 5.2. Navigating System 65 5.2.1. Structure of the Navigating System 65 5.2.2. Algorithm of the Navigating System 65 5.2.3. Assumption of the Navigating System 69 5.3. Result of Navigating System 70 5.3.1. Results of the Travel Time Prediction 70 5.3.2. Results in Scenario 1 71 5.3.3. Results in Scenario 2 79 5.3.4. Results in Scenario 3 81 Chapter 6. Conclusion and Future Works 85 6.1. Conclusion 85 6.2. Future Work 87 Bibliography 88 Abstract in Korean 100Docto