We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small high-accuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using cross-validation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets.

Irrelevant features and the subset selection problem

Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods

Introduction to linear and nonlinear programming

/pdf/lectu-re-notes-in-economics-and-mathematical-systems-4gmrols5ux.pdf

Lectu re Notes in Economics and Mathematical Systems

Economics and Information Theory

This book presents a systematic introduction to a new generation of models for solving dynamic travel choice problems including traveler's destination choice, departure/arrival time choice and route choice. These models are expected to function as off-line travel forecasting and evaluation tools, and eventually as on-line prediction and control models in advanced traveler information and traffic management systems. In addition to a rich set of new formulations and solution algorithms, the book provides a summary of the necessary mathematical background and concludes with a discussion of the requirements for model implementation.

Modeling dynamic transportation networks

The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints...

A new class of instantaneous dynamic user-optimal traffic assignment models

I Dynamic Transportation Network Analysis.- 1 Introduction.- 1.1 Requirements for Dynamic Modeling.- 1.2 Urban Transportation Network Analysis.- 1.3 Overview of Dynamic Network Models.- 1.4 Hierarchy of Dynamic Network Models.- 1.5 Notes.- II Mathematical Background.- 2 Variational Inequalities and Continuous Optimal Control.- 2.1 Variational Inequality Problems.- 2.1.1 Definitions.- 2.1.2 Existence and Uniqueness.- 2.1.3 Relaxation Algorithm.- 2.2 Continuous Optimal Control Problems.- 2.2.1 Definitions.- 2.2.2 No Constraints.- 2.2.3 Equality and Inequality Constraints.- 2.2.4 Equality and Nonnegativity Constraints.- 2.3 Hierarchical Optimal Control Problems.- 2.3.1 Static Two-Person Games.- 2.3.2 Dynamic Games.- 2.3.3 Bilevel Optimal Control Problems.- 2.4 Notes.- 3 Discrete Optimal Control and Nonlinear Programming.- 3.1 Discrete Optimal Control Problems.- 3.1.1 No Constraints.- 3.1.2 Equality and Inequality Constraints.- 3.1.3 Equality and Nonnegativity Constraints.- 3.2 Nonlinear Programming Problems.- 3.2.1 Unconstrained Minimization.- 3.2.2 General Constraints.- 3.2.3 Linear Equality and Nonnegativity Constraints.- 3.2.4 Discrete Optimal Control and Nonlinear Programs.- 3.3 Solution Algorithms.- 3.3.1 One Dimensional Minimization.- 3.3.2 Frank-Wolfe Algorithm.- 3.4 Notes.- III Deterministic Dynamic Route Choice.- 4 Network Flow Constraints and Definitions of Travel Times.- 4.1 Flow Conservation Constraints.- 4.2 Definitions.- 4.3 Flow Propagation Constraints.- 4.3.1 Type I.- 4.3.2 Type II.- 4.3.3 Type III.- 4.4 First-In-First-Out Constraints.- 4.5 Link Capacity and Oversaturation.- 4.5.1 Maximal Number of Vehicles on a Link.- 4.5.2 Maximal Exit Flow from a Link.- 4.5.3 Constraints for Spillback.- 4.6 Notes.- 5 Ideal Dynamic Route Choice Models.- 5.1 An Example with Two Parallel Routes.- 5.2 Definition of an Ideal State.- 5.3 A Route-Time-Based Model.- 5.3.1 Route-Time-Based Conditions.- 5.3.2 Dynamic Network Constraints.- 5.3.3 The Variational Inequality Problem.- 5.4 A Link-Time-Based Model.- 5.4.1 Link-Time-Based Conditions.- 5.4.2 The Variational Inequality Problem.- 5.5 A Numerical Example.- 5.6 A Multi-Class Route-Cost-Based Model.- 5.6.1 Multi-Class Route-Cost-Based Conditions.- 5.6.2 Dynamic Network Constraints.- 5.6.3 The Variational Inequality Problem.- 5.7 A Multi-Class Link-Cost-Based Model.- 5.7.1 Multi-Class Link-Cost-Based Conditions.- 5.7.2 The Variational Inequality Problem.- 5.8 Notes.- 6 A Solution Algorithm for an Ideal Route Choice Model.- 6.1 Statement of the Algorithm.- 6.1.1 Discrete VI Model for the Link-Time-Based Case.- 6.1.2 Relaxation Procedure and Optimization Problem.- 6.1.3 The Frank-Wolfe Method.- 6.2 Solving the LP Subproblem.- 6.3 Computational Experience.- 6.4 Notes.- 7 Instantaneous Dynamic Route Choice Models.- 7.1 Definition of an Instantaneous State.- 7.2 A Route-Time-Based Model.- 7.2.1 Route-Time-Based Conditions.- 7.2.2 Dynamic Network Constraints.- 7.2.3 The Variational Inequality Problem.- 7.3 A Link-Time-Based Model.- 7.3.1 Link-Time-Based Conditions.- 7.3.2 The Variational Inequality Problem.- 7.4 Solution Algorithm.- 7.4.1 Discrete VI Model for the Link-Time-Based Case.- 7.4.2 Relaxation Procedure and Optimization Program.- 7.4.3 The Frank-Wolfe Method.- 7.4.4 Numerical Example.- 7.5 Notes.- 8 Extensions of Instantaneous Route Choice Models.- 8.1 Optimal Control Model 1.- 8.1.1 Model Formulation.- 8.1.2 Optimality Conditions.- 8.1.3 DUO Equivalence Analysis.- 8.2 Optimal Control Model 2.- 8.2.1 Model Formulation.- 8.2.2 Optimality Conditions.- 8.3 A Multi-Class Route-Cost-Based Model.- 8.3.1 Multi-Class Route-Cost-Based Conditions.- 8.3.2 Dynamic Network Constraints.- 8.3.3 The Variational Inequality Problem.- 8.4 A Multi-Class Link-Cost-Based Model.- 8.4.1 Multi-Class Link-Cost-Based Conditions.- 8.4.2 The Variational Inequality Problem.- 8.5 Notes.- IV Stochastic Dynamic Route Choice.- 9 Ideal Stochastic Dynamic Route Choice Models.- 9.1 Redefinition of Dynamic Travel Times.- 9.2 Formulation of the Model.- 9.2.1 Network Constraints.- 9.2.2 Stochastic Route Choice and the Ideal SDUO State.- 9.2.3 Two Popular Route Choice Functions.- 9.2.4 Ideal Route Choice Conditions and VI Problem.- 9.2.5 Analysis of Dispersed Route Choice.- 9.3 Solution Algorithm.- 9.3.1 The Discrete Variational Inequality Problem.- 9.3.2 The Relaxation Method.- 9.3.3 Method of Successive Averages.- 9.3.4 Summary of the Solution Algorithm.- 9.3.5 A Logit-Based Ideal Stochastic Loading.- 9.3.6 Proof of the Algorithm.- 9.4 Numerical Example.- 9.5 Notes.- 10 Instantaneous Stochastic Dynamic Route Choice Models.- 10.1 Formulation of the Model.- 10.1.1 Network Constraints.- 10.1.2 Definition of an Instantaneous SDUO State.- 10.1.3 Instantaneous Route Choice Conditions and VI Problem.- 10.2 Solution Algorithm.- 10.2.1 The Discrete Variational Inequality Problem.- 10.2.2 The Relaxation Method.- 10.2.3 Method of Successive Averages.- 10.2.4 Summary of the Solution Algorithm.- 10.2.5 A Logit-Based Instantaneous Stochastic Loading.- 10.2.6 Proof of the Algorithm.- 10.3 An Instantaneous Optimal Control Model.- 10.4 Numerical Example.- 10.5 Notes.- V General Dynamic Travel Choices.- 11 Combined Departure Time/Route Choice Models.- 11.1 Additional Network Constraints.- 11.2 A Route-Based Model.- 11.2.1 Route-Based Conditions.- 11.2.2 Dynamic Network Constraints.- 11.2.3 The Variational Inequality Problem.- 11.3 A Link-Based Model.- 11.3.1 Link-Based Conditions.- 11.3.2 The Variational Inequality Problem.- 11.4 Solution Algorithm and An Example.- 11.4.1 Discrete Variational Inequality Problem.- 11.4.2 Relaxation Procedure and Optimization Problem.- 11.4.3 Numerical Example.- 11.5 Notes.- 12 Combined Mode/Departure Time/Route Choice Models.- 12.1 The Combined Travel Choice Problem.- 12.2 Individual Travel Choice Problems.- 12.2.1 Mode Choice Problem.- 12.2.2 Departure Time/Route Choice for Motorists.- 12.3 The Link-Time-Based Model.- 12.3.1 Network Constraints.- 12.3.2 The Variational Inequality Problem.- 12.4 Notes.- VI Implications for ITS.- 13 Link Travel Time Functions for Dynamic Network Models.- 13.1 Functions for Various Purposes.- 13.2 Stochastic Link Travel Time Functions.- 13.2.1 Moving Queue Concept.- 13.2.2 Cruise Time.- 13.2.3 Delay and Link Travel Time Functions.- 13.3 Deterministic Link Travel Time Functions.- 13.4 Implications of the Proposed Functions.- 13.4.1 Number of Link Flow Variables.- 13.4.2 Physical Constraints for Link Traffic Flow.- 13.4.3 Notes on Functions for Arterial Links.- 13.5 Functions for Freeway Segments.- 13.6 Notes.- 14 Implementation in Intelligent Transportation Systems.- 14.1 Implementation Issues.- 14.1.1 Traffic Prediction.- 14.1.2 Dynamic Route Guidance.- 14.1.3 Integrated Traffic Control/Information System.- 14.1.4 Incident Management.- 14.1.5 Congestion Pricing.- 14.1.6 Operations and Control for AHS.- 14.1.7 Transportation Planning.- 14.2 Practical Considerations.- 14.2.1 Rolling Horizon Implementation.- 14.2.2 Traveler Knowledge of Information.- 14.2.3 Response to Current and Anticipated Conditions.- 14.2.4 Flow-Based vs. Vehicle-Based Models.- 14.2.5 Different Types of Travelers.- 14.3 Data Requirements.- 14.3.1 Time-Dependent O-D Matrices.- 14.3.2 Network Geometry and Control Data.- 14.3.3 Traffic Flow Data.- 14.3.4 Traveler Information.- 14.4 Notes.- References.- Author Index.- List of Figures.- List of Tables.

Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach

In transportation planning, a large class of problems is characterized by multiple levels of decision making. Examples include selection of links for capacity improvements (network design), pricing of freight transportation services and traffic signal setting. In each of these problems, government or industry officials make one set of decisions, which seek to improve the network’s performance. At another level, users make choices with regard to route, mode, origin-destination, etc. Although the responses of users to a given improvement can be predicted, their decisions cannot be dictated. For example, officials choose locations for network improvements, and drivers then choose whatever routes they perceive to be best. Likewise, freight carriers determine shipment rates and transit times, and shippers choose the best mode of shipment. In this paper, we show how to formulate such problems as bilevel programming models, and propose solution algorithms for evaluation. For the transportation network design problem, we show that this model can be solved exactly for networks with a few hundred nodes. The general form of a bilevel program is

A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows☆

A formulation of the network design problem as a bilevel linear program is presented which admits both the convex and concave investment functions. It also allows a more general representation of travel cost functions than a previous formulation by LeBlanc and Boyce (1986).

David E. Boyce

Papers

Modeling dynamic transportation networks

A new class of instantaneous dynamic user-optimal traffic assignment models

Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach

A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows☆

A general bilevel linear programming formulation of the network design problem