Anthony Chen

Constraint handling in genetic algorithms using a gradient-based repair method

Constraint handling is one of the major concerns when applying genetic algorithms (GAs) to solve constrained optimization problems. This paper proposes to use the gradient information derived from the constraint set to systematically repair infeasible solutions. The proposed repair procedure is embedded into a simple GA as a special operator. Experiments using 11 benchmark problems are presented and compared with the best known solutions reported in the literature. Our results are competitive, if not better, compared to the results reported using the homomorphous mapping method, the stochastic ranking method, and the self-adaptive fitness formulation method.

Travel time reliability with risk-sensitive travelers

In recent empirical studies on values of time and reliability, many have suggested that travelers are interested not only in travel time saving but also in reduction in travel time variability. Variability introduces uncertainty for travelers such that they do not know exactly when they will arrive at their destination. Thus, it is considered as a risk (or an added cost) to a traveler making a trip. Continuing research is reported on route choice models and the effect on travel time reliability in an uncertain environment caused by demand and supply variations. The goal is to examine what the aggregate impact of changes in variability might be on network assignment and how travelers with different risk-taking behaviors respond to these changes.

Stochastic Transportation Network Design Problem with Spatial Equity Constraint

Equity issues and demand uncertainty are two important issues in the network design problem (NDP). Spatial equity in NDP is concerned with the benefit distribution among network users. By considering demand uncertainty, a more realistic evaluation of the network performance given a network improvement plan can be obtained. Two stochastic models that consider both spatial equity and demand uncertainty are formulated: an expected-value model and a chance-constrained model. Both models are solved by a simulation-based genetic algorithm procedure. The genetic algorithm is used to solve NDP, and stochastic simulation is used to simulate the demand uncertainty. The results of numerical experiments are provided to demonstrate the significance of the equity issue and demand uncertainty in NDP.

Computational study of state-of-the-art path-based traffic assignment algorithms

Recent research has demonstrated and established the viability of applying path-based algorithms to the traffic equilibrium problem in reasonably large networks. Much of the attention has been focused on two particular algorithms: the disaggregate simplicial decomposition (DSD) algorithm and the gradient projection (GP) algorithm. The purpose of this paper is to evaluate the performance of these two path-based algorithms using networks of realistic size. Sensitivity analysis is performed on randomly generated networks to examine the performance of the algorithms with respect to network sizes, congestion levels, number of origin-destination (OD) pairs, and accuracy levels. In order to be empirically convincing, a realistic large-scale network, known as the ADVANCE network, is also used to show that path-based algorithms are a viable alternative in practice.

Stochastic multi-objective models for network design problem

Transportation network design problem (NDP) is inherently multi-objective in nature, because it involves a number of stakeholders with different needs. In addition, the decision-making process sometimes has to be made under uncertainty where certain inputs are not known exactly. In this paper, we develop three stochastic multi-objective models for designing transportation network under demand uncertainty. These three stochastic multi-objective NDP models are formulated as the expected value multi-objective programming (EVMOP) model, chance constrained multi-objective programming (CCMOP) model, and dependent chance multi-objective programming (DCMOP) model in a bi-level programming framework using different criteria to hedge against demand uncertainty. To solve these stochastic multi-objective NDP models, we develop a solution approach that explicitly optimizes all objectives under demand uncertainty by simultaneously generating a family of optimal solutions known as the Pareto optimal solution set. Numerical examples are also presented to illustrate the concept of the three stochastic multi-objective NDP models as well as the effectiveness of the solution approach.

Transport Network Design Problem under Uncertainty: A Review and New Developments

This paper aims to provide a state-of-the-art review of the transport network design problem (NDP) under uncertainty and to present some new developments on a bi-objective-reliable NDP (BORNDP) model that explicitly optimizes the capacity reliability and travel time reliability under demand uncertainty. Both are useful performance measures that can describe the supply-side reliability and demand-side reliability of a road network. A simulation-based multi-objective genetic algorithm solution procedure, which consists of a traffic assignment algorithm, a genetic algorithm, a Pareto filter, and a Monte-Carlo simulation, is developed to solve the proposed BORNDP model. A numerical example based on the capacity enhancement problem is presented to demonstrate the tradeoff between capacity reliability and travel time reliability in the NDP.

C-logit stochastic user equilibrium model: formulations and solution algorithm

This article considers the stochastic user equilibrium (SUE) problem with the route choice model based on the C-logit function. The C-logit model has a simple closed-form analytical probability expression and requires relatively lower calibration efforts and represents a more realistic route choice behaviour compared with the multinomial logit model. This article proposes two versions of the C-logit SUE model that captures the route similarity using different attributes in the commonality factors. The two versions differ with respect to the independence assumption between cost and flow. The corresponding stochastic traffic equilibrium models are called the length-based and congestion-based C-logit SUE models, respectively. To formulate the length-based C-logit SUE model, an equivalent mathematical programming formulation is proposed. For the congestion-based C-logit SUE model, we provide two equivalent variational inequality formulations. To solve the proposed formulations, a new self-adaptive gradient projection algorithm is developed. The proposed formulations and new solution algorithm are tested in two well-known networks. Numerical results demonstrate the validity of the formulations and solution algorithm.

Alpha Reliable Network Design Problem

Uncertainties are unavoidable in engineering applications. A new model is proposed for designing networks under uncertainty of future demands. The objective is to minimize the total travel time budget required to satisfy the total travel time reliability constraint while considering the route choice behavior of network users. The model adopts the value-at-risk risk measure instead of the utility function to model planner risk preferences. It allows the planners to specify their risk preferences by using a confidence level of alpha on the total travel time reliability. This alpha reliable network design model is formulated as a stochastic bilevel optimization problem. The upper-level subprogram is a variant of the chance-constrained model that minimizes the total travel time budget subject to a chance constraint with a user-specified confidence level, a budget constraint, and design variable constraints; the lower-level subprogram is a user-equilibrium problem under demand uncertainty. A simulation-based genetic algorithm procedure is developed to solve this complex network design problem (NDP). Two numerical examples are presented to illustrate the features of the proposed NDP model.

Mean-Variance Model for the Build-Operate-Transfer Scheme Under Demand Uncertainty

A mean-variance model was developed for determining the optimal toll and capacity in a build-operate-transfer (BOT) roadway project subject to traffic demand uncertainty. This mean-variance model involves two objectives: maximizing mean profit and minimizing the variance (or standard deviation) of profit. The variance associated with profit is considered as a risk. Because maximizing expected profit and minimizing risk are often conflicting, there may not be a single best solution that can simultaneously optimize both objectives. Hence, it is necessary to explicitly consider this as a multiobjective problem so that a set of nondominated solutions can be generated. In this study, the optimal toll and capacity selection for the BOT problem under demand uncertainty is formulated as a special case of the stochastic network design problem. A simulation-based multiobjective genetic algorithm was developed to solve this stochastic bilevel mathematical programming formulation. Numerical results are also presented as a case study.

A Bi-objective Traffic Counting Location Problem for Origin-destination Trip Table Estimation

In this study, we consider the bi-objective traffic counting location problem for the purpose of origin-destination (O-D) trip table estimation. The problem is to determine the number and locations of counting stations that would best cover the network. The maximal coverage and minimal resource utilization criteria, which are generally conflicting, are simultaneously considered in a multi-objective manner to reveal the tradeoff between the quality and cost of coverage. A distance-based genetic algorithm (GA) is used to solve the proposed bi-objective traffic counting location problem by explicitly generating the non-dominated solutions. Numerical results are provided to demonstrate the feasibility of the proposed model. The primary results indicate that the distance-based GA can produce the set of non-dominated solutions from which the decision makers can examine the tradeoff between the quality and cost of coverage and make a proper selection without the need to repeatedly solve the maximal covering problem with different levels of resource.