Numerical Studies on Reformulation Techniques for Continuous Network Design with Asymmetric User Equilibria

2010 ◽  
Vol 1 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Michael Ferris ◽  
Henry X. Liu
Keyword(s):  
Nonlinear Programming ◽  
Network Design ◽  
Mathematical Program ◽  
Network Design Problem ◽  
Complementarity Constraints ◽  
Nonlinear Programming Problem ◽  
Design Problems ◽  
Nonlinear Complementarity ◽  
Numerical Studies ◽  
Constraints Model

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation techniques for the lower level nonlinear complementarity, the original bilevel formulation can be converted to a single level nonlinear programming problem. We show that certain reformulations are more effective than others to solve the proposed MPCC model. Recommendations are thus provided on how to choose a reformulation of the continuous network design problem that can be solved effectively and/or efficiently.

Numerical Studies on Reformulation Techniques for Continuous Network Design with Asymmetric User Equilibria

2012 ◽  
pp. 138-157
Author(s):  
Xuegang (Jeff) Ban ◽  
Michael Ferris ◽  
Henry X. Liu
Keyword(s):  
Nonlinear Programming ◽  
Network Design ◽  
Network Design Problem ◽  
Complementarity Constraints ◽  
Nonlinear Programming Problem ◽  
Design Problems ◽  
Single Level ◽  
Nonlinear Complementarity ◽  
Numerical Studies ◽  
Constraints Model

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation techniques for the lower level nonlinear complementarity, the original bilevel formulation can be converted to a single level nonlinear programming problem. We show that certain reformulations are more effective than others to solve the proposed MPCC model. Recommendations are thus provided on how to choose a reformulation of the continuous network design problem that can be solved effectively and/or efficiently.

scholarly journals A Methodology for Increasing Convergence Speed of Traffic Assignment Algorithms Based on the Use of a Generalised Averaging Function

2020 ◽  
Vol 10 (16) ◽  
pp. 5698
Author(s):  
Marilisa Botte ◽  
Mariano Gallo ◽  
Mario Marinelli ◽  
Luca D’Acierno
Keyword(s):  
Network Design ◽  
Traffic Assignment ◽  
Convergence Speed ◽  
Network Design Problem ◽  
Traffic Flows ◽  
Assignment Problems ◽  
Design Problems ◽  
Method Of Successive Averages ◽  
Parameter Values ◽  
Real Scale

In this paper, we propose a generalisation of the Method of Successive Averages (MSA) for solving traffic assignment problems. The generalisation consists in proposing a different step sequence within the general MSA framework to reduce computing times. The proposed step sequence is based on the modification of the classic 1/k sequence for improving the convergence speed of the algorithm. The reduction in computing times is useful if the assignment problems are subroutines of algorithms for solving Network Design Problems—such algorithms require estimation of the equilibrium traffic flows at each iteration, hence, many thousands of times for real-scale cases. The proposed algorithm is tested with different parameter values and compared with the classic MSA algorithm on a small and on two real-scale networks. A test inside a Network Design Problem is also reported. Numerical results show that the proposed algorithm outperforms the classic MSA with reductions in computing times, reaching up to 79%. Finally, the theoretical properties are studied for stating the convergence of the proposed algorithm.

A Hybrid Lagrangian Relaxation and Tabu Search Method for Interdependent-Choice Network Design Problems

2011 ◽  
pp. 294-324 ◽  
Author(s):  
Chi Xie ◽  
Mark A. Turnquist ◽  
S. Travis Waller
Keyword(s):  
Tabu Search ◽  
Network Design ◽  
Lagrangian Relaxation ◽  
Optimization Problems ◽  
Search Method ◽  
Network Design Problem ◽  
Design Problems ◽  
Network Design Problems ◽  
Tabu Search Method ◽  
Algorithmic Logic

Hybridization offers a promising approach in designing and developing improved metaheuristic methods for a variety of complex combinatorial optimization problems. This chapter presents a hybrid Lagrangian relaxation and tabu search method for a class of discrete network design problems with complex interdependent-choice constraints. This method takes advantage of Lagrangian relaxation for problem decomposition and complexity reduction while its algorithmic logic is designed based on the principles of tabu search. The algorithmic advance and solution performance of the method are illustrated by implementing it for solving a network design problem with lane reversal and crossing elimination strategies, arising from urban evacuation planning.

scholarly journals Optimization of Process Design Problems Using Differential Evolution Algorithm

2016 ◽  
Vol 15 (2) ◽  
pp. 89
Author(s):  
A.M. Gujarathia ◽  
G. Vakili-Nezhaad ◽  
M. Vatani
Keyword(s):  
Differential Evolution ◽  
Network Design ◽  
Design Problem ◽  
Differential Evolution Algorithm ◽  
Network Design Problem ◽  
Design Problems ◽  
De Algorithm ◽  
Evolution Algorithm ◽  
Lle Data ◽  
Reactor Network

 A modified differential evolution algorithm (MDE) has been used for solving different process related design problems (namely calculation of the NRTL and Two-Suffix Margules activity coefficient models parameters in 20 ternary extraction systems including different ionic liquids and reactor network design problem). The obtained results, in terms of root mean square deviations (rmsd) for these models are satisfactory, with the overall values of 0.0023 and 0.0170 for 169 tie-lines for NRTL and Two-Suffix Margules models, respectively. The results showed that the MDE algorithm results in better solutions compared to the previous work based on genetic algorithm (GA) for correlating liquid-liquid equilibrium (LLE) data in these systems. MDE also outperformed DE algorithm when tested on reactor network design problem with respect to convergence and speed. 

scholarly journals An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

2017 ◽  
Vol 29 (6) ◽  
pp. 569-580
Author(s):  
Guangmin Wang ◽  
Junwei Yu ◽  
Shubin Li
Keyword(s):  
Network Design ◽  
Design Problem ◽  
Transportation Network ◽  
User Equilibrium ◽  
Network Design Problem ◽  
Total System ◽  
Complementarity Constraints ◽  
Mathematical Programs ◽  
Investment Cost ◽  
Non Linear

Continuous network design problem (CNDP) is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE) to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC) by describing UE as a non-linear complementarity problem (NCP). To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB) function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP) by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.

scholarly journals Visualising the Operation of Evolutionary Algorithms Optimising Water Distribution Network Design Problems

10.29007/j62b ◽  
2018 ◽  
Author(s):  
David Walker ◽  
Matthew Craven
Keyword(s):  
Evolutionary Algorithms ◽  
Network Design ◽  
Water Distribution ◽  
Distribution Network ◽  
Water Distribution Network ◽  
Network Design Problem ◽  
Complex Nature ◽  
Design Problems ◽  
Distribution Network Design ◽  
Water Distribution Network Design

Multi-objective evolutionary algorithms (MOEAs) are well known for their ability to optimise the water distribution network design problem. However, their complex nature often restricts their use to algorithm experts. A method is proposed for visualising algorithm performance that will enable an engineer to compare different optimisers and select the best optimisation approach. Results show that the convergence and preservation of diversity can be shown in a simple visualisation that does not rely on in-depth MOEA experience.

High Speed Information Network Planning using Stochastic Optimization Method

2013 ◽  
Author(s):  
Ki-Sang Song ◽  
Arun K. Somani
Keyword(s):  
Stochastic Optimization ◽  
Network Design ◽  
Multimedia Information ◽  
High Speed ◽  
Minimum Cost ◽  
Optimization Method ◽  
Multimedia Communication ◽  
Network Design Problem ◽  
Information Network ◽  
Traffic Characteristics

From the 1994 CAIS Conference: The Information Industry in Transition McGill University, Montreal, Quebec. May 25 - 27, 1994.Broadband integrated services digital network (B-ISDN) based on the asynchronous transmission mode (ATM) is becoming reality to provide high speed, multi bit rate multimedia communications. Multimedia communication network has to support voice, video and data traffics that have different traffic characteristics, delay sensitive or loss sensitive features have to be accounted for designing high speed multimedia information networks. In this paper, we formulate the network design problem by considering the multimedia communication requirements. A high speed multimedia information network design alogrithm is developed using a stochastic optimization method to find good solutions which meet the Quality of Service (QoS) requirement of each traffic class with minimum cost.

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