Combinatorial and Continuous Models for the Optimization of Traffic Flows on Networks

Fügenschuh, Armin; Herty, Michaël; Klar, Axel; Martín, Alexander

doi:10.1137/040605503

Cited by 46 publications

(30 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We repeat the 'recycling trick' of Section 2.2 for capital flows by assuming that production costs as well as profits incurred by the actual nodes k = 1 : K are deposited at node k = 0, the virtual supplier / customer node. We therefore replace (7) by (8) i.e. the profits p k f k and the production costs c k φ k are virtually paid to the node k = 0.…”

Section: Steady State Money Flowsmentioning

confidence: 99%

“…The answer to this question is given in the following Lemma 3.3 For any primitive distribution matrix A, and for any set of production costs c k , k = 1 : K and profits p k , k = 1 : K there exists a pricing strategy β k , k = 0 : K such that the steady state product flow, given in Lemma 3.2, produces steady state capitals κ k , k = 0 : K, as defined in (8).…”

Section: Steady State Money Flowsmentioning

confidence: 99%

“…The optimization of routing strategies for networks of almost arbitrary complexity has been investigated in [11] using an adjoint calculus approach. In this paper, we use a different approach, namely using a mixed integer program (MIP) [8] , [15]. To develop an understanding of the structure of possible optimal solutions, all possible steady states are first characterized and investigated analytically.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimization of order policies in supply networks

Göttlich

Herty

Ringhofer

2010

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to develop a model which allows for the study and optimization of arbitrarily complex supply networks, including order policies and money flows. We propose a mathematical description that captures the dynamic behavior of the system by a coupled system of ordinary differential delay equations. The underlying optimization problem is solved using discretization techniques yielding a mixed-integer programming problem.

show abstract

Section: Steady State Money Flowsmentioning

confidence: 99%

Section: Steady State Money Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimization of order policies in supply networks

Göttlich

Herty

Ringhofer

2010

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…Various optimization problems for traffic flow, based on the Lighthill-Whitham conservation law model, have been considered in [8,9,10,11]. For an introduction to differential games and for recent applications to traffic flow on networks we refer to [6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Nash equilibria for a model of traffic flow with several groups of drivers

Bressan

Han

2012

ESAIM: COCV

View full text Add to dashboard Cite

Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κ i drivers, sharing the same departure and arrival costs ϕ i (t), ψ i (t). For any given population sizes κ 1 , . . . , κ n , we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible nonuniqueness, and a characterization of this Nash equilibrium solution, are also discussed.

show abstract

“…Many applications can also be found in chemical engineering [6], such as chemical processes control [7], life cycle optimization for sustainable design [20] and production planning in multi-plant facilities [23]. Other applications include channel interference [11] and optimal resource management [39] in wireless networks, optimal path for vehicles [1,21], tra c modeling [18], conflict resolution involving multiple aircraft [37] and flight clearance [15].…”

mentioning

confidence: 99%

Guided dive for the spatial branch-and-bound

2017

View full text Add to dashboard Cite

We study the spatial Brand-and-Bound algorithm for the global optimization of nonlinear problems. In particular we are interested in a method to find quickly good feasible solutions. Most spatial Branch-and-Bound-based solvers use a non-global solver at a few nodes to try to find better incumbents. We show that it is possible to improve the branching rules and the node priority by exploiting the solutions from the non-global solver. We also propose several smart adaptive strategies to choose when to run the non-global solver. We show that despite the time spent in solving more NLP problems in the nodes, the new strategies enable the algorithm to find the first good incumbents faster and to prove the global optimality faster. Numerous easy, medium size as well as hard NLP instances from the Coconut library are benchmarked. All experiments are run using the open source solver Couenne.

show abstract

Combinatorial and Continuous Models for the Optimization of Traffic Flows on Networks

Cited by 46 publications

References 19 publications

Optimization of order policies in supply networks

Optimization of order policies in supply networks

Nash equilibria for a model of traffic flow with several groups of drivers

Guided dive for the spatial branch-and-bound

Contact Info

Product

Resources

About