Multi-Objective Pricing Optimization for a High-Speed Rail Network Under Competition

2019 ◽  
Vol 2673 (7) ◽  
pp. 215-226 ◽  
Author(s):  
Huizhuo Cao ◽  
Xuemei Li ◽  
Vikrant Vaze ◽  
Xueyan Li
Keyword(s):  
High Speed ◽  
Programming Model ◽  
Pareto Frontier ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
High Speed Rail ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Single Objective

Multi-objective pricing of high-speed rail (HSR) passenger fares becomes a challenge when the HSR operator needs to deal with multiple conflicting objectives. Although many studies have tackled the challenge of calculating the optimal fares over railway networks, none of them focused on characterizing the trade-offs between multiple objectives under multi-modal competition. We formulate the multi-objective HSR fare optimization problem over a linear network by introducing the epsilon-constraint method within a bi-level programming model and develop an iterative algorithm to solve this model. This is the first HSR pricing study to use an epsilon-constraint methodology. We obtain two single-objective solutions and four multi-objective solutions and compare them on a variety of metrics. We also derive the Pareto frontier between the objectives of profit and passenger welfare to enable the operator to choose the best trade-off. Our results based on computational experiments with Beijing–Shanghai regional network provide several new insights. First, we find that small changes in fares can lead to a significant improvement in passenger welfare with no reduction in profitability under multi-objective optimization. Second, multi-objective optimization solutions show considerable improvements over the single-objective optimization solutions. Third, Pareto frontier enables decision-makers to make more informed decisions about choosing the best trade-offs. Overall, the explicit modeling of multiple objectives leads to better pricing solutions, which have the potential to guide pricing decisions for the HSR operators.

scholarly journals Comparative Study of Knee-Based Algorithms for Many-Objective Optimization Problems

2018 ◽  
Vol 12 (1) ◽  
pp. 7-16
Author(s):  
Saad M. Alzahrani ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Knee Region ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Small Set ◽  
Optimum Solution

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.

Collective intelligence approaches in interactive evolutionary multi-objective optimization

2020 ◽  
Vol 28 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Daniel Cinalli ◽  
Luis Martí ◽  
Nayat Sanchez-Pi ◽  
Ana Cristina Bicharra Garcia
Keyword(s):  
Collective Intelligence ◽  
Real Life ◽  
Decision Makers ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Trade Offs ◽  
Life Problems ◽  
Conflicting Objectives ◽  
Optimal Set

Abstract Evolutionary multi-objective optimization algorithms (EMOAs) have been successfully applied in many real-life problems. EMOAs approximate the set of trade-offs between multiple conflicting objectives, known as the Pareto optimal set. Reference point approaches can alleviate the optimization process by highlighting relevant areas of the Pareto set and support the decision makers to take the more confident evaluation. One important drawback of this approaches is that they require an in-depth knowledge of the problem being solved in order to function correctly. Collective intelligence has been put forward as an alternative to deal with situations like these. This paper extends some well-known EMOAs to incorporate collective preferences and interactive techniques. Similarly, two new preference-based multi-objective optimization performance indicators are introduced in order to analyze the results produced by the proposed algorithms in the comparative experiments carried out.

Evolutionary Multi-Objective Optimization for Assignment Problems

2011 ◽  
pp. 364-387
Author(s):  
Mark P. Kleeman ◽  
Gary B. Lamont
Keyword(s):  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Assignment Problems ◽  
Multi Objective ◽  
Advantages And Disadvantages ◽  
Single Objective

Assignment problems are used throughout many research disciplines. Most assignment problems in the literature have focused on solving a single objective. This chapter focuses on assignment problems that have multiple objectives that need to be satisfied. In particular, this chapter looks at how multi-objective evolutionary algorithms have been used to solve some of these problems. Additionally, this chapter examines many of the operators that have been utilized to solve assignment problems and discusses some of the advantages and disadvantages of using specific operators.

scholarly journals Sen's Multi Objective Optimization (MOO) Technique-An Extension

2020 ◽  
Vol 06 (09) ◽  
pp. 77-79
Author(s):  
Chandra Sen
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

Linear programming has been very popular for achieving (maximizing or minimizing) a single objective with certain constraints. However, when objectives are more than one, linear programming becomes inefficient. Sen's multi-objective optimization (MOO) technique [1] is efficient in achieving multiple objectives simultaneously. Few modifications in Sen's MOO technique are proposed for improving its applicability for solving multi-objective optimization problems.

scholarly journals Sustainable Water Resources Management in an Arid Area Using a Coupled Optimization-Simulation Modeling

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 885 ◽  
Author(s):  
Siamak Farrokhzadeh ◽  
Seyed Hashemi Monfared ◽  
Gholamreza Azizyan ◽  
Ali Sardar Shahraki ◽  
Maurits Ertsen ◽  
...  
Keyword(s):  
Ecosystem Services ◽  
Water Resources ◽  
Environmental Data ◽  
Multi Objective Optimization ◽  
Wetland Ecosystems ◽  
Multi Objective ◽  
Sustainable Water Resources Management ◽  
Trade Offs ◽  
Conflicting Demands ◽  
Conflicting Objectives

Severe water scarcity in recent years has magnified the economic, social, and environmental significance of water stress globally, making optimal planning in water resources necessary for sustainable socio-economic development. One of the regions that is most affected by this is the Sistan region and its Hamoun wetland, located in south-east Iran. Water policies are essential to sustain current basin ecosystem services, maintaining a balance between conflicting demands from agriculture and the protection of wetland ecosystems. In the present study, a multi-objective optimization model is linked with the Water Evaluation and Planning (WEAP) software to optimize water allocation decisions over multiple years. We formulate and parameterize a multi-objective optimization problem where the net economic benefit from agriculture and the supply of environmental requirements were maximized, to analyze the trade-off between different stakeholders. This problem is modeled and solved for the study area with detailed agricultural, socio-economic, and environmental data for 30 years and quantification of ecosystem services. By plotting Pareto sets, we investigate the trade-offs between the two conflicting objectives and evaluate a possible compromise. The results are analyzed by comparing purely economic versus multi-objective scenarios on the Pareto front. Finally, the disadvantages and advantages of these scenarios are also qualitatively described to help the decision process for water resources managers.

scholarly journals Modelling Diversity of Solutions

2020 ◽  
Vol 34 (02) ◽  
pp. 1528-1535
Author(s):  
Linnea Ingmar ◽  
Maria Garcia de la Banda ◽  
Peter J. Stuckey ◽  
Guido Tack
Keyword(s):  
General Framework ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Solution ◽  
Single Objective

For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimization problems, as they have no single “best solution” and, thus, it is useful to find a representation of the non-dominated solutions (the Pareto frontier). However, it also applies to single objective optimization problems, where one may be interested in finding several (close to) optimal solutions that illustrate some form of diversity. The same applies to satisfaction problems. This is because models usually idealize the problem in some way, and a diverse pool of solutions may provide a better choice with respect to considerations that are omitted or simplified in the model. This paper describes a general framework for finding k diverse solutions to a combinatorial problem (be it satisfaction, single-objective or multi-objective), various approaches to solve problems in the framework, their implementations, and an experimental evaluation of their practicality.

Rational Design of Vehicles: I — Multi-Objective Optimization

2001 ◽  
Author(s):  
David M. Paulus ◽  
Richard A. Gaggioli
Keyword(s):  
Objective Function ◽  
Fuel Economy ◽  
Rational Design ◽  
Multiple Objectives ◽  
Relative Importance ◽  
Multi Objective Optimization ◽  
Straightforward Manner ◽  
Multi Objective ◽  
Single Objective

Abstract The customer for a vehicle typically has several desiderata, such as top speed, fuel economy, range, acceleration, .... Generally, these desiderata are conflicting. So, in order to deduce a single objective function, a means is needed for weighting (implicitly if not explicitly) the relative importance of these desiderata. That is, for weighting these “multiple objectives.” This paper presents a rational methodology for developing a single-objective function to be optimized during the design of a vehicle. The methodology does require answers from the customer(s) to a straightforward set of questions, referring to the desiderata. Based on the answers, the objective function follows, mathematically, in a straightforward manner. An application to a light, personal aircraft serves as a case study.

Robust ascent trajectory design and optimization of a typical launch vehicle

2018 ◽  
Vol 232 (24) ◽  
pp. 4601-4614 ◽  
Author(s):  
Jafar Roshanian ◽  
Ali A Bataleblu ◽  
Masoud Ebrahimi
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Launch Vehicle ◽  
Model Parameters ◽  
Trajectory Design ◽  
Nsga Ii ◽  
Trade Off ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Single Objective

Robustness and reliability of the designed trajectory are crucial for flight performance of launch vehicles. In this paper, robust trajectory design optimization of a typical LV is proposed. Two formulations of robust trajectory design optimization problem using single-objective and multi-objective optimization concept are presented. Both aleatory and epistemic uncertainties in model parameters and operational environment characteristics are incorporated in the problem, respectively. In order to uncertainty propagation and analysis, the improved Latin hypercube sampling is utilized. A comparison between robustness of the single-objective robust trajectory design optimization solution and deterministic design optimization solution is illustrated using probability density functions. The multi-objective robust trajectory design optimization is executed through NSGA-II and a set of feasible design points with a good spread is obtained in the form of Pareto frontier. The final Pareto frontier presents a trade-off between two conflicting objectives namely maximizing injection robustness and minimizing gross lift-off mass of launch vehicle. The resulted Pareto frontier of the multi-objective robust trajectory design optimization shows that with 1% increase in gross mass, the robustness of the design point to the considered uncertainties can be increased about 80%. Also, numerical simulation results show that the multi-objective formulation is a necessary approach to achieve a good trade-off between optimality and robustness.

Multi-Objective Optimal Control of Under-Actuated Bogie System of High Speed Trains

2016 ◽  
Author(s):  
Yousef Sardahi ◽  
Yuan Yao ◽  
Jian-Qiao Sun
Keyword(s):  
Feedback Control ◽  
High Speed ◽  
Dynamic Performance ◽  
State Feedback Control ◽  
Frobenius Norm ◽  
Feedback Controls ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
High Speed Trains

Feedback controls are important to the improvement of dynamic performance of high-speed trains. However, designing an active control for these vehicles is a very challenging task because the control system is usually under-actuated and has to meet multiple conflicting objectives. Examples of conflicting objectives include designing a highly relative stable system while minimizing the control efforts or maximizing the capability of the system to reject external disturbances. In addition, the mathematical models of these systems are not completely controllable and observable. This paper studies multi-objective optimal design of feedback controls for a sub-system of high-speed trains, i.e. the bogie system. The bogie system can be decomposed such that the observable and controllable components of the model are used to stabilize the internal states and therefore the overall system. A linear mathematical model of the system is used in the design. The controllable and the observable states of the model are separated to form a state-feedback control to drive the internal modes and the whole system to stability. A multi-objective genetic algorithm is used to search for the feedback control gains to optimize three objectives: the Frobenius norm of the control law, relative stability and the disturbance rejection. The solutions of the multi-objective optimization provide various trade-offs among the objectives. Numerical simulations show that the proposed control designs can stabilize the system even at a high critical speed of 500 km/h.

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