Multi-objective Bi-level Programming Model Research Articles

Estimation of travel flux between urban blocks by combining spatio-temporal and purpose correlation

Understanding the travel flux between urban blocks is fundamental for traffic demand prediction, urban area planning and urban traffic management. However, the uncertainty of human mobility patterns and the complexity of urban transportation systems usually yield challenges in accurately estimating the travel flux within a city. Thus, we propose a novel travel flux estimation method that integrates traffic flow characteristics (traffic volume and travel time), spatio-temporal autocorrelation, and travel purpose correlation. First, the geographically weighted method was used to model and verify the spatio-temporal autocorrelation of origin–destination flows, whereas the purpose correlation of origin–destination flows was expressed through the function feature vectors of urban blocks. Then, a multi-objective bi-level programming model, according to the generalized least squares method, was constructed to estimate the travel flux between blocks. This was used to solve the problem of accurate estimation of travel flux by combining microscopic traffic flow characteristics with macroscopic spatio-temporal and purpose characteristics. Finally, an empirical analysis of the Hankou district, Wuhan City, demonstrated that in contrast to the existing method, the accuracy of the proposed method for predicting the human travel flux improved by approximately 20%. The estimated results were consistent with the spatial distribution pattern of human travel. Moreover, these results can provide targeted decision support for planning urban spaces, allocating urban resources, and guiding vehicular traffic.

Multiobjective bilevel programming model for multilayer perceptron neural networks

The architecture of multilayer perceptron (MLP) neural networks dictates the network's performance. However, aiming at the specific classification problems, suitable architectures of MLPs must be determined beforehand. More often, the design decisions rely on a trial and error learning and the experience knowledge. To automatically design an MLP's network architecture and optimize network parameters, a multiobjective bilevel programming model is built. In this model, a multiobjective optimization problem is constructed in the upper level for obtaining a set of Pareto optimal architectures of the MLPs, considering network complexity, training error rate, and validation error rate, while a single-objective optimization problem is established in the lower level to search for the optimum network parameters for a given network architecture. For dealing with this model efficiently, a novel multiobjective hierarchical learning algorithm (MOHLA) is proposed, in which an integer-coding NSGA-II is developed as the upper-level optimizer for a set of Pareto optimal network structures of the MLPs, while a non-iterative method is regarded as the lower-level solver for the MLPs' connection parameters. After a set of trained MLPs is obtained finally by using MOHLA, a selective ensemble strategy is adopted for improving identification accuracy. Three types of multiobjective bilevel programming models are investigated and compared in the experiments. Moreover, the proposed MOHLA is compared with several state-of-the-art learning approaches on various classification problems. The experimental results confirm that MOHLA performs well.

An inexact bi-level multi-objective modeling approach for managing agricultural water-food-carbon-land-ecology-nutrition nexus in an arid area

Multiple subsystems such as water, food, land, carbon, ecology, and nutrition are closely intertwined, and the resulting complexity and uncertainty pose challenges to water resource management. This study proposes an optimization framework from a novel water-food-carbon-land-ecology-nutrition (WONDER) nexus perspective for the integrated management of agricultural and ecological water resources. Firstly, the irrigation priority ranking of decision-making units (DMU) is obtained based on the remote sensing indices from the Google Earth Engine (GEE) platform. Secondly, the ecological satisfaction degree, which aggregates carbon sink satisfaction degree and ecological water demand satisfaction degree, is proposed to characterize the degree of achieving the pre-given ecological objectives. Then, the above two indicators (i.e., the irrigation priority ranking and the ecological satisfaction degree) are integrated with a fuzzy-interval credibility-constrained bi-level multi-objective programming model to realize: (1) reconciling conflicts in food nutrition, food security, economic development, and ecological conservation; (2) making trade-offs among the positions and preferences of different decision-makers; (3) dealing with the dual uncertainties of fuzzy-interval parameters; (4) obtaining optimal agricultural and ecological water allocation schemes. The applicability of the model is verified by taking Hongyashan Irrigation District of Minqin County as an example. The results show that: (1) the irrigation priority ranking for the DMUs is: DMU 10 > DMU 9 > DMU 4 > DMU 5 > DMU 1 > DMU 11 > DMU 6 > DMU 8 > DMU 7 > DMU 2 > DMU 3; (2) the ratio of agricultural to ecological water allocation in the irrigation district is about 3:1, which is consistent with the water use characteristics of this area; (3) the total water allocation during the whole growth period for different crops is mainly determined by planting area, and the ranking of the water allocation is: sunflower > maize > wheat > seed melon. Moreover, compared with the single-level models, the inexact bi-level multi-objective model can well coordinate the upper and lower decision-makers and the multiple decision objectives under the WONDER nexus. Therefore, the proposed framework can provide the scientific basis for balancing agricultural and ecological water management and conflicting objectives in similar irrigation districts through involving multiple subsystems and perspectives.

Multi-objective optimization of cordon sanitaire considering operation cost and queueing equity

ABSTRACT This paper aims topropose a method to determine the optimal deployment of cordon sanitaire for epidemic control. A bi-level multi-objective programming model is proposed where the lower level is transportation system equilibrium with queueing time to predict link traffic flow, and the upper level is queueing network design, which is a multi-objective integer nonlinear programming model. The primary objective is to minimize the total operation cost of servers with a predetermined waiting time constraint, and the secondary objective is to reach queueing equity. A heuristic algorithm is designed where the method of successive averages is adopted for the lower-level model, and a genetic algorithm is designed for the upper-level model. The computational results show that the methods can find a good heuristic optimal solution. These methods are useful for planners to determine the optimal deployment of cordon sanitaire for disease control and prevention purposes.

Optimizing water allocation in an inter-basin water diversion project with equity-efficiency tradeoff: A bi-level multiobjective programming model under uncertainty

Achieving optimal water allocation in an inter-basin water diversion project is a challenge that involves multilevel stakeholders, and the uncertainty and disequilibrium of water allocation further intensify competition among different stakeholders. This study proposes a bi-level multiobjective programming model for water allocation in inter-basin water diversions that considers equilibrium sustainability. The model integrates interval parameter programming, fuzzy credibility-constrained programming, bi-level multiobjective programming, and the Gini coefficient into a general framework. The model not only balances the stakeholders at different levels to ensure water allocation equity but also comprehensively considers the fuzzy uncertainty of parameters and constraints to obtain the interrelationship among water diversion, water allocation satisfaction, and efficiency objectives. The developed model was applied to allocate water for the Hanjiang-to-Weihe Water Diversion Project in Shaanxi Province, China. The results showed that 1) the model derived a feasible tradeoff between upper basin manager and lower regional managers under different water diversion scenarios; 2) water allocations and objectives at each level are sensitive to changes in the credibility of water diversion; 3) the new model improves the equity of water allocation and ensures the efficient allocation to various stakeholders at each level based on a comparison of the proposed model with a model that does not consider equilibrium. The proposed model can help decision makers choose the optimal scheme based on their acceptable risk level to achieve a more efficient and sustainable water allocation for inter-basin water diversions.

A bi-level multi-objective programming model for water resources management under compound uncertainties in Dongjiang River Basin, Greater Bay Area of China

To facilitate regional water resources allocation, an integrated bi-level multi-objective programming (IBMP) model with dual random fuzzy variables was developed in this research The proposed model was derived through incorporating dual random fuzzy variables, multi-objective programming, and interval parameter programming within a bi-level optimization framework. This approach improved upon the previous bi-level programming methods and had two advantages. Firstly, it was capable of reflecting tradeoffs among multiple conflict preferences for water related bi-level hierarchical decision-making processes. Secondly, random fuzzy variables were used to tackle the dual uncertainties in both sides of the constraints, which were characterize as probability density functions and discrete intervals. Then, a real-world water resources planning problem was employed for illustrating feasibility of the application of IBMP model in Dongjiang river watershed of south China. Results reflected the alternative decisions for water allocation schemes under a set of probability levels and fuzzy α - cut levels, which can support in-depth analysis of tradeoffs among multiple levels and objective values. Moreover, modeling comparison analysis was undertaken to illustrate the performances of the proposed model.

Location planning of electric vehicle charging station with users’ preferences and waiting time: multi-objective bi-level programming model and HNSGA-II algorithm

Interactive users’ preferences and waiting time together have great impact on charging station network design of electric vehicles (EVs), but only waiting time was considered in previous studies. To fill this research gap, this paper addresses a location planning problem for EV charging stations, which considers users’ preferences and waiting time simultaneously. The problem is formulated as a multi-objective bi-level programming model, the upper level model determines locations and capacity options of charging stations with the objectives of minimising total cost and minimising total service tardiness, and the lower level model determines the allocation of users to stations with the objective of minimising total travel time. A hybrid non-dominated sorting genetic algorithm II (HNSGA-II) with embedded level determination algorithm (LDA) and a partial enumeration algorithm (PEA) are proposed, respectively, to solve the model. Furthermore, managerial analysis is implemented to verify the advantages of considering users’ preferences in reducing charging service tardiness and saving cost compared with the mode of no considering users’ preferences. And sensitivity analysis is also performed to provide managerial insights for EV charging station location practice. Finally, a real-world case study is conducted to verify the applicability of the proposed approach in solving practical location planning problems.

Optimal management of cultivated land coupling remote sensing-based expected irrigation water forecasting

This study proposed a novel cultivated land planning approach coupling expected irrigation water prediction and crop planting structure optimization. Under the guidance of the expected irrigation water prediction, the development of agricultural planting strategies was proposed through the cultivated land planning method to improve the efficiency of water use and ensure agricultural production. This approach was consisted of two models: a combination forecasting model was developed for estimating expected irrigation water with help of remote sensing data (RSCM); and a bi-level multiobjective programming model for planning crop planting structure (BMPSOM) was formulated for crop planting structure programming. Then, the proposed approach applied to a real-world case in Northwest China for verifying its validity. Results show that: 1) the forecast accuracy of the combination forecast model has been greatly improved compared to the single forecast model, the accuracy test results are RMSE = 0.25 × 108 m3, MAPE = 0.78%; 2) the use of remote sensing data can reflect the soil moisture with spatial variability in the forecast; 3) BMPSOM model can well reflect the leader-follower relationship and make tradeoff among multiple objectives of each decision maker in tackling practical problem. Application has proved that the agricultural planting strategy formulated by this approach can not only ensure economic benefits but also increase food production under limited water resources. Therefore, this method has good application prospects in areas where water resources are scarce.

Reliability-based equitable transit frequency design

Fairness is an important criterion for achieving sustainable urban development. While most existing studies focus on accessing or evaluating the fairness condition of a given transit network, this study explicitly incorporates fairness as an objective in the planning step. A multi-objective bilevel programming model is developed where the lower level problem is the reliability-based transit assignment problem and the upper level problem is to determine optimal frequency settings to simultaneously minimise the total effective travel cost and maximise the network fairness condition. A multi-objective Artificial Bee Colony algorithm is developed to solve the bilevel model. Numerical studies find that: (1) increasing the frequency may not improve the fairness condition; (2) there is a tradeoff between the two objectives (3) the effect of passengers’ risk aversion attitude on the fairness measurement depends on the frequency setting; it could either amplify the fairness measurements or have no impact.

Multiobjective Environmentally Sustainable Optimal Design of Dedicated Connected Autonomous Vehicle Lanes

The emergence of connected autonomous vehicles (CAVs) is not only improving the efficiency of transportation, but also providing new opportunities for the sustainable development of transportation. Taking advantage of the energy consumption of CAVs to promote the sustainable development of transportation has attracted extensive public attention in recent years. This paper develops a mathematical approach to investigating the problem of the optimal implementation of dedicated CAV lanes while simultaneously considering economic and environmental sustainability. Specifically, the problem is described as a multi-objective bi-level programming model, in which the upper level is to minimize the system-level costs including travel time costs, CAV lane construction cost, and emission cost, whereas the lower level characterizes the multi-class network equilibrium with a heterogeneous traffic stream consisting of both human-driven vehicle (HVs) and CAVs. To address the multi-objective dedicated CAV lane implement problem, we propose an integrated solution framework that integrates a non-dominated sorting genetic algorithm II (NSGA-II) algorithm, diagonalized algorithm, and Frank–Wolfe algorithm. The NSGA-II was adopted to solve the upper-level model, i.e., hunting for the optimal CAV lanes implementation schemes. The diagonalized Frank–Wolfe (DFW) algorithm is used to cope with multi-class network equilibrium. Finally, numerical experiments were conducted to demonstrate the effectiveness of the proposed model and solution method. The experimental results show that the total travel time cost, total emission cost, and total energy consumption were decreased by about 12.03%, 10.42%, and 9.4%, respectively, in the Nguyen–Dupuis network as a result of implementing the dedicated CAV lanes.

A Bi-Level Multi-Objective Optimization Model for Micro-Circulation Road Networks in the Open Block Area Considering Traffic Pollution and Intersection Delays

It is important for urban traffic micro-circulation to improve the density of urban branch road networks by opening roads inside blocks. To reasonably optimize the micro-circulation road network in the open block area, a bi-level multi-objective programming model that considers traffic pollution and intersection delays was developed. In this paper, the goals of minimizing traffic pollution and total travel cost are added to the upper-level programming model and the user equilibrium assignment model with the consideration of intersection delay was presented as the lower-level programming model. A modified genetic algorithm (GA) embedded with the Frank-Wolfe algorithm was designed to solve the established model. The traffic conditions of arterial roads and micro-circulation branch roads before and after optimizing the micro-circulation block road network were compared and analyzed by a numerical example. The results demonstrated that the bi-level programming model can effectively determine the traffic direction of branch roads and the forbidden situation of intersections in the micro-circulation network. Compared with the closed block, the average saturation of the main trunk road decreased from 0.97 to 0.83 with a decline ratio of 14.43% after optimizing the micro-circulation network in the open block area; the average saturation of the secondary trunk road decreased from 0.86 to 0.77, with a decline ratio of 10.47%. The travel time cost decreased by approximately 6.55%, and the traffic pollution decreased by approximately 3.40%, which verified the optimization effect of the model and the algorithm.

Research on Logistics Distribution Route Based on Multi-objective Sorting Genetic Algorithm

With the continuous development of society, the social division of labor is further improved, and social production tends to be highly specialized and industrialized. Moreover, enterprise production is increasingly internationalized, and sales are gradually expanding. Therefore, the multi-objective sequencing in logistics distribution is incorporated into the path optimization of the logistics system, and a multi-objective bi-level programming model of time and cost is established. What is more, considering the limitations of the traditional algorithm in solving multi-objective problems, the low-dimensional multi-objective problem is selected, and according to the actual situation, the inheritance strategy of genetic factors is adopted to solve the more targeted rapid dominating sorting genetic problem. Besides, the specific conditions and characteristics of the model determine the encoding method, which is brought into the operation of the cross-mutation law and the interruption of individual populations, so that the building foundation of the model is improved. Based on the further theoretical research on the distribution efficiency of logistics system, the corresponding mathematical model is constructed by using the planning method, and the single cost target is transformed into the time and cost double objective, and the improved fast non dominated sorting genetic algorithm with elite strategy is used to solve the problem, which has certain theoretical innovation. Through simulation, the optimal or near optimal path of distribution vehicles in a certain area is given, which has certain practicality and reference value for the optimization of actual logistics distribution path.

Authority–enterprise equilibrium based mixed subsidy mechanism for carbon reduction and energy utilization in the coalbed methane industry

As coalbed methane, the natural gas adsorbed in coal seams, is a greenhouse gas that is 21 times stronger than CO2, coalbed methane extraction significantly influences carbon reduction and energy conservation efforts. While the injection of CO2 into coal seams is known to effectively enhance coalbed methane recovery, this process has been limited because of high investment and production costs. Therefore, to promote the application of CO2 injection techniques in coalbed methane industry, this paper proposes an authority–enterprise equilibrium based mixed subsidy mechanism which combines direct subsidies with indirect tax-incentives. Specifically, a multi-objective bi-level programming model is established under uncertainty to assign a practical constraint and achieve a trade-off between the local authority and the coalbed methane plants. A practical case validates the feasibility and efficiency of the proposed method, proving that an authority–enterprise equilibrium based mixed subsidy mechanism is able to achieve carbon emissions reductions and conserve energy. Further analysis indicated that the marginal energy efficiency gains were greater than the authority costs under a strict energy utilization policy and that the environmental protection target had larger impacts on the coalbed methane plant performances.

Carbon emissions market adjustment in the electricity supply sector: A government perspective

The atmospheric warming associated with anthropogenic climate change can be mitigated by pricing carbon emissions and especially through carbon emissions trading schemes (ETS). To this end, a multi-objective bi-level programming model that considers the mutual interactions between the government and power projects is developed to determine an appropriate carbon price to achieve carbon intensity minimization and revenue maximization. Goal programming is employed for the multi-objective programming and an interactive particle swarm optimization and simplex method (IPSO-SM) mechanism is developed to solve the proposed model, the effectiveness of which is verified in a real-life case study. The results suggest that the government can adjust carbon emissions market by auctioning or repurchasing carbon allowances to achieve a balance between environmental protection and economic development, and that the carbon trading decisions of the power projects depended on the comparison of the carbon shadow prices and market carbon price, which constituted the bidding mechanism, formed the carbon price supply and demand curve, and ultimately determined the carbon price.

Bilevel Optimization for the Hazmat Transportation Problem with Lane Reservation

In this study, we investigate a bilevel optimization model for the hazmat transportation problem with lane reservation. The problem lies in selecting lanes to be reserved in the network and planning paths for hazmat transportation tasks. The trade-off among transportation cost, risk, and impact on the normal traffic is considered. By using the traffic flow theory, we quantify the impact on the normal traffic and modify the traditional risk measurement model. The problem is formulated as a multiobjective bilevel programming model involving the selection of reserved lanes for government and planning paths for hazmat carriers. Two hybrid metaheuristic algorithms based on the particle swarm optimization algorithm and the genetic algorithm, respectively, are proposed to solve the bilevel model. Their performance on small-scale instances is compared with exact solutions based on the enumeration method. Finally, the computational results on large-scale instances are compared and sensitivity analysis on the key parameters is presented. The results indicate the following: (1) Both algorithms are effective methods for solving this problem, and the method based on the particle swarm optimization algorithm requires a shorter computation time, whereas the method based on the genetic algorithm shows more advantages in optimality. (2) The bilevel model can effectively reduce the total risk of the hazmat transportation while considering the interests of hazmat carriers and ordinary travellers. (3) The utilization rate of reserved lanes increases with an increasing number of tasks. Nevertheless, once the proportion of hazmat vehicles becomes excessive, the advantage of reducing the risk of the reserved lanes gradually decreases.

Collaborative Optimization of Vehicle and Charging Scheduling for a Bus Fleet Mixed With Electric and Traditional Buses

To address sustainable development issues of urban traffic, electric buses will join traditional bus system, and the scheduling of bus fleet should be adjusted due to the distinct features of electric buses. To this end, this paper develops a Multi-objective Bi-level programming model to collaboratively optimize the vehicle scheduling and charging scheduling of the mixed bus fleet under the operating conditions of a single depot. The upper level determines the vehicle scheduling to minimize the operating cost and carbon emissions under the constraints of connecting time between trips and the limited driving range of electric buses. The lower level is a charging scheduling problem that considers the charging time and the limited driving distance constraint to minimize the charging cost. The proposed model is solved with an integrated heuristic algorithm. The vehicle scheduling problem is addressed with the iterative neighborhood search algorithm based on simulated annealing, while the charging scheduling problem is solved with a greedy dynamic selection strategy based on the approach of multi-stage decision. Finally, case study is carried out based on a mixed bus fleet in Beijing, and the results validate the availability of the proposed model and solution algorithm.

A Multiobjective Bilevel Programming Model for Environmentally Friendly Traffic Signal Timings

Rapid urbanization and mobility needs of road users increase traffic congestion and delay on urban road networks. Thus, local authorities aim to reduce users’ total travel time through providing a balance between traffic volume and capacity. To do this, they optimize traffic signal timings, which is one of the most preferred methods, and thus they can increase the reserve capacity of a road network. However, more travel demand along with more reserve capacity leads to vehicle emissions problem which has become quite dangerous for road users, especially in developing countries. Therefore, this study presents a multiobjective bilevel programming model which considers both the maximization of reserve capacity of a road network and the minimization of vehicle emissions by aiming to achieve environmentally friendly signal timings. At the upper level, Pareto-optimal solutions of the proposed multiobjective model are found based on differential evolution algorithm framework by using the weighted sum method. Stochastic traffic assignment problem is presented at the lower level to evaluate the users’ reactions. Two signalized road networks are chosen to show the effectiveness of the proposed model. The first one is a small network consisting two signalized intersections that are used to show the effect of the weighting factor on the proposed multiobjective model. The other road network with 96 O-D pairs and 9 signalized intersections is chosen as the second numerical application to investigate the performance of the proposed model on relatively large road networks. It is believed that results of this study may provide useful insights to local authorities who are responsible for regulating traffic operations with environmental awareness at the same time.

Research on the Allocation of Flood Drainage Rights of the Sunan Canal Based on a Bi-level Multi-Objective Programming Model

To reduce flood disasters and optimize of the comprehensive benefit of the water basin, the allocation of regional flood drainage rights is of great significance. Using the “top-down” allocation mode, we consider the influence of the social, economic, and ecological environments, flood drainage demand and efficiency, and other factors on the allocation of flood drainage rights. A bi-level multi-objective programming model from the perspective of fairness and efficiency is established for the allocation. The Sunan Canal is taken as a typical case study. The model is solved by the multi-objective optimal allocation method and the master–slave hierarchical interactive iteration algorithm. After three iterations of the initial solution, the allocation of flood drainage rights in six flood control regions finally reach an effective state. The results of the model were compared with results based on historical allocation principles, showing that the bi-level multi-objective programming model, based on the principles of fairness and efficiency, is more in line with the current social and economic development of the canal. In view of the institutional background of water resources management in China and the flood drainage pressure faced by various regions, the allocation of flood drainage rights should be comprehensively considered in combination with various factors, and the market mechanism should be utilized to optimize the allocation.

A simulation-based bi-level multi-objective programming model for watershed water quality management under interval and stochastic uncertainties.

A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, interval parameter programming and stochastic chance-constrained programming into a general bi-level multi-objective programming framework. The SISBLMOP model can handle multiple uncertainties expressed as discrete intervals and probability density functions in both the simulation and optimization processes. System complexities, including the hierarchy structure of upper- and lower-level decision makers, can also be addressed in the model. The proposed model is applied to a real-world case study of the Xinfengjiang Reservoir Watershed in South China to identify the satisfactory implementation levels of multiple best management practices (BMPs). The model results show that multiple BMP schemes for water quality management can be obtained under different upper- and lower-level decision-making and risk-violation scenarios, reflecting the cooperation and gaming results of the two-level decision makers. Consequently, the corresponding BMP implementation costs are acceptable to both the upper- and lower-level decision makers. The model is widely applicable and can be effectively used for water quality management under multiple uncertainties and complexities.

Recycling-equilibrium strategy for phosphogypsum pollution control in phosphate fertilizer plants

Excessive phosphogypsum waste has caused significant environmental contamination and has consequently become a serious threat to sustainable socio-economic development. This paper proposes a recycling-equilibrium strategy from a regional policy perspective that integrates circular economic theory and modeling techniques to resolve phosphogypsum-related pollution problems. Specifically, three typical conflicts are analyzed to describe the problem complexity, and a multi-objective bi-level programming model is formulated under uncertainty for the assignment of practical disposal limits to achieve a compromise agreement between the multiple decision makers. A solution approach that employs fuzzy theory, an acceptable reduction target, and Karush-Kuhn-Tucker conditions is developed to identify the optimum phosphogypsum stack allowance allocation mechanism for regional authorities and an optimal purchase-transportation plan for the phosphate fertilizer plants. The results from the practical case validated the feasibility and efficiency of the formulated method and proved that a recycling-equilibrium strategy based stack allowance allocation mechanism could successfully achieve phosphogypsum pollution mitigation. The practical application findings were: (1) different phosphate fertilizer plants have different sensitivities towards changing stack reduction targets; (2) local authority revenue and phosphogypsum stack quantities are mainly impacted by environmental protection targets; (3) allocating larger stack allowances to phosphate fertilizer plants with smaller emissions coefficients can realize better phosphogypsum reduction.