Multi-objective Bi-level Programming Model Research Articles

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.

Multi-Objective Bi-Level Programming for the Energy-Aware Integration of Flexible Job Shop Scheduling and Multi-Row Layout

The flexible job shop scheduling problem (FJSSP) and multi-row workshop layout problem (MRWLP) are two major focuses in sustainable manufacturing processes. There is a close interaction between them since the FJSSP provides the material handling information to guide the optimization of the MRWLP, and the layout scheme affects the effect of the scheduling scheme by the transportation time of jobs. However, in traditional methods, they are regarded as separate tasks performed sequentially, which ignores the interaction. Therefore, developing effective methods to deal with the multi-objective energy-aware integration of the FJSSP and MRWLP (MEIFM) problem in a sustainable manufacturing system is becoming more and more important. Based on the interaction between FJSSP and MRWLP, the MEIFM problem can be formulated as a multi-objective bi-level programming (MOBLP) model. The upper-level model for FJSSP is employed to minimize the makespan and total energy consumption, while the lower-level model for MRWLP is used to minimize the material handling quantity. Because the MEIFM problem is denoted as a mixed integer non-liner programming model, it is difficult to solve it using traditional methods. Thus, this paper proposes an improved multi-objective hierarchical genetic algorithm (IMHGA) to solve this model. Finally, the effectiveness of the method is verified through comparative experiments.

A de-centralized bi-level multi-objective model for integrated production and transportation problems in closed-loop supply chain networks

ABSTRACTThe increase in the development of proper channels for recycling and disposal of the manufactured products have motivated the study of closed loop supply chains. The closed loop supply chain networks can be considered as a strong tool for attaining the goals of sustainable development. The customers are not the terminating destination for the products in closed loop supply chain networks. However, after some recycling or refurbishing processes the product once again enters the supply chain networks. The involvement of forward and reverse flow of the products makes the closed loop supply chain networks very complex. As, there may be several conflicting objectives related to the closed loop supply chains, in this paper, we have proposed a bi-level multi-objective programming model for these networks. Bi-level programming problems deal with the situations where decisions are to be taken at two different hierarchical levels. We have considered three objective functions which are distributed among these two levels in such a manner that the decision makers solves for a single objective at each level. A solution procedure is also discussed for solving the proposed model.

An export coefficient based inexact fuzzy bi-level multi-objective programming model for the management of agricultural nonpoint source pollution under uncertainty

In this research, an export coefficient based inexact fuzzy bi-level multi-objective programming (EC-IFBLMOP) model was developed through integrating export coefficient model (ECM), interval parameter programming (IPP) and fuzzy parameter programming (FPP) within a bi-level multi-objective programming framework. The proposed EC-IFBLMOP model can effectively deal with the multiple uncertainties expressed as discrete intervals and fuzzy membership functions. Also, the complexities in agricultural systems, such as the cooperation and gaming relationship between the decision makers at different levels, can be fully considered in the model. The developed model was then applied to identify the optimal land use patterns and BMP implementing levels for agricultural nonpoint source (NPS) pollution management in a subcatchment in the upper stream watershed of the Miyun Reservoir in north China. The results of the model showed that the desired optimal land use patterns and implementing levels of best management of practices (BMPs) would be obtained. It is the gaming result between the upper- and lower-level decision makers, when the allowable discharge amounts of NPS pollutants were limited. Moreover, results corresponding to different decision scenarios could provide a set of decision alternatives for the upper- and lower-level decision makers to identify the most appropriate management strategy. The model has a good applicability and can be effectively utilized for agricultural NPS pollution management.

A multi-objective model for cordon-based congestion pricing schemes with nonlinear distance tolls

Congestion pricing is an important component of urban intelligent transport system. The efficiency, equity and the environmental impacts associated with road pricing schemes are key issues that should be considered before such schemes are implemented. This paper focuses on the cordon-based pricing with distance tolls, where the tolls are determined by a nonlinear function of a vehicles’ travel distance within a cordon, termed as toll charge function. The optimal tolls can give rise to: 1) higher total social benefits, 2) better levels of equity, and 3) reduced environmental impacts (e.g., less emission). Firstly, a deterministic equilibrium (DUE) model with elastic demand is presented to evaluate any given toll charge function. The distance tolls are non-additive, thus a modified path-based gradient projection algorithm is developed to solve the DUE model. Then, to quantitatively measure the equity level of each toll charge function, the Gini coefficient is adopted to measure the equity level of the flows in the entire transport network based on equilibrium flows. The total emission level is used to reflect the impacts of distance tolls on the environment. With these two indexes/measurements for the efficiency, equity and environmental issues as well as the DUE model, a multi-objective bi-level programming model is then developed to determine optimal distance tolls. The multi-objective model is converted to a single level model using the goal programming. A genetic algorithm (GA) is adopted to determine solutions. Finally, a numerical example is presented to verify the methodology.

Integrating Equality and Stability to Resolve Water Allocation Issues with a Multiobjective Bilevel Programming Model

AbstractWith rapid economic and social development, increasing water demands have made water scarcity a worldwide issue. Equitable, stable, and efficient water allocation, which includes water resources management and conflicting water demand management, needs a valid resolution. This paper develops a multiobjective bilevel model with the upper level reflecting the river basin authority’s allocation principle of equity and stability and the lower level aimed at ensuring maximal economic benefit effiency for each subarea. The Gini coefficient is introduced to seek equity in the water allocation strategies, a power index is applied to ensure stability in the water allocation solutions, and an economic efficiency function is designed to maximize the economic benefit efficiency in each subarea. The proposed multiobjective bilevel water allocation model is then applied to a case study in Qujiang River Basin in China, and demonstrates that the proposed model provides reasonable and practical water allocation st...

Administrative and market-based allocation mechanism for regional water resources planning

The aim of this paper is to present an administrative and market-based optimization method for solving a problem of regional water resources allocation by considering a hierarchical structure under multiple uncertainties. To accomplish this, a multi-objective bi-level programming model is developed based on the water right distribution in a river basin. In this model, the stream flow (i.e., water supply) and water demand are considered as a fuzzy random variable and a random fuzzy variable, respectively. The regional authority, the leader in the hierarchy, seeks to maximize the total benefit to society while simultaneously minimizing pollution emissions. The sub-areas, the followers in the hierarchy, seek to maximize their own economic benefits. To deal with the inherent uncertainty, a transformation of variables into fuzzy variables is done, and through the expected value operation, the fuzzy variables are subsequently transformed into determined ones. For solving the complex non-linear bi-level programming model, a bi-level interactive method based on satisfactory solution with global–local–neighbor adaptive particle swarm optimization (GLN-aPSO) is designed as a combined solution method. A case study is presented to demonstrate the applicability and efficiency of this method. The interactive solutions associated with different minimal satisfactory degrees of the two objectives in the upper level have been generated. They can help the regional authority and the sub-areas to identify desired water allocation schemes according to their preferences and practical conditions, as well as facilitate in-depth analyses of tradeoffs between the objectives in the two levels. Finally, to verify that it is reasonable to use bi-level programming the results are compared with those of using single level programming.

Multidemand Multisource Order Quantity Allocation with Multiple Transportation Alternatives

This paper focuses on a multidemand multisource order quantity allocation problem with multiple transportation alternatives. To solve this problem, a bilevel multiobjective programming model under a mixed uncertain environment is proposed. Two levels of decision makers are considered in the model. On the upper level, the purchaser aims to allocate order quantity to multiple suppliers for each demand node with the consideration of three objectives: total purchase cost minimization, total delay risk minimization, and total defect risk minimization. On the lower level, each supplier attempts to optimize the transportation alternatives with total transportation and penalty costs minimization as the objective. In contrast to prior studies, considering the information asymmetry in the bilevel decision, random and fuzzy random variables are used to model uncertain parameters of the construction company and the suppliers. To solve the bilevel model, a solution method based on Kuhn-Tucker conditions, sectional genetic algorithm, and fuzzy random simulation is proposed. Finally, the applicability of the proposed model and algorithm is evaluated through a practical case from a large scale construction project. The results show that the proposed model and algorithm are efficient in dealing with practical order quantity allocation problems.

Retrofitting Transportation Network Using a Fuzzy Random Multiobjective Bilevel Model to Hedge against Seismic Risk

This paper focuses on the problem of hedging against seismic risk through the retrofit of transportation systems in large-scale construction projects (LSCP). A fuzzy random multiobjective bilevel programming model is formulated with the objectives of the retrofit costs and the benefits on two separate levels. After establishing the model, a fuzzy random variable transformation approach and fuzzy variable approximation decomposition are used to deal with the uncertainty. An approximation decomposition-based multi-objective AGLNPSO is developed to solve the model. The results of a case study validate the efficiency of the proposed approach.

A new multi-objective bi-level programming model for energy and locality aware multi-job scheduling in cloud computing

How to reduce power consumption of data centers has received worldwide attention. By combining the energy-aware data placement policy and locality-aware multi-job scheduling scheme, we propose a new multi-objective bi-level programming model based on MapReduce to improve the energy efficiency of servers. First, the variation of energy consumption with the performance of servers is taken into account; second, data locality can be adjusted dynamically according to current network state; last but not least, considering that task-scheduling strategies depend directly on data placement policies, we formulate the problem as an integer bi-level programming model. In order to solve the model efficiently, specific-design encoding and decoding methods are introduced. Based on these, a new effective multi-objective genetic algorithm based on MOEA/D is proposed. As there are usually tens of thousands of tasks to be scheduled in the cloud, this is a large-scale optimization problem and a local search operator is designed to accelerate convergent speed of the proposed algorithm. Finally, numerical experiments indicate the effectiveness of the proposed model and algorithm.

Control Risk for Multimode Resource-Constrained Project Scheduling Problems under Hybrid Uncertainty

AbstractRisk control in project management has been receiving increasing attention in recent years. This paper proposes an approach based on a risk-assessment program and demonstrates how this can be extended to enhance the multimode resource-constrained project-scheduling problem (MRCPSP) to realize risk control and effective scheduling. The main contribution of this paper is to provide a means to control scheduling and material-purchasing risks by using a bilevel decision framework to identify risk and conduct a focused evaluation. Specifically, this paper establishes a hybrid uncertain multiobjective bilevel programming model and introduces an expected-value operator to deal with the hybrid uncertainty. A multiswarm differential-updating particle swarm optimization is developed to support the model calculations. Worthiness and efficiency of the proposed approach is validated using a case study. This approach can help improve scheduling strategies and ensure realistic project-planning.

Using Bi-level Multi-Objective Programming in Passenger Structure Optimization for Comprehensive Transportation Channel

The economic structure is the lifeblood of national economic development. Passenger structure within comprehensive transportation channel (CTC) is the key to play a higher efficiency and to operate normally of an integrated transport system. This paper analyzes the ideas of PTS optimization within CTC using bi-level planning strategies. And then a bi-level multi-objective programming model is established in this paper, in which the upper level takes the builders and government’s concern into account, such as system efficiency, transport capacity, capital investment. The lower level is a network equilibrium model based on a generalized cost function, while Channel saturation entropy index is introduced in the response function. A particle swarm optimization algorithm is designed to efficiently solve this NP-hard model. Finally, numerical implementations based on Beijing-Shanghai Channel are carried out to account for the performance of our model and algorithm.

Modeling and Simulation of Bus Priority Oriented Urban Road Network Elastic Equilibrium

As the poor applicability of rail transit and elevated road limited by economy, population and many other factors, the waste of road resources caused by bus lane, maximizing application of available road resources and bus facilities, reducing the environmental pollution is the critical issue faced by current situation of urban transportation development in China. Guided by Bus Priority Oriented, utilized comprehensive techniques, such as ABC classification, bi-level programming model, sensitivity analysis, this paper constructed a theoretical frame of elastic equilibrium based on system optimization. Taking time and environment as optimized objectives, This paper established the Bi-Level multiobjective programming model based on travel time, and programmed with MATLAB for the calculation. Finally, the case study is illustrated. the software VISSIM was adopted to realize the simulation of the volume before and after the implementation of elastic plan in urban areas of PingDingshan. The simulation results showed the validity and feasibility of the modeling and simulation of Bus Priority Oriented urban road network elastic equilibrium.

A Nonlinear Multiobjective Bilevel Model for Minimum Cost Network Flow Problem in a Large‐Scale Construction Project

The aim of this study is to deal with a minimum cost network flow problem (MCNFP) in a large‐scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO) developed to solve the model. The Shuibuya Hydropower Project is used as a real‐world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.

A FUZZY MULTI-OBJECTIVE BILEVEL DECISION SUPPORT SYSTEM

In a bilevel decision problem, both the leader and the follower may have multiple objectives, and the coefficients involved in these objective functions or constraints may be described by some uncertain values. To express such a situation, a fuzzy multi-objective bilevel (FMOBL) programming model and related solution methods are introduced. This research develops a FMOBL decision support system through implementing the proposed FMOBL methods.

Decentralized multi-objective bilevel decision making with fuzzy demands

Decisions in a decentralized organization often involve two levels. The leader at the upper level attempts to optimize his/her objective but is affected by the follower; the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. When model a real-world bilevel decision problem, it also may involve fuzzy demands which appear either in the parameters of objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously in achieving a solution. This study addresses both fuzzy demands and multi-objective issues and propose a fuzzy multi-objective bilevel programming model. It then develops an approximation branch-and-bound algorithm to solve multi-objective bilevel decision problems with fuzzy demands. Finally, two case-based examples further illustrate the proposed model and algorithm.