Bi-level Multi-objective Model Research Articles

Stackelberg game based optimal water allocation from the perspective of energy-water nexus: A case study of Minjiang River, China

Energy and water are interdependent. Water is essential for energy production, and energy is indispensable for water processes. This paper develops a Stackelberg game based bi-level multi-objective model for optimal water allocation under uncertainties from an energy-water nexus perspective, which considers energy-related water consumption and water-related energy production. It handles the hierarchical decision-making problem between the river basin authority and the subareas, as well as the tradeoffs between social equality and ecological damage. The upper level of the model makes schemes on water allocation for multiple subareas, and the lower level decides on water allocation for different types of power generation. To generate reasonable and practical strategies for water allocation, ɛ-constraint method and KKT conditions are used. A case study of Minjiang River, China is given to demonstrate the applicability and practicality. Scenarios analysis is also conducted to demonstrate the effectiveness of the model and the effects of the control parameter changes. The results indicate that the river basin authority would allocate larger water resources to the subareas with higher energy demand. It is concluded that the proposed allocation method is advantageous to the subareas with higher water utilization efficiency. The proposed bi-level model demonstrates its reasonableness and superiority to the single-level model. Policy implications are finally provided to support the sustainable development of energy-water nexus.

Social welfare and equality equilibrium based carbon tax subsidy incentive approach for biomass-coal co-firing towards carbon emissions

The lack of effective and scientifically supported policy measures has led to poor application of biomass-coal co-firing. A bi-level multi-objective model is developed to formulate a reasonable carbon tax subsidy policy and optimal biomass-coal co-firing plan, which considers the interactive relationship between authority and coal-fired power plants, and achieves a trade-off between social benefits, subsidy fairness, and environmental protection. A case study and scenarios demonstrate the feasibility and effectiveness of the proposed model. The ϵ-constraint method and Karush–Kuhn–Tucker conditions are employed to optimize the global equilibrium. The results indicate that model can achieve Stackelberg equilibrium between the hierarchical decision-makers with conflicting objectives, and the subsidy allocation is highly equitable. Sensitivity analyses show that the carbon tax subsidy policy can enhance biomass fuels utilization and encourage active participation of coal-fired power plants in achieving cleaner production. These findings provide a reference role for the authority to develop scientific subsidy mechanisms and coal-fired power plants to rationalize the planning of biomass-coal co-firing for power generation.

Resilience-economy-environment equilibrium based configuration interaction approach towards distributed energy system in energy intensive industry parks

Because unexpected, high-impact, extreme events and disasters can seriously threaten power system safety and resilience, there has been an increased research focus on power system resilience. This study proposes a bi-level multi-objective model for industrial park distributed energy configuration optimization to deal with extreme events, which considers the interactions between the authority and the industrial park in a leader–follower decision process and seeks to trade-off between economic cost, environmental protection, and power system resilience. An interactive algorithm is designed and the ɛ-constraint method is used to convert the model into a bi-level single objective model to solve the proposed complex model. A case example from an industrial park in Wuxi, Jiangsu Province, China, is given to demonstrate the practicality and efficiency of the proposed optimization method. The joint analysis of the power supply and financial losses found that a distributed energy system with an optimal resilience configuration could guarantee 95.85% of demand for three consecutive hours after an extreme event, maintain more than 50% of demand at any time, and reduce power outage financial losses at any time to a minimum of 0.232 million CNY. Based on the analyses and discussion, this model was proven to provide a reasonable and practical strategy for a resilience-economy-environment trade-off in industrial park distributed energy systems.

A bi-level multi-objective optimization model for inter-provincial carbon emissions transfer tax on electricity production

Low-carbon electricity development is crucial for achieving China's carbon peaking and carbon neutrality goals. The current carbon reduction territorial management model (CRTMM) can only bring short-term carbon reduction and is not enough to motivate provinces to further reduce carbon. However, few studies focus on the inter-provincial coordinated electricity carbon reduction. To overcome the shortcomings of the CRTMM and fill the research gap, this study creatively presents an original bi-level multi-objective inter-provincial carbon emissions transfer tax model (CETTM) on electricity generation in China, where the central government is the upper-level decision maker (leader) and provincial governments are the lower-level decision makers (followers). As the leader, the central government pursues overall maximum economic benefit and minimum pollutant emissions, and as the followers, provincial governments endeavor to maximize internal economic benefits. To ensure the scientificity and accuracy of the calculation results, an improved NSGA-II algorithm is designed to solve the model. Data from Anhui, Qinghai, Heilongjiang, and Jiangsu provinces are then used for empirical analysis to validate the model. The findings demonstrate that the CETTM is superior to the CRTMM in reducing carbon emissions, lowering pollutant emissions and improving economic benefits. The CETTM reduces CO2 emissions by 20.04 × 106 tons, lowers pollutant emissions by 10.65 × 104 tons, and increases benefits by 101.99 × 108 CNY in contrast to the CRTMM. The robustness of the model is verified using a sensitivity analysis. Finally, this study proposes policy recommendations for the CETTM implementation.

Modelling a bi-level multi-objective post-disaster humanitarian relief logistics network design problem under uncertainty

Post-disaster humanitarian relief logistics focuses on managing the supply and shipment of relief items. Owing to the complexity arising from the hierarchical decision relationship and the uncertainties of demand and transportation, it is challenging to develop an effective humanitarian relief logistics network (HRLN). A globalized robust bi-level multi-objective HRLN model involving uncertainties in transportation time, transportation cost and demand is developed to address this problem, in which an upper-level decision-maker focuses on the allocation problem and a lower-level decision-maker considers the supply problem. For tractability, the goal programming approach is employed to trade off conflicting timeliness, satisfaction and operational cost objectives. The proposed globalized robust bi-level HRLN model is reformulated as its globalized robust counterpart formulations under two different perturbation structures. The primal–dual approach is adopted to transform the bi-level models into equivalent mixed-integer conic programs. A case study concerning an Iranian earthquake is conducted to prove the performance of the proposed model. Globalized robust models are more flexible and able to immunize against uncertainty by comparison with traditional robust optimization and deterministic solutions. The managerial insights of using the globalized robust bi-level optimization approach are reported for disaster response management. The design of an emergency aviation network to circumvent the effects of COVID-19 could be considered in future research.

Carbon emission allowance allocation based on a bi-level multi-objective model in maritime shipping

To mitigate carbon emissions from maritime shipping, this study investigates the strategies and performance of allocating carbon emission allowances (CEAs) with the cap-and-trade mechanism among shipping companies. Using a bi-level model solved by the multi-objective particle swarm optimization algorithm based on Pareto solution set, the interactions between decisions of the government and shipping companies are well characterized. The results of the benchmark scenario indicate that all shipping companies’ optimal carbon emissions decrease annually during the planning period, and a larger company usually exhibits a better emission reduction performance. However, economic benefits of shipping companies and the society display an annually declining trend due to additional carbon emission reduction costs. The sensitivity analysis demonstrates that the decreasing carbon prices lead to more emissions, while the optimal total carbon emissions decrease as carbon reduction costs increase. These findings create implications for multiple stakeholders to formulate their own carbon emissions mitigation strategies under the cap-and-trade mechanism.

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.

Quartet trade-off for regional water resources allocation optimization with multiple water sources: A decentralized bi-level multi-objective model under hybrid uncertainty

Multiple uncertainties from water resource allocation have posed new challenges to balanced regional development. On the one hand, in the context of global water shortage crisis, groundwater, as an important water supply module, is facing severe risk of shortage. On the other hand, the regional authorities need to coordinate the contradictory water demand brought by the heterogeneous water use objectives from multiple water use levels, and these demands are also subject to complex uncertainties. How to mitigate the risks posed by uncertainties, ensure regional water security and balance participants, is attracting the keen attention of decision-makers around the world. Therefore, this study establishes a decentralized bi-level multi-objective regional water resources allocation (RWRA) optimization model under hybrid uncertainty, aiming at an optimal quartet trade-off of equity, sustainability, equilibrium, and efficiency. To deal with the hybrid uncertainty in the model, water demand is set as a random fuzzy number, and the groundwater constraint is combined with fuzzy chance-constrained programming (FCCP). Then, the decentralized bi-level multi-objective model is solved by the bi-level interactive method based on the satisfactory solution incorporated with the chaotic-particle swarm optimization (CPSO) algorithm. The proposed model and solution approach are then applied to the Dongjiang River Basin in Guangdong Province of China to verify the validity and utility of the model. The results show that (1) the model can effectively meet the different objectives requirements of regional authority and sub-areas; (2) groundwater constraint parameters has a significant impact on the model results, especially the Gini coefficient decreases by 13.6% when groundwater is used as a water source supplement; (3) from single-level model to decentralized bi-level model, the satisfactory balance of the two levels increases from 0.1457 to 0.793, which indicates that the decentralized bi-level model makes the two levels more balanced than the single-level model. Based on the results, some management recommendations for participants are finally provided.

Optimal configuration of hybrid energy systems considering power to hydrogen and electricity-price prediction: A two-stage multi-objective bi-level framework

This paper develops a two-stage multi-objective bi-level framework to optimize the sizing of a grid-connected electricity-hydrogen system. Firstly, a multi-objective bi-level capacity configuration optimization model considering the different functional orientations of hydrogen energy and electricity-price prediction is established. Then, to solve the above multi-objective bi-level model, a two-stage solution algorithm is proposed. In stage one, the CPLEX solver and non-dominated sorting genetic algorithm II are employed to obtain the solutions of the developed optimization model. In stage two, an entropy method is applied to get the importance of the three objectives of the outer model, whereas a cumulative prospect theory is used to rank the best Pareto solution. Finally, an industrial park in Aksai Kazak Autonomous County is chosen for case study, the results show: (1) the best capacity configuration alternative, which includes 22 wind turbines, 210 photovoltaic panels, 2 gas turbines, 2 fuel cells, 1 electrolyzer, and 3 hydrogen tanks, owns the NPB of 161,503 CNY, the ACE of 93,111 kg, and the LOEC of 603,874 kWh. (2) the ACE with the weight of 0.527 is the most important objective. (3) Sensitivity analysis on electricity price fluctuations of ±5% and ±10% presents that the proposed approach is robust.

Bi-level fuzzy stochastic-robust model for flexibility valorizing of renewable networked microgrids

This paper presents a new bi-level multi-objective model to valorize the microgrid (MG) flexibility based on flexible power management system. It considers the presence of renewable and flexibility resources including demand response program (DRP), energy storage system and integrated unit of electric spring with electric vehicles (EVs) parking (IUEE). The proposed bi-level model in the upper-level maximizes expected flexibility resources profit subject to flexibility constraints. Also, in the lower level, minimizing MG energy cost and voltage deviation function based on the Pareto optimization technique is considered as the objective functions; it is bounded by the linearized AC optimal power flow constraints, renewable and flexibility resources limits, and the MG flexibility restrictions. In the following, the proposed bi-level model using Karush–Kuhn–Tucker (KKT) technique is converted to a single-level counterpart, and the fuzzy decision-making method is employed to achieve the best compromise solution. Further, hybrid stochastic-robust programming models uncertain parameters of the proposed model, so that stochastic programming models uncertainties associated with demand, energy price, and the maximum renewables active generation. Also, to capture the flexible potential capabilities of the IUEE, robust optimization models the EVs’ parameters uncertainty. Finally, numerical results confirm the proposed model could jointly improve operation, economic and flexibility conditions of the MG and turned it to a flexi-optimized-renewable MG. • Bi-level model to value the microgrid flexibility is presented. • Integrated unit of electric spring with electric vehicles is modeled. • The paper deals with maximizing flexibility value in renewable microgrids. • Fuzzy stochastic/robust optimization is proposed to handle uncertainty.

Joint optimisation of park-and-ride facility locations and alternate traffic restriction scheme under equilibrium flows

Alternate traffic restriction (ATR) schemes manage traffic congestion by prohibiting a proportion of cars from entering a predetermined ATR area during specific time periods. Under the ATR scheme, Park-and-Ride (P&R) often becomes more popular as travelers can park cars at P&R facilities and avoid driving into the ATR area. This paper proposes a multi-objective bi-level model that jointly optimizes the P&R facility locations and the ATR scheme (the ATR areas and the proportion of restricted private cars). The upper-level model minimizes the total travel cost and total emission cost, and maximizes consumer surplus. The lower-level model characterizes the user equilibrium of travel modes and route choices. The non-dominated sorting genetic algorithm is adapted to solve the proposed multi-objective bi-level model, where a gradient project algorithm is used for solving the lower-level model. Numerical studies are conducted to test and illustrate the applicability of the model and algorithms.

Optimal trade-off of integrated river basin water resources allocation considering water market: A bi-level multi-objective model with conditional value-at-risk constraints

The predictable water shortage crisis is intensifying due to frequent extreme weather caused by climate change and human activities. Motivated by urgent practical needs of more scientific and balanced river basin water resources allocation (RBWRA) schemes, a comprehensive bi-level multi-objective programming (BLMOP) model for RBWRA considering uncertain risks and water market is constructed in this paper, which pursues the objectives of environmental protection, equality, and economic development. River basin authority, as the leader of RBWRA, is committed to reducing pollutants while introducing Gini coefficient to maintain the equality of economic development between sub-areas. Meanwhile, the sub-areas (i.e., followers) are dedicated to improving the economic benefit. In addition, the water market is introduced as water redistribution mechanism and its effect is probed into in detail. Moreover, conditional value-at-risk (CVaR) constraints are integrated into the model to control the economic loss caused by the risks of uncertain water availability. To solve the BLMOP model, a novel bi-level interaction based adaptive global equilibrium optimization (BI-aGEO) approach is proposed, which can obtain the best equilibrium solution that satisfies all decision-making participants. Furthermore, the proposed model and approach are applied to the Hanjiang River Basin in central China to elaborate on their feasibility and effectiveness. Results show that the proposed model is effective in ensuring the sustainability, equality and efficiency of RBWRA. The introduction of water market is shown to be able to improve water efficiency and promote water conservation and CVaR constraints play a significant role in controlling economic risks. Finally, some managerial suggestions are provided for different RBWRA participants for more scientific and effective integrated water resources management (IWRM).

Optimization of Urban Shelter Locations Using Bi-Level Multi-Objective Location-Allocation Model.

Recently, global natural disasters have occurred frequently and caused serious damage. As an important urban space resource and public service facility, the reasonable planning and layout optimization of shelters is very important to reduce the disaster loss and improve the sustainable development of cities. Based on the review of location theory and models for shelter site selection, this study constructs a bi-level multi-objective location-allocation model, an accessibility, economy, and efficiency (AEE) model, based on sequential decision logic to maximize the economic sustainability and social utility. The model comprehensively considers factors such as the level of decision-making, the utilization efficiency, and capacity constraints of shelters. The gravity model is introduced to simulate the decision-making behavior of evacuees. A calculation example and its solution prove the high practicability and operability of the AEE model in an actual shelter site selection and construction investment, which can achieve the global optimization of evacuation time and the maximization of the use efficiency of the shelters under the financial constraints. It provides a scientific and effective decision-making method for the multi-objective location optimization problem of shelters.

Bi-Level Multi-Objective Planning Model of Solar PV-Battery Storage-Based DERs in Smart Grid Distribution System

This paper presents a novel bi-level multi-objective model for planning solar PV-battery storage (PV-BS) based DERs in Smart grid distribution system (SGDS). The planning of Solar PV and battery storage (BS) in the distribution system presents severe complexities for the system planner due to their inherent attributes. The detailed analysis considering all three planning aspects, namely technical, economics, and environmental, is presented, assisting in the efficient and reliable planning operation. The four test cases are formulated based upon the life cycle cost, unserved energy, penetration level, and social welfare. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">level-1</i> proceeds with evaluating the DERs sizing along with penetration level and serves as an input to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">level-2</i> for computing the optimal placement for DERs. The proposed model is implemented on the IEEE-33 bus distribution system and solved using Butterfly-PSO (BF-PSO) algorithm. The detailed parametric and sensitivity analysis presented may aid the system planners in terms of planning preview. The simulation results validate the effectiveness of the proposed work by showing significant improvement in bus voltage profiles (up to 4%) and reduction in total power losses (up to 45%). The highest penetration level is observed for Case 2 (70%), which also corresponds to the highest LCC (k <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula> 147094) and thus results in the lowest emission cost (k <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula> 4920).

A bi-level multi-objective location-routing model for municipal waste management with obnoxious effects.

Municipal waste management is a complex problem. This paper develops a bi-level multi-objective location-routing model for municipal waste management that considers the interests of both the government and the sanitation companies. The government as the leader decides on the location and scale of the waste recycling centers to reduce the obnoxious effects and ensure cost effectiveness, and the sanitation company as the follower decides on the waste collection routing plans based on the government-approved locations to minimize the logistics cost. An improved hybrid NSGA-II is then developed to solve the proposed model. Two initial solution methods are employed: clustering for the leader and a Clarke and Wright method for the follower. Non-dominated sorting and best-cost route crossover operator are used to improve the effectiveness of NSGA-II. Based on Prins (24 instances) and Barreto (13 instances) benchmarks, the experimental results indicated that the improved operator had strong competitiveness and a better performance than previous methods, with the improved algorithm achieving the best average gaps of 0.18% and 0.24% and improving the best-known solutions in some instances. The model and solution methodology are illustrated using a waste collection problem in Tianjin, from which practical insights are derived.

A bilevel whale optimization algorithm for risk management scheduling of information technology projects considering outsourcing

Information Technology (IT) outsourcing can help enterprises to improve their core competitiveness and save costs. But the schedule risk in IT outsourcing process may bring huge losses. Based on the theory of distributed decision making (DDM), a bi-level multi-objective schedule risk management model is established with considering the project schedule risk and risk management cost. In addition, a bi-level Whale Optimization Algorithm (BiWOA) is designed to solve the problem and compared with the original whale optimization algorithm (WOA) and the moth–flame​ optimization (MFO). Three numerical examples are designed to test the effectiveness of the model. And the analysis of results show that it can effectively control the schedule risks of IT outsourcing projects. The influence of different preference degree of the client on the decision result is also analyzed. The effectiveness of bi-level whale optimization algorithm is proved by solving and analyzing the numerical examples. It demonstrated that bi-level whale optimization algorithm is more competitive with higher accuracy and the ability to escape from local optima and can solve the problem more effectively.

A bi-level multi-objective location-routing optimization model for disaster relief operations considering public donations

In recent years, the number and severity of natural disasters occurring in various regions of the world have increased dramatically incurring heavy financial and human losses. Therefore, decision-makers have been concerned with ways of providing relief to reduce the losses. Here, we present a multi-objective bi-level model for disaster location-routing problem that provides the needed supplies through multiple suppliers, considering the supply risk. Moreover, to reduce the risk and increase efficiency, special attention is given to people's help for supplying goods having high priority and low risk. At the first level of the model, the cost and time objectives are considered, and at the second level, the risk and efficiency objectives are considered. To solve the bi-level model, first we solved the follower's perspective model using the augmented epsilon constraint method to convert the second level objectives to a single-objective. Then, using the KKT conditions, the bi-level model is converted to a linear single-level bi-objective model, which is solved by the augmented epsilon constraint method. To validate the model, the suburb of Sari in Iran is selected as a case study and the model is solved by the CPLEX/GAMS. The results show that the lower-risk goods with higher priorities should be supplied by public donations to increase efficiency in provision of relief. The results of sensitivity analysis demonstrate that commodities are not supplied merely by public donations, because if the inventories of Red Cross and Red Crescent decrease, or level of demand rises, exogenous suppliers and/or general public donations can provide goods.

Stackelberg game based co-firing biomass with coal under carbon cap-and-trade regulation

Coal-fired power industry is under enormous pressure to accomplish carbon emission reduction targets. This paper proposes a bi-level multi-objective model for co-firing biomass with coal under carbon cap-and-trade regulation which considers a leader-follower Stackelberg game between the authority and the coal-fired power plants. The upper level regards social welfare maximization and allocation satisfaction maximization as its multiple objectives, while the lower level attempts to maximize the profits of each coal-fired power plant. The inherent uncertainty prompts the motivation for employing fuzzy set theory to characterize the uncertain parameters and determine their exact values. A case study from Shandong Province, China is provided to demonstrate the practicality and efficiency of the optimization model. [Formula: see text]-constraint method and interactive algorithm are used to solve the model, and furthermore the solutions associated with different free carbon emission quota levels and minimal allocation satisfactions have been generated to examine the influences. Based on the analysis and discussion, the methodology can meet the carbon emission reduction goals and transit to a lower-carbon power generation. It also assists the decision makers to develop desired quota allocation strategy in accordance with their attitudes and actual conditions.

Multi-modal urban transit network design considering reliability: multi-objective bi-level optimization

Due to the presence of transportation infrastructure in metropolitan areas, authorities often seek to modify the capacity of existing urban transportation links. Therefore, to meet travel demands, it is necessary to consider public transport (PT) modes and carry out systematic planning. In this research, assuming the existence of urban transportation infrastructure, we develop a mathematical model to determine the amount of link capacity increase for the dual-mode PT network. Such an increase in capacity can improve the network capacity and travel time reliabilities under both normal and peak traffic conditions. To investigate this issue, travel demand is assumed to follow a lognormal distribution under normal conditions. Then, the total travel time and flow through the links are calculated and applied to the model using the Monte Carlo method. In this study, we assume that the links of both transport modes forming a path are interdependent. Moreover, due to NP-hardness, we propose the PSO algorithm with dynamic parameters to solve the multi-objective bi-level model. Considering two public transport modes, we develop the algorithm for a part of the urban transportation network in Tehran, Iran.

Lexicographic multi-objective road pricing optimization considering land use and transportation effects

This paper develops a bi-level multi-objective model for road pricing optimization considering land use and transportation effects. The upper-level problem determines a cordon-based road pricing scheme, while the lower-level problem models the interaction between land use and transportation. To facilitate decision-making in a scenario characterized by a hierarchical ordering of objectives, a novel α-conditional lexicographic optimization method is established, which uses an α value to capture the decision-maker's perceived acceptability of the trade-off between different objectives with respect to the hierarchical objective ordering. The properties associated with this approach are derived, and an algorithm to find the α-conditional lexicographic dominance solutions is developed. To solve the model, a revised genetic algorithm is further developed to illustrate how the proposed α-conditional lexicographic optimization method can be embedded into existing heuristic or metaheuristic methods. A case study using data from Jiangyin, China, demonstrates the significance of considering land use effects when evaluating road pricing scenarios. The results reveal the trade-off between transportation and various land use objectives and the variation of such a trade-off among different types of traffic analysis zones. It is demonstrated that the proposed α-conditional lexicographic approach can improve most of the land use objective values while ensuring that the total travel time is constrained within an acceptable range, enabling a balance between various land use and transportation objectives.