Multi-objective Mixed Integer Nonlinear Programming Research Articles

An improved deep Q-network approach for charging sequence scheduling with optimal mobile charging cost and charging efficiency in wireless rechargeable sensor networks

Mobile charging is a practical solution to overcome energy constraints in wireless rechargeable sensor networks (WRSNs). It utilizes a mobile charger (MC) to charge sensors based on the wireless power transfer technique via a charging scheduling scheme. However, how to schedule MC to achieve higher charging efficiency with less mobile charging cost, while ensuring network functionality remains a challenge. Specifically, the mobile charging cost is the total energy consumed by the MC during the charging task. This paper studies the charging sequence scheduling problem with optimal mobile charging cost and charging efficiency (CSCE), considering dynamic changes in sensor energy consumption. Moreover, we model the CSCE as a multi-objective mixed integer nonlinear programming. To address this issue, we propose an improved deep Q network approach for CSCE (IDQN-CSCE), where the MC acts as an agent to explore the WRSN and determine a charging policy based on the charging demand of sensors. IDQN-CSCE employs Q-learning and deep Q-networks (DQN) to train the Q-table and DQN network simultaneously. Charging actions are selected based on probability, and the probability of using Q-learning decreases as iteration steps increase. Additionally, we design a novel reward function consisting of a weighted sum of rewards and penalties fed back by the environment after performing a charging action. Simulation results show that IDQN-CSCE achieves higher charging efficiency than other baseline approaches with less mobile charging cost.

Development and evaluation of an online home energy management strategy for load coordination in smart homes with renewable energy sources

In this paper, a real time implementable load coordination strategy is developed for the optimization of electric demands in a smart home. The strategy minimizes the electricity cost to the home owner, while limiting the disruptions associated with the deferring of flexible power loads. A multi-objective nonlinear mixed integer programming is formulated as a sequential model predictive control, which is then solved using genetic algorithm. The load shifting benefits obtained by deploying an advanced coordination strategy are compared against a baseline controller for various home characteristics, such as location, size and equipment. The simulation study shows that the deployment of the smart home energy management strategy achieves approximately 5% reduction in grid cost compared to a baseline strategy. This is achieved by deferring approximately 50% of the flexible loads, which is possible due to the use of the stationary energy storage.

Leveraging cost-effectiveness of photovoltaic-battery system in metro station under time-of-use pricing tariff

As the cornerstone of contemporary urban transit infrastructure, the metro rail transit system significantly contributes to both energy consumption and carbon emissions. Recognizing the potential of rooftop photovoltaic (PV) applications in elevated stations to mitigate the carbon footprint of the metro system, harnessing this potential becomes imperative for advancing toward a cleaner future in the metro transit sector. However, the techno-economic feasibility of the rooftop PV application in elevated metro stations has not been fully reported in existing literature. Addressing this research gap, our study delves into the impact of the photovoltaic-battery (PVB) system on energy conservation and economic benefits within the elevated stations of a metro line in Beijing, China, and a multi-objective nonlinear mixed-integer programming (MIP) is formulated under a 3-tier time-of-use tariff scheme for minimizing grid load and maximizing economic benefits. The results demonstrate that the incorporation of both the battery energy storage device and the PV subsystem leads to an 8.3% and 19.2% reduction in annualized costs, respectively. When applied across the entire metro line, the PVB system is anticipated to yield a substantial annualized cost reduction ranging from 26.1% to 47.8%. Moreover, outcomes from the multi-objective MIP optimization reveal that the simultaneous achievement of economic benefits maximization and grid load minimization is infeasible, and the weighted sum method offers a decision-making platform for investors to choose one option or another according to extra criteria.

Train rescheduling and platforming in large high-speed railway stations

To deal with train delays in large high-speed railway stations, a multi-objective mixed-integer nonlinear programming (MO-MINLP) optimization model was proposed. The model used the arrival time, departure time, track occupation, and route selection as the decision variables and fully considered the station infrastructure layout, train operational requirements, and time standards as limiting factors. The optimization objective was to minimize train delays and reduce track and route adjustments. To realize the large-scale and rapid solution of the MO-MINLP model, this study proposed a rolling horizon optimization algorithm that used “half an hour” as a time interval and solved the rescheduling and platforming problem of each time interval step-by-step. In numerical experiments, 227 train movements under delay circumstances in Hangzhoudong station were optimized by using the proposed model and solution algorithm. The results show that the proposed MO-MINLP model could resolve route conflicts, compress unnecessary dwell times, and reduce train delays; the solution algorithm could efficiently increase the computational speed. The maximum solution time for optimizing the 227 train movements is 15 min 24 s.

Stochastic multi-benefit planning of mobile energy storage in reconfigurable active distribution systems

This paper proposes a multi-benefit planning framework for mobile energy storage systems (MESSs) in reconfigurable active distribution systems (DSs). The goal of this framework is to improve the DS operation and reliability through achieving four objectives: (1) minimizing the DS costs, (2) minimizing the DS energy losses, (3) improving the DS voltage profiles, and (4) minimizing the expected energy not supplied (EENS) in the system. The developed framework determines optimal decisions associated with the network reconfiguration as well as the MESS sizes and locations, taking into account the variations in DS loads, energy prices, and renewable energy sources. The planning problem in this study is formulated as a stochastic multi-objective mixed-integer nonlinear programming problem, which is solved using a genetic algorithm (GA)-based hybrid optimization method. The proposed framework is tested using a case study of an active DS that includes various types of energy sources and load demands. Comparing the results of the developed planning framework with the base-case system demonstrates the efficacy of the planning framework and the techno-economic benefits of MESSs, where the proposed framework with MESSs successfully achieved significant improvements in the DS operating cost, energy losses, voltage profiles, and EENS. The advantages of MESSs are also verified through a comparison with stationary energy storage systems.

Multi-objective location-allocation optimization of temporary delivery points for medical supplies during large-scale epidemic outbreaks

The surge in the demand for medical supplies and the lack of service delivery points in the early stages of an epidemic are likely to exacerbate the spread of the epidemic and create serious inequities in distribution. To more effectively allocate medical supplies during large-scale epidemic outbreaks, we develop a multi-objective mixed integer nonlinear programming model incorporating appointment allocation rules to optimize the locations of delivery points, the flow of medical supplies among different nodes, and the appointment allocation rules. The model aims to minimize the number of infected individuals in the study area, infection risks at delivery points, and total cost and service level deviation at the demand points. To achieve such objectives, we adopt the hierarchy optimization method and ε-constraint method encompassing model complexity and applicability. The practicality of our model is demonstrated through a numerical case for mask allocation in accordance with appointment allocation rules during COVID-19 in 2020 based on real population distribution data of Xipu Subdistrict in Pidu District, Chengdu, China. The results reveal trade-offs between different objectives. In addition, related suggestions are provided for variations in demand satisfaction rate, the number of individuals at each delivery point and appointment allocation rules.

A location-inventory model for the sustainable supply chain of perishable products based on pricing and replenishment decisions: A case study.

In recent decades, changes in people's lifestyles and occupations have led to new food consumption patterns around the world, with a notable growth in the demand for ready meals and meat products. Accordingly, the food industry has tried to transform the global food culture by promoting its more profitable products to become able to set a higher price for meat. Considering the short lifetime of products in perishable food supply chains, inventory decisions are considered crucial. In addition, the demand for perishable food products is greatly affected by their freshness. In this paper, we develop a multi-objective mixed-integer non-linear programming model for a four-level sustainable supply chain (SC) of a perishable product with price-dependent demand and deterioration rates. The SC consists of suppliers, a production center (PC), distribution centers (DCs), and retailers. We aim to ascertain the optimal pricing policy and cycle length to maximize profit, achieve specific social objectives, and minimize the total cost and adverse environmental impacts. The proposed model determines the deterioration rate of each product according to its expiration date, the optimal location of supply-side facilities, and the flow rate between the facilities based on the selected mode of delivery. The products are delivered to the retailers by a mechanized transportation system either directly from the PC or indirectly through the DCs. Finally, an actual case study is provided to demonstrate the applicability of the model and our theoretical results under real-world conditions. We solve the case study by a preemptive fuzzy goal programming method and perform several sensitivity analyses on the results. By performing simultaneous sensitivity analyses on the demand and expiration dates, the optimal values of the problem's parameters are determined. The optimal values help decision-makers make optimal decisions regarding the selling price of products and replenishment times. The model is applicable to supply chains of any perishable items with expiration dates.

Techno-economic-environmental analysis of direct-contact membrane distillation systems integrated with low-grade heat sources: A multi-objective optimization approach

Membrane distillation (MD) is an emerging desalination technology powered by low-grade thermal energy. This paper presents the multi-objective optimal design of the membrane distillation desalination plant. The heat sources are supercritical CO2 (sCO2) Brayton cycle waste heat and geothermal energy. Multi-objective mixed-integer nonlinear programming models are developed to optimize the integrated systems' design and operating conditions based on economic and environmental metrics. The models consider the simultaneous optimization of water production costs (wpc) and environmental impacts (wpei). The environmental performance is quantified through a life cycle assessment using the widely used ReCiPe 2016 method, enabling the identification of the main environmental hotspots throughout the plant's life cycle. Our methodology demonstrates the sustainability of MD desalination plants through various case studies. The results indicate that an appropriate MD system design can significantly reduce the environmental burden with a slight increase in cost. For the sCO2-MD scenario, a cost-effective design can achieve a minimum wpc of 0.758 $/m3 and a minimum wpei of 0.172 Pt/m3 in an environmentally friendly design. A balanced design can reduce the environmental impact by 31.30% with a slight cost increase of 4.48% compared to a cost-effective design. The minimum wpc and minimum wpei for the geothermal MD (GTMD) scenario are 412.27% and 215.94% higher, respectively, compared to the sCO2-MD scenario. Moreover, reducing the wpei of the GTMD system is also more expensive, requiring a 10.67% increase in cost to reduce the environmental impact by 21.65%.

Multi-objective energy-efficient hybrid flow shop scheduling using Q-learning and GVNS driven NSGA-II

The urgent mission for carbon peak and carbon neutrality is demanding greater industrial sustainability. Energy-efficient hybrid flow shop scheduling problem (EEHFSP) has been raising increasing attention in recent years. This paper studies a new EEHFSP with uniform machines to minimize total tardiness, total energy cost, and carbon trading cost. Time-of-use tariffs and power down strategies are simultaneously adopted. A novel multi-objective mixed-integer nonlinear programming model for the problem is proposed. To solve the model, we propose a Q-learning and general variable neighborhood search (GVNS) driven non-dominated sorting genetic algorithm II (QVNS-NSGA-II). The novelty of the algorithm is that we incorporate Q-learning into GVNS to guide premium adaptive operator selection throughout the shaking and local search processes. A distinguishing feature is that the states and actions of Q-learning are set as neighborhood structures and local search operators. The Q-learning-driven GVNS is embedded into NSGA-II to promote the exploration and exploitation capability. Experimental results show that the proposed QVNS-NSGA-II outperforms NSGA-II, improved Jaya, and modified MOEA/D in terms of the quantity, quality of Pareto solutions, and computational efficiency. Sensitivity analysis also derives several managerial implications. The proposed approach can be applied to improve sustainability and productivity for hybrid flow shop manufacturers.

Omni-fulfillment network design for supply chain service platform considering cost, service and resilience tradeoffs

Supply chain service platform (SCSP) plays an indispensable role in omni-fulfillment supply chain network services in the digital economy era. In this context, this paper studies the omni-fulfillment supply chain network design considering cost, service, and resilience tradeoffs. The problem is modeled as a multi-objective mixed integer nonlinear programming (MOMINLP) model based on omni-fulfillment services. To improve the solving efficiency, the model is linearized, and a tailored multi-objective optimization algorithm is developed. The significant advantage of this algorithm is that the multi-loop skipping mechanism is embedded in the Epsilon-constraint method to obtain the Pareto front faster. The effectiveness of the proposed decision-making framework is verified by real-case data. Numerical results show that the proposed algorithm outperforms AUGMECON2 algorithm in terms of problem size and computational time. In the case of order segmentation, the shorter the delivery time of goods, the higher the cost of the supply chain network. Furthermore, implementing capacity redundancy in the central warehouse can mitigate the impact of different disrupting scenarios.

Robust sustainable canola oil-based biodiesel supply chain network design under supply and demand uncertainty.

The excessive consumption of fossil fuels has sparked debates and caused environmental damage, leading the global community to search for a suitable alternative. To achieve sustainable development goals and prevent harmful climate scenarios, the world needs to increase its use of renewable energy. Biodiesel, a clean and eco-friendly fuel with a high flash point and more lubrication than petroleum-based fuels, and without the emission of harmful environmental gases, has emerged as one of the fossil fuel alternatives. To promote the mass-level production of biodiesel, a sustainable supply chain (SC) that does not depend on laboratory production is necessary. For this purpose, this research proposes a multi-objective mixed-integer non-linear mathematical programming (MINLP) model to design a sustainable canola oil-based biodiesel supply chain network (CO-BSCND) under supply and demand uncertainty. This mathematical model aims to minimize the total cost (TC) and total carbon emission while maximizing the total number of job opportunities simultaneously. A scenario-based robust optimization (SBRO) approach is applied to deal with uncertainty. The proposed model is implemented in a real case study in Iran, and numerical experiments and sensitivity analysis are conducted to demonstrate its applicability. The results of this research demonstrate that designing a sustainable supply chain network for the production and distribution of biodiesel fuel is achievable. Moreover, this mathematical modeling makes mass-scale production of biodiesel fuel a possibility. In addition, the SBRO method adopted in this research enables managers and researchers to explore the design conditions of the supply chain network by controlling the uncertainties that affect it. This approach allows the chain's performance to be as close as possible to the actual conditions. As a result, the SBRO method enhances the efficiency of the supply chain network and boosts productivity toward achieving desired goals.

A multi-objective multi-criteria decision-making approach for sustainable vaccine distribution, inventory control (R,s,S policy), and waste management considering risk assessment, a case study

Vaccines play a vital role in monitoring and preventing the growth of contagious diseases. As of December 2019, With the prevalence of corona worldwide, all communities, particularly developing countries, came across irresistible challenges in providing a proper vaccine for citizens. Moreover, accurate waste control is of great importance, particularly in the context of infectious medical waste. To address mentioned difficulties regarding vaccine inventory ordering & waste management, this paper develops a sustainable multi-objective mixed-integer non-linear programming (MINLP) formulation. In order to examine real goals, all three proposed objective functions are regulated in compliance with the obtained result of the risk assessment. besides, for exploring the applicability of the proposed network, a real case study in one of the central cities in Iran, Kashan province, is considered. Two test problems have also been defined, encompassing small and medium size solutions. The LP-metric and goal programming approaches are utilized to solve the model. According to one of the sensitivity analysis results, extending the review period will be conducive to proliferation in the amount of order quantity and subsequently, imposing more costs on the chain at a particular time and getting the opportunity from countries to capitalize monetary values in other public affairs.

Novel empty train return strategy and passenger control strategy to satisfy asymmetric passenger demand: A joint optimization with train timetabling

Big cities’ bi-directional metro lines often have unbalanced passenger demand, i.e., up-directional passenger demand is oversaturated but down-directional passenger demand is unsaturated. In recent years, the method to relieve congestion in oversaturated direction has attracted much attention, but many problems in the unsaturated direction have not gotten as much attention, e.g., the waste of transportation resources caused by low loading rate, and the insufficient utilization of platform space resources caused by less waiting passengers. To address these problems, this paper introduces a new collaborative optimization model for the train timetable, passenger control and rolling stock schedule on a bi-directional metro line with unbalanced passenger demand. With consider the real-time state of bi-directional platform passengers, a platform passenger control strategy is designed to promote the utilization of platform resources, and an empty train return strategy is proposed to transfer transportation resources to oversaturated direction. To characterize the problem mathematically, a multi-objective mixed-integer nonlinear programming model (MINLP) is formulated to minimize the passengers’ waiting time, the difference of bi-directional platform passenger density and the use cost of trains. An effective heuristic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) and the adaptive large neighborhood search (ALNS) is designed to find high-quality solutions for the proposed model. Finally, five sets of numerical examples based on the Beijing metro Batong line, are conducted to validate the performance of the proposed method in this paper. The experimental results demonstrate the method can fully utilize the transportation and platform resources of the unsaturated direction, to improve transport efficiency and relieve platform congestion of oversaturated direction.

Tapping into the potential CO2 emission reduction of a crude oil transportation system from carbon footprint perspective

With more countries adopting a net-zero carbon emission goal, low carbon has become the focus of the transformation of the petroleum industry. Improper operations of the crude oil transportation system, one of the primary energy consumers of oilfields, usually cause severe environmental problems. Following the life cycle assessment method and considering the special process characteristics of the crude oil transportation system, a detailed carbon footprint analysis was conducted from the design to the recycling phase to identify the key phase for carbon emission control. Combined with process modifications, a multi-objective operation optimization model constrained by thermal constraints and insertion oil was developed to reach economic and environmental goals. Then, the multi-objective mixed integer nonlinear programming model was turned into a mixed integer linear programming model by the piecewise linearization method and augmented ε-constraint method. The models were validated using a typical case. The carbon footprint analysis showed that the average CO2e emissions were 2.68 t CO2e/(104 km m3•a) over the lifecycle, and the CO2e emissions during the operation phase were the highest (74.04%) among all phases. Moreover, the optimization model reduced the total cost and CO2e emissions by up to 18.72% and 16.97%. Additionally, sensitivity analysis revealed that the optimal operation scheme was highly sensitive to the crude oil price and transportation volume. The total CO2e emissions per unit volume exhibited a concave trend as the transportation volume increased, indicating the existence of an optimal transportation volume that achieved the lowest emissions. The study captured the weak points of carbon emissions over the lifecycle and tapped into potential CO2 emission reduction, providing a reference for the design and operation of the future pipeline system.

Optimising location, inventory and transportation in a sustainable closed-loop supply chain

Operations management researchers and practitioners have shown increasing interest in incorporating sustainability into supply chain (SC) design models. This means that sustainability must be considered in all aspects of the SC, including location, inventory and transportation (LIT) decisions. Hence the aim of this article is to propose an optimisation model that incorporates: (i) LIT decisions in an integrated manner; (ii) the three sustainability (3S) aspects, i.e. economic, environmental and social, into each named decisions; and (iii) a closed-loop supply chain (CLSC) structure. The proposed formulation is a multi-objective mixed integer non-linear programming (MO-MINLP) model whose objectives consider minimisation of economic and social costs (economic aspect) and carbon emissions (environmental aspect), and maximisation of the social impact of SC operations (social aspect). A transformation technique is applied to one of the objective functions, which results in an MO-MILP model solved by the lexicographic method. This article focuses on commodity industries where only one finished product is manufactured. Hence the 3S-LIT model is validated with a randomly generated dataset and against a recently published alternative model applied to the copper mining industry.

An inexact multi-objective mixed-integer nonlinear programming approach for water-soil-fertilizer management under uncertainty considering “footprint family-planetary boundary” assessment

Water, energy, and food (WEF) are interlinked and create a dynamic system that impacts both human well-being and ecology. Given the importance of ecology within the WEF system, water resources serve as the core issue. The allocation of water resources in irrigation districts is a challenging problem for the coordinated development of agricultural production, water resources, and the ecological environment. The integration of stochastic multi-objective programming, fuzzy credibility-constrained programming, and mixed integer programming offers a solution to this issue, with the construction of a fuzzy credibility-constrained stochastic multi-objective mixed-integer nonlinear programming model. The applicability and validity of this model were verified by applying it to the Kaikong Irrigation District (KID) of the Tarim River Basin in northwest China, with notable findings indicating that the optimized system reduces agricultural costs by 5.82%, increases irrigation water use efficiency by 1.80%, and reduces global warming potential by 6.45%. This study investigates the effects of diverse allocation strategies of water and land resources on the social, economic, and ecological subsystems and their interactions by downscaling four subprocesses PBs to the KID scale. The optimization model reveals that only the nitrogen footprint of Kuerle City surpasses the nitrogen boundary of the KID. The proposed solutions based on the model can encourage the green and ecologically-friendly development of agricultural production and can be applied to agricultural systems in arid regions with similar conditions.

Reliable design optimization for industrial hybrid energy systems with uncertain sustainable energy

More and more attention has been paid to the industrial hybrid energy systems which comprise fossil energy and renewable energy for achieving carbon neutrality. Wherein, the uncertainty of renewable energy, fluctuation of energy requirement from process units, and failure rate of energy conversion devices have significant effects on the reliability of industrial hybrid energy systems and thus restrict the application and promotion. How to simultaneously address these issues for realizing the reliable design of industrial hybrid energy systems has been a matter of great concern and challenge. Hence, a systematic reliable design optimization method is presented in this study to tackle these challenges. In this study, the two-stage stochastic programming method is implemented to conduct the uncertain optimization in dealing with the uncertainty of renewable energy and fluctuation of energy requirement, while a mixed stand-by redundancy allocation problem is proposed for simultaneously enhancing the reliability and minimizing the number of stand-by devices. A multi-objective mixed integer non-linear programming framework using reliability and total annual cost as the dual objectives is then formulated and applied to a refinery site for the reliable design optimization of the industrial hybrid energy system. According to the solution results, compared to the minimum total annual cost scheme without stand-by redundancy, the maximum reliability of the industrial hybrid energy system can reach 0.9878 using the stand-by redundancy strategy. As a result, the reliability can be significantly enhanced by 44%, with only a 5% increment of the total annual cost. Moreover, a Pareto frontier under multi-objective optimization is constructed, and the optimization schemes at the Pareto frontier can realize the trade-off between reliability and the total annual cost of the industrial hybrid energy system. Subsequently, a reliability-gain index is proposed to further evaluate the trade-off schemes and thus guide the choice of appropriate design schemes.

A Smart Decision Support Framework for Sustainable and Resilient Supplier Selection and Order Allocation in the Pharmaceutical Industry

Supplier selection and order allocation (SS-OA) are two of the most important strategic decisions for supply chain network design and operation. If sustainability and resilience criteria are taken into consideration together and a holistic sustainable and resilient SS-OA is carried out, it may enable the supply chain network to perform better when subjected to disruption scenarios. In this research paper, a novel comprehensive multi-phase, multi-period sustainable, and resilient SS-OA decision support framework has been proposed. This framework integrates fuzzy multi-criteria decision-making (MCDM) techniques with a fuzzy multi-objective mixed integer nonlinear programming (MOMINLP) mathematical model to optimize triple bottom line (TBL) sustainability and resilience criteria simultaneously for a multi-modal, multi-echelon supply chain network. The proposed framework has been implemented using real-time data collected from the pharmaceutical industry. The results show that among the TBL sustainability criteria, product price, past business, innovative capability, and information disclosure rank as the most significant sub-criteria for the DMs in the pharmaceutical industry, while robustness and flexibility are considered the most valued attributes for potential suppliers as far as the resilience criterion is concerned. An assessment of the results has revealed that transfer cost and custom clearance cost together comprise more than two-thirds of the overall cost of the supply chain network. It has also been noted that inland transportation of goods is dominated by rail as the most preferred mode of transport. Transportation by rail is particularly preferred by suppliers located in geographically contiguous countries.

Integrated optimization of demand-driven timetable, train formation plan and rolling stock circulation with variable running times and dwell times

Timetable, train formation plan and rolling stock circulation are the key operational issues for efficient railway operation. The three issues are optimized sequentially based on the order of the operational plan. Sequential optimization manner cannot balance the costs of the three stages effectively and could create an infeasible solution for a later stage when the resources are limited. In addition, because of the computational complexity, multiple variable elements, such as the variable running times, variable dwell times and the coupling/decoupling operations, of a transportation system are ignored. This paper focuses on optimizing timetable, train formation plan and rolling stock circulation simultaneously to minimize costs and meet passenger demand. The key to solving the problem is to determine operation times (i.e., arrival times, departure times, running times and dwell times), the formation type of each train service and rolling stock connections (including the turnaround operations and the coupling/decoupling operations) between these train services. Considering the passenger costs and operator costs, a multi-objective mixed-integer nonlinear programming (MINLP) model is proposed to minimize the total passenger waiting time (TWT), the number of rolling stocks (NR), the number of formations (NF) and the number of coupling/decoupling operations (NC) based on a time–space network. The multi-objective MINLP model is further reformulated into a single-objective mixed-integer linear programming (MILP) model by logical linearizing, piecewise linearizing and fuzzy programming. A numerical example is used in which the exact solution of MINLP obtained by the BARON solver is compared with the approximate solution of MILP obtained by the CPLEX solver to verify the effectiveness of the piecewise linearization. Finally, the model is tested on a real-world case study of the Jinshan Line in Shanghai. The CPLEX solver can efficiently produce the approximate solution within a given computation time in acceptable gaps. The results demonstrate that the integrated model can reduce the number of rolling stocks and improve the utilization rate of rolling stocks. Furthermore, the integrated model can effectively resolve the shortage of rolling stocks when only one depot has rolling stocks or the number of available rolling stocks is limited. In addition, considering the multiple variable elements have a significant effect on the improvement of all the objectives and reduce both the passenger costs and the operator costs.

Multi-energy optimization under the water-energy-carbon nexus in a typical iron and steel plant

The multi-energy system in iron and steel plants has strong coupling characteristic, which makes the energy distribution complex and difficult in energy management. Additionally, the steel works is a manufacture process with high-carbon emissions, and it is vital to assess the environmental stress from the sights of nexus between energy, water and carbon emission. In this study, a multi-energy and multi-objective mixed integer non-linear programming (MINLP) model is established to optimize the energy system under the water-energy-carbon nexus in iron and steel plant. And the multi-energy is considered the couple of gas-steam-electricity. The multi-objective functions include the economic performance, the CO2 emissions, the water generation, and the global energy efficiency. Due to the contradictory of the objective functions, the utopia tracking approach is used to normalize and assess the functions. To fit the actual situation of the equipment, this paper made a fitting curve for the energy efficiency of the equipment. The minimum economic operation cost results show that the studied iron and steel plant has great potential in reducing economic cost (7.6 %), emission mitigation (4.7 %), system water production improvement (807 t) and global energy efficiency (54.48 %). Besides, the research will help the iron and steel plant to reach the carbon peak and carbon neutrality target.