Multi-objective Nonlinear Programming Research Articles

AC energy islands for the optimal integration of offshore wind energy resources: Operation strategies using multi-objective nonlinear programming

The increasing need for integrating offshore wind generation into power systems has highlighted energy islands as a promising solution. Such islands also could incorporate responsive infrastructure for improving grid flexibility such as energy storage and hydrogen production. AC energy islands could be particularly cost–benefit effective for short and medium distances between wind power parks and onshore grids. However, the implementation of AC energy islands presents challenges from the viewpoints of voltage stability, power dispatch and reliable operation. This paper develops optimal operation strategies for AC energy islands including: i) a nonlinear optimal power flow approach for controlling the reactive power compensation systems; ii) a finite horizon mathematical programming approach for the management of BESS and hydrogen production systems; and iii) a multi-objective programming approach for maximizing the active power delivered to the onshore power grid while minimizing the nodal voltage deviations simultaneously. Results show that the single-objective approach for real and reactive power dispatch reduces voltage deviations by around 20 % and line currents by over 70 % in the evaluated test system, compared to the non-optimal scenario. Moreover, the incorporation of energy storage in AC energy island test system increased the capacity for power dispatch over 10 %. Additionally, the multi-objective approach is effective in aligning the nodal voltages with nominal values and maximizing the power delivered to the onshore grid. Results show that with a small 1% reduction in power delivery, the proposed multi-objective approach achieved an approximate 50 % decrease in nodal voltage compared to the single-objective approach.

Adapting to climate change in arid agricultural systems: An optimization model for water-energy-food nexus sustainability

Sustainable management of water, energy, and food (WEF) under climate change will be a significant challenge for arid agricultural systems. This study developed a fractional non-linear multi-objective programming (FNLMOP) model to optimize resource allocation and improve agricultural sustainability in these systems under climate change. The model was designed in the framework of the WEF nexus to simultaneously improved energy productivity (profit/energy), and water productivity (profit/water), while mitigating environmental damage (damage to groundwater resources/output) and ensuring food security in an arid watershed in Iran. The long Ashton research station weather generator (LARS-WG) and the coupled model intercomparison project 6 (CMIP6) were employed to project climate parameters for both future dry and wet conditions. The sustainability of the optimal solutions was then assessed using a hybrid criteria importance through intercriteria correlation (CRITIC)-VIKOR approach. The optimal solutions revealed a reduction in the land under cultivation and produced less water-intensive crops. The optimization model can ensure WEF security, enhancing agricultural system sustainability by optimizing crop cultivation patterns and resource allocation. Current crop choices were highly inefficient with the bigger changes being from the current crops to optimal crops. Climate change showed a substantial but lesser influence on optimal crop choice.

Finding Efficient Solutions in Interval Multi-Objective Linear Programming Models by Uncertainty Theory

Interval multi-objective linear programming (IMOLP) ímodels are one of the methods to tackle uncertainties. In this paper, we propose two methods to determine the efficient solutions in the IMOLP models through the expected value, variance and entropy operators which have good properties. One of the most important properties of these methods is to obtain different efficient solutions set according to decision makers’ preferences as available information. We first develop the concept of the expected value, variance and entropy operators on the set of intervals and study some properties of the expected value, variance and entropy operators. Then, we present an IMOLP model with uncertain parameters in the objective functions. In the first method, we use the expected value and variance operators in the IMOLP models and then we apply the weighted sum method to convert an IMOLP model into a multi-objective non-linear programming (MONLP) model. In the second method, the IMOLP model using the expected value, variance and entropy operators can be converted into a multi-objective linear programming (MOLP) model. The proposed methods are applicable for large scale models. Finally, to illustrate the efficiency of the proposed methods, numerical examples and two real-world models are solved.

Multi-Objective Constrained Optimization Model and Molten Iron Allocation Application Based on Hybrid Archimedes Optimization Algorithm

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace’s production capacity and the steelmaking converter’s consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods.

Rheological modelling of carbonyl-iron particles (CIP) paraffin oil-based magneto-rheological fluids

New types of magneto-rheological fluids are increasingly being developed lately, but there is a dearth of information on the performance of commonly used rheological models for emerging MRFs such as carbonyl-iron particles (CIP) paraffin-oil-based MRF. This work aims to investigate the performance of some rheological models for application in predicting shear stress and yield strength in an emerging MRF suitable for flow-mode applications. CIP, low viscosity paraffin oil, and lithium grease were used as magnetic particles, carrier fluid, and additives, respectively, to prepare the MRF. Based on different mixing proportions determined with the Taguchi method of experimental design, sixteen samples were prepared following a standard procedure. For each sample, the values of viscosity and shear stress were determined using a viscometer and rheometer, respectively, with an incorporated self-developed magnetic device. By fitting the data and using the multi-objective nonlinear programming solver in Micro-soft Excel to determine optimum parameters for each model, the Bingham Model, Herschel–Buckley Model, Casson Model, Cross models, and Power-law were used to model the experimental data. Predicted shear stress values and yield strength were then analyzed using ANOVA at a 5% confidence level. The relative errors were determined using RMSE, Mean Square Error, and Mean Absolute Error. There was a significant variation in the predicted outcomes of all the models. Overall, all the models gave relatively acceptable results. However, the Herschel-Buckley model gave the best results, while the Casson model gave the worst results, judging by their values of errors. It is shown that the Herschel-Buckley model should be best used for predicting the rheological characteristics of CIP and paraffin oil-based MRF.

A fairness-based multi-objective distribution and restoration model for enhanced resilience of supply chain transportation networks

Disruptive events play a significant role in the performance of supply chain networks (SCNs) due to their high dependency on transportation networks. Therefore, it is critical to develop coordinated strategies that consider (i) efficient restoration plans for the transportation network (TN) and (ii) distribution plans for downstream SCN, which consider critical aspects such as road congestion, travel time, and required service levels. Thus, we propose a novel multi-objective non-linear mixed-integer programming (NMIP) model to deal with disruptions in transportation networks while maximizing SCN performance. We developed a model for optimal restoration that reduces the effects of disruptions that disrupt the performance of the road TN and SCNs while considering a fair distribution of commodities. The model provides optimal restoration strategies for the TN after unpredicted events, not only based on a cost-effectiveness approach but also on the fair distribution of commodities among demand nodes on a complex network structure with a multi-supplier, multi-demand, and multi-commodity framework. To illustrate the model's capabilities, we study the transportation of commodities in Colombia and how disruptions impact their SCN performance. The results show that a fairness-based distribution helps to obtain satisfaction rates faster when compared to restoration plans based on cost-effectiveness only.

Delivering Goods Sustainably: A Fuzzy Nonlinear Multi-Objective Programming Approach for E-Commerce Logistics in Taiwan

With the booming development of e-commerce, the importance of controlling carbon emissions has become increasingly prominent in Taiwan. This study explores the trade-offs among time, cost, quality, and carbon emissions (TCQCE) in e-commerce logistics. Will carbon emissions mitigation lead to decreased logistics efficiency and increased costs? This article differs from other studies that use precise numbers and linear model situations. This study adopts fuzzy theory, nonlinear methods, and multi-objective programming models closer to the actual situation to study the decision-making between delayed logistics delivery times and reduced carbon emissions. This article also uses Project D as a case to enhance readers’ understanding of decision-making methods in real-life e-commerce logistics cases. The results show that extended delivery times could significantly reduce carbon emissions, ranging from 5259.31 to 419,199.60 tons, and reduce delivery quality under the 90.00% threshold and even under 75.25%. Extending delivery times is a viable business strategy, particularly by extending delivery to push carbon reduction policies to minimize environmental impact. However, consumer acceptance is crucial, as consumers willing to embrace longer wait times can significantly contribute to emission mitigation and support businesses committed to sustainability. This research uses a fuzzy nonlinear multi-objective programming model (FNMOPM) to contribute novel time management to mitigate carbon emissions. Moreover, this study uses a fuzzy and nonlinear approach to fill in the gaps of previous research to balance the efficiency and carbon emission mitigation goals of ESG (environmental, social, and governance) principles. The framework presented in this article solves the complex trade-off situations in the TCQCE issues. This article provides practical, actionable guidance for decision-making regarding sustainable e-commerce logistics, instilling confidence in its implementation.

توصيف حل البرمجة غير الخطية متعددة الأهداف ذات دوال هدف استقرابية و معلمات ضبابية في القيود

This paper presents a solution to multiple objective non-linear programming (MONLP) problems with rough objective functions and constraints with fuzzy parameters, we offer an algorithm to solve this type of problem, where we deal with multiple objective functions first, then with the fuzziness of the constraint parameter Characterizing, second and third, we deal with the roughness of the objective function. So, the problem finally turns into a non-linear programming problem with crisp objective functions and constraints. Finally, an illustrative example is given to show the application of the algorithm. Keywords: Multiobjective non-linear programming (MONLP), rough function, Fuzzy number, Ranking function.

Coupling management ecosystem service supply-supply trade-offs and supply–demand trade-offs: Framework and practice

Ecosystem services (ESs) are the bridge between ecosystem and social system, and how to effectively manage different types of ES trade-offs is the key barrier to ensure that ecosystems provide sustainable benefits for human beings. The objective of this study is to propose a theoretical and methodological framework for the coupled management of ES supply-supply trade-offs and demand-demand trade-offs and to propose an ES trade-offs management scheme for the study area (Jiangxi Province) according to this framework. In this study, we evaluated the provision of ES and the intensity of two types of ES trade-offs in the study area through InVest model, and explored the driving mechanism of the two types of ES trade-offs through redundancy analysis. Finally, we proposed a land use structure in the study area that alleviates the intensity of both types of ES trade-offs through multi-objective nonlinear programming. The results showed that: (1) the water yield service supply in Jiangxi Province showed a pattern of high in the north and low in the south, and the carbon sequestration service supply showed a pattern of high in the south and low in the north. (2) The supply-supply trade-off intensity of two ES is generally low in the north and high in the south, and the supply–demand trade-off intensity of water yield service and carbon sequestration service is basically high in the densely populated area in the north of Jiangxi. (3) Forestland area, farmland area and water area are the supply–demand trade-off driving forces of water yield service and carbon sequestration service, grassland area is an independent driving force of carbon sequestration service, and farmland area and cultivated land area are the supply-supply trade-off driving forces. The study shows that in order to achieve the lowest supply-supply trade-off intensity and supply–demand trade-off intensity in Jiangxi Province at the same time, the forestland should reach at least 104470 km2, the water area should reach 12,900.7 km2, the farmland area should reach 281333.3 km2, and the grassland area should increase to 15,457.9 km2. The results are expected to provide a new perspective for ecosystem management research.

Research on Pricing and Replenishment Strategies for Vegetable Commodities Based on an Enhanced Nonlinear Objective Programming Model

With the increasing consumption of fresh food ingredients in the Chinese market and the perishable nature of vegetable commodities, which represent the largest proportion, optimizing procurement strategies plays a crucial role in enhancing the profitability of supermarkets. This has garnered significant attention from scholars and practitioners. Drawing on principles from microeconomics, this study employs multiple linear regression to describe the relationship between pricing and sales volume. Additionally, time series forecasting methods are utilized. By considering both supermarket profitability and social welfare maximization as optimization objectives, single-objective optimization and multi-objective nonlinear programming models are established. Various decision strategies for supermarkets under different scenarios are discussed, and a satisfactory decision is obtained by solving the models using differential evolution algorithm. Through research on the expected conditions and data provided by real supermarkets, this paper provides guidance for intelligent supermarket procurement strategies and supply chain management in practical settings.

Multi-objective non-linear programming problem with rough interval parameters: an application in municipal solid waste management

In dealing with the real-world optimization problems, a decision-maker has to frequently face the ambiguity and hesitancy due to various uncontrollable circumstances. Rough set theory has emerged as an indispensable tool for representing this ambiguity because of its characteristic of incorporating agreement and understanding of all the involved specialists and producing more realistic conclusions. This paper studies an application of the rough set theory for a multi-objective non-linear programming problem that originates for the management of solid wastes. Municipal solid waste management is a global problem that affects every country. Because of the poor waste management system in many nations, the bulk of municipal solid waste is disposed of in open landfills with no recovery mechanism. Hence, an effective and long term waste management strategy is the demand of the day. This research offers an incinerating, composting, recycling, and disposing system for the long-term management of the municipal solid waste. A model for the municipal solid waste management with the goal of minimizing the cost of waste transportation, cost of waste treatment and maximizing the revenue generated from various treatment facilities is developed under rough interval environment. To tackle the conflicting nature of different objectives, an approach is proposed that gives the optimistic and pessimistic views of the decision-maker for optimizing the proposed model. Also, the biasness/preference of the decision-maker for a specific objective is handled by establishing the respective non-linear membership and non-membership functions instead of the linear ones. Finally, to demonstrates the practicality of the proposed methodology, a case study is solved and the obtained Pareto-optimal solution has been compared to those obtained by the existing approaches.

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.

A product family-based supply chain hypernetwork resilience optimization strategy

In product manufacturing, the supply chain can be adversely affected by the occurrence of uncertain risk events. Optimizing supply chain resilience is a challenging multi-objective nonlinear programming problem. Due to the development of mass customization production modes, manufacturing enterprises are more concerned with the service supply capability for a given product family. However, optimizing supply chain resilience while considering the product family is neglected in existing works. To tackle it, this paper first establishes a product family-based supply chain hypernetwork, mapping the product bill of materials to the potential suppliers. Second, a product family-based supply chain hypernetwork resilience optimization strategy (PF-SCHROS) is proposed using an improved genetic algorithm. Experiments are carried out to compare the proposed strategy with the traditional methods including interior point method, sequential quadratic programming, and genetic algorithm. Results show that our approach greatly reduces the loss originating from supplier chain disruption and can adequately improve supply chain service capability in various disruption scenarios.

Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment

Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it’s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions and the constraints are linear Diophantine fuzzy numbers (LDFNs). Here we find the solution of the nonlinear programming problem by using Karush-Kuhn-Tucker condition. A numerical example is presented.

A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem

In this study, we propose a novel multi-objective nonlinear mixed-integer mathematical programming model for the transit network design and frequency setting problem that aims at designing the routes and determining the frequencies of the routes to satisfy passenger demand in a transit network. The proposed model incorporates the features of real-life transit network systems and reflects the views of both passengers and the transit agency by considering the in-vehicle travel time, transfers, waiting times at the boarding and transfer stops, overcrowding and under-utilization of vehicles, and vehicle fleet size. Unlike previous studies that simplify several aspects of the transit network design and frequency setting problem, the proposed model is the first to determine routes and their frequencies simultaneously from scratch, i.e., without using line and frequency pools while considering the aforementioned issues, such as transfers and waiting. We solve the proposed model using Gurobi. We provide the results of what-if analyses conducted using a real-world public bus transport network in the city of Kayseri in Türkiye. We also present the results of computational tests implemented to validate and verify the model using Mandl benchmark instances from the literature. The results indicate that the model produces better solutions than the state-of-the-art algorithms in the literature and that the model can be used by public transit planners as a decision aid.

A Decision-Making Model to Determine Dynamic Facility Locations for a Disaster Logistic Planning Problem Using Deep Learning

Disaster logistics management is vital in planning and organizing humanitarian assistance distribution. The planning problem faces challenges, such as coordinating the allocation and distribution of essential resources while considering the severity of the disaster, population density, and accessibility. This study proposes an optimized disaster relief management model, including distribution center placement, demand point prediction, prohibited route mapping, and efficient relief goods distribution. A dynamic model predicts the location of post-disaster distribution centers using the K-Means method based on impacted demand points’ positions. Artificial Neural Networks (ANN) aid in predicting assistance requests around formed distribution centers. The forbidden route model maps permitted and prohibited routes while considering constraints to enhance relief supply distribution efficacy. The objective function aims to minimize both cost and time in post-disaster aid distribution. The model deep location routing problem (DLRP) effectively handles mixed nonlinear multi-objective programming, choosing the best forbidden routes. The combination of these models provides a comprehensive framework for optimizing disaster relief management, resulting in more effective and responsive disaster handling. Numerical examples show the model’s effectiveness in solving complex humanitarian logistics problems with lower computation time, which is crucial for quick decision making during disasters.

FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS

Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.

Dynamic and harmonious allocation of irrigation water resources under climate change: A SWAT-based multi-objective nonlinear framework

Efficient allocation of water resources in irrigation districts can alleviate regional water shortages and promote sustainable irrigated agriculture development. However, existing research on water resource allocation in irrigation districts does not address the lack of coordination within the “diversion-delivery-irrigation” chain for multiple water sources and users in a changing environment. Hence, poor water supply and demand matching, low efficiency and poor climate change responses pose challenges for efficient water resource allocation in irrigation districts. Therefore, this study couples the SWAT runoff simulation model with a multiobjective nonlinear programming model and proposes a weather-driven dynamic and optimal allocation model for multiple water sources. This model accounts for fluctuations in water supply and fine-tunes the allocation of water resources to different water sources, different channels and different crop fertility periods in the irrigation area. The model is designed to achieve synergistic improvements in water supply and demand, economic efficiency, equity in water distribution and efficiency in water use. The model was applied to the Qindeli Irrigation District in Heilongjiang Province. The results show that an increase in water supply at the head of the channel promotes a synergistic increase in economic efficiency and water supply and demand matching. This model can improve water use efficiency under water scarcity by reasonably optimizing the water use structure of the irrigation district. Compared with the traditional irrigation method, the optimized model saves 4 % of water and increases yield by 399 kg/ha, economic efficiency by 0.2 yuan per cubic meter of water, water use efficiency by 9 %, and water supply and demand matching by >80 % at all stages of fertility. The model ensures that water resources are allocated in an equitable manner at all levels.

An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α, we can solve DM from the set of α-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α-cut analysis bestowing the degree α given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.