Multi-objective Nonlinear Programming Research Articles

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.

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.

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.

A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

AbstractGlobal air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the $\varepsilon$ -constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gökçen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

A class of nonlinear multi-objective mixed integer programming model for oil and gas portfolio and algorithm solution

This paper is concerned with the oil & gas assets portfolio. A multi-objective portfolio model of oil & gas assets is studied from two perspectives—scale and revenue. Considering the nonlinear and integer constraints in the model, a class of oil & gas assets portfolio model of nonlinear multi-objective mixed integer programming is established. The weight of the multi-objective is solved by the support vector machine model. A hybrid genetic algorithm, which uses the position displacement strategy of the particle swarm optimizer as a mutation operation, is applied to the optimization model. Finally, two examples are applied to verify the effectiveness of the model and algorithm.

Multiobjective Collaborative Optimization Method for the Urban Rail Multirouting Train Operation Plan

The Train Operation Plan (TOP) of urban rail transit (URT) is a comprehensive plan for the operation of trains, the use of facilities and equipment, and the organization of other operational tasks. The TOP should not only be formulated in terms of time-varying passenger flow periods, but it should also be arranged to consider the substitutability of trains between multiple routes combined with the passenger choice. Based on the principle of “operating by the flow” and the requirement for precise allocation of transport capacity for multiple routes, this article constructs a multiobjective nonlinear integer programming model by taking the minimized generalized travel cost of passengers, total running mileage of trains, fluctuation of trains for each route (as optimization targets), and the combination of requirements of both headways and fully loaded rates as constraints. A multiobjective genetic-based algorithm is designed to simultaneously optimize the TOP and the two-way train stopping time in each period. Finally, the proposed model and algorithm are validated with the real data from the Guangzhou Metro Line 2. The results show that the Pareto optimal TOP and dynamic train stopping time are significantly improved compared to the original values.

Multi-objective optimization for AGV energy efficient scheduling problem with customer satisfaction

<abstract><p>In recent years, it has been gradually recognized that efficient scheduling of automated guided vehicles (AGVs) can help companies find the balance between energy consumption and workstation satisfaction. Therefore, the energy consumption of AGVs for the manufacturing environment and the AGV energy efficient scheduling problem with customer satisfaction (AGVEESC) in a flexible manufacturing system are investigated. A new multi-objective non-linear programming model is developed to minimize energy consumption while maximizing workstation satisfaction by optimizing the pick-up and delivery processes of the AGV for material handling. Through the introduction of auxiliary variables, the model is linearized. Then, an interactive fuzzy programming approach is developed to obtain a compromise solution by constructing a membership function for two conflicting objectives. The experimental results show that a good level of energy consumption and workstation satisfaction can be achieved through the proposed model and algorithm.</p></abstract>

Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions

This paper introduces cooperative continuous static games (CCSG) with parameters in the cost functions of the players and in the right-hand side of the constraints. The CCSG is converted into the corresponding multi-objective nonlinear programming problem. The resulted nonlinear programming problem is converted into the single objective nonlinear programming problem through the use of the weighted sum method. A solution method for obtaining the stability set of the second kind without differentiability for the CCSG is presented using Karush-Kuhn-Tucker conditions. A numerical example is given for the illustration.

Multi-objective non-linear solid transportation problem with fixed charge, budget constraints under uncertain environments

ABSTRACT Transportation-based models are widely used to solve real-life problems such as supply chain problems, inventory level problems, business models, management problems, etc. The parameters of these problems have been conventionally measured as deterministic. However, these parameters have vagueness due to the uncertainty in the data sets. Such uncertainty of the parameters is generally measured using randomness (probability theory) or fuzziness (fuzzy theory), with certain assumptions and limitations. Closed intervals interpretation is another concept to deal with the uncertainties of real-world issues in recent decades, avoiding the limitations in probability theory and fuzzy set theory. This study formulates a fixed-charged multi-objective non-linear solid transportation with parameters such as availability of items, conveyance capacity, transportation cost, requirement, and budget for destinations in the form of closed intervals, where objectives are minimization of total transportation cost and action of time under the restriction over budget. An efficient solution procedure is developed with the help of interval analysis based on the parametric perception of intervals. Initially, the objective functions are converted into a crisp function using multiple integrations, and as a result, the problem is converted into a deterministic multi-objective non-linear programming problem. In addition, a real-world numerical problem is considered for testing the developed solution process for greater comprehension and clarity.