Nonlinear Multi-objective Optimization Research Articles

An Actual Case Study of a Deterministic Multi-Objective Optimization Model in a Defined Contribution Faculty Pension System

The optimal management of pension funds has become increasingly critical. As the population ages, the effective management of pension funds is essential for the social security system. The primary goal of this paper is to develop a deterministic nonlinear multi-objective optimization model to determine the contribution rates in a defined contribution pension system. The computational optimization model was implemented using the LINGO language. In the first part of this study, three main scenarios were analyzed considering different inflation rates, focusing on the objective function that minimizes the salary percentages workers pay when saving for a specified period while aiming to achieve a certain number of coverage years. The first scenario assumes that the worker desires an economic quality equivalent to their working life, showing that contribution rates range from 10% to 30% (with a 3% inflation rate). The second scenario posits that the worker only requires 80% of their equivalent salary during retirement, resulting in contribution rates directly proportional to those in scenario 1 (using the same parameters). The third scenario speculates that inflation may reach 7% per year, causing contribution rates to rise significantly from 40% to 80%. Finally, the Pareto front illustrates the trade-off between the contribution rate and the coverage years based on scenario 1 parameters.

Lagrange’s Interpolation Embedded Multi-objective Genetic Algorithm to Solve Non-linear Multi-objective Optimization Problems

Lagrange’s Interpolation Embedded Multi-objective Genetic Algorithm to Solve Non-linear Multi-objective Optimization Problems

Integrated LI-NSGA-II Approach for Solving the Non-linear Multi-objective Optimization Problem

Real-world engineering projects frequently involve complex, non-linear multi-objective optimization challenges. Traditional methods like PERT/CPM and basic heuristics often fail to provide optimal solutions in such scenarios. Multi-objective evolutionary algorithms, such as genetic algorithms and non-dominated sorting genetic algorithms, are more effective for identifying true Pareto solutions. Among these, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is a well-known algorithm for solving multi-objective optimization problems. This study presents an integrated approach, called LI-NSGA-II, which combines Lagrange's Interpolation (LI) with NSGA-II to solve non-linear multi-objective optimization problems in real-world projects. In this LI-NSGA-II approach, LI is used to handle the non-linearity of competing objectives, whereas NSGA-II optimizes these objectives to find optimal solutions. The outcomes achieved through the LI-NSGA-II approach are ideal for real-time monitoring and control of non-linear multi-objective optimization problems.

Underwriting Decision Modeling Based on Regional Hazard Assessment and Urban Resilience

In recent years, frequent extreme weather disasters have posed serious challenges to the economic social, and post-disaster recovery capabilities of places such as the United States, and original insurance models and payout strategies are difficult to adapt. Scientific assessment and response to natural disaster risks have become a key topic. This paper presents the Urban Resilience Index (URI) derived from 18 indicators. The ability of the city itself is rationally assessed for disaster resilience, which better helps insurance companies predict the loss compensation caused by disasters. This study starts by analyzing the risk of disasters in various regions of the United States, takes the intensity and frequency of disasters and the toughness of the city's resistance to disasters into account, and uses nonlinear multi-objective optimization to derive the threshold value of the payout strategy in a certain region to be around 0.21 and 0.94, respectively, and at the same time, after the control of the scalar function of the number of iterations is between 10 and 15 times, the final determination of the insurance model that responds to the different regions and verifies. The insurance model to cope with other areas is finally determined and its feasibility is verified.

An Activity Network Design and Charging Facility Planning Model Considering the Influence of Uncertain Activities in a Game Framework

In the planning of public charging facilities and the charging activity network of users, there is a decision-making conflict among three stakeholders: the government, charging station enterprises, and electric vehicle users. Previous studies have described the tripartite game relationship in a relatively simplistic manner, and when designing charging facility planning schemes, they did not consider scenarios where users’ choice preferences undergo continuous random changes. In order to reduce the impacts of queuing phenomenon and resource idleness on the three participants, we introduce a bilateral matching algorithm combined with the dynamic Huff model as a strategy for EV charging selection in the passenger flow problem based on the three-dimensional activity network of time–space–energy of users. Meanwhile, the Dirichlet distribution is utilized to control the selection preferences on the user side, constructing uncertain scenarios for the choice of user charging activities. In this study, we establish a bilevel programming model that takes into account the uncertainty in social responsibility and user charging selection behavior. Solutions for the activity network and facility planning schemes can be derived based on the collaborative relationships among the three parties. The model employs a robust optimization method to collaboratively design the charging activity network and facility planning scheme. For this mixed-integer nonlinear multi-objective multi-constraint optimization problem, the model is solved by the NSGA-II algorithm, and the optimal compromise scheme is determined by using the EWM-TOPSIS comprehensive evaluation method for the Pareto solution set. Finally, the efficacy of the model and the solution algorithm is illustrated by a simulation example in a real urban space.

A Non-Linear Multi-Objective Service Composition Optimization for Smart Agriculture with Lagrange’s Interpolation-based Evolutionary Algorithm

A Non-Linear Multi-Objective Service Composition Optimization for Smart Agriculture with Lagrange’s Interpolation-based Evolutionary Algorithm

Enhancing hosting capacity for electric vehicles in modern power networks using improved hybrid optimization approaches with environmental sustainability considerations

The increasing adoption of electric vehicles (EVs) presents both opportunities and challenges for power networks. While EVs have the potential to reduce carbon emissions, accommodating their growing power demand requires careful planning to prevent overloading and mitigate environmental impacts. This paper introduces an integrated hosting capacity model to facilitate higher EV penetration while maintaining environmental standards. In addition to EV charging stations, the model incorporates transmission lines, reactive power compensators, energy storage systems, and thyristor-controlled series compensators to ensure a reliable power supply. The model aims to maximize EV charging station deployment, minimize greenhouse gas emissions, and optimize net present value through hosting capacity strategies. Three hosting capacity plans are proposed to analyze the impact of prioritizing one of these objectives over the others in network configurations. Accurate EV demand forecasting is critical for this model, and a swarm intelligence forecasting algorithm is proposed to explore various forecasting approaches. The model is complex and involves nonlinear multi-objective optimization. To solve it, a new hybrid optimization algorithm is introduced, combining the features of the Marine Predators Algorithm and the Honey Badger Algorithm. Three hybridization schemes—Series Hybrid Scheme, Population Division Scheme, and Switching Strategy Scheme—are developed to address the optimization challenges effectively. The results show that the first and second hybridization schemes are the most effective for solving the EV load forecasting models, with a robustness of at least 90%. In contrast, the robustness of the third scheme reaches only 30% in some models. Simulation studies on the IEEE 9-bus network and the IEEE 30-bus system validate the model’s effectiveness in integrating EVs while achieving environmental sustainability objectives. The findings show the superiority of the proposed hybrid schemes in solving the hosting capacity model in terms of finding optimal solutions. However, the third scheme required less computing time than the others, with its convergence time being at least 33.3% shorter.

Pareto-critical equilibrium condition for non-linear multiobjective optimization problems with applications

The new (necessary) Pareto-critical equilibrium condition (PCEC) discussed in this study is based on the Pareto-critical condition for non-linear optimization problems. The proposed condition is evaluated by defining a multiobjective optimization problems (MOOPs) subject to a set of constraints. Then this MOOPs is converted to a single objective optimization problem by using the available optimization techniques, for instance, the weighted sum method, and solved by the non-linear Nelder-Mead simplex method. The obtained solution points satisfy the proposed PCEC of an unconstrained multiobjective optimization problem (MOOPs) under the convexity assumption. This PCEC is evaluated in a search that either results in a point inside the feasible region or a point for which the PCEC holds. The resulting Pareto-critical equilibrium condition is globally valid for convex problems. Numerical experiments are carried out in order to clarify the proposed condition's validity. Moreover, the proposed PCEC is used to place a downlink transmit beamforming system base station in an ideal position as a first application and is also employed in situations where there are multiple agents working towards a common goal as a second application.

MILP-Based Approach for High-Altitude Region Pavement Maintenance Decision Optimization

Affected by climatic factors (e.g., low temperature and intense ultraviolet radiation), high-altitude regions experience numerous pavement diseases, which compromise driving safety and negatively impact user travel experience. Timely planning and execution of pavement maintenance are particularly critical. In this paper, considering the characteristics of pavement maintenance in high-altitude regions (e.g., volatility of traffic volume, seasonality of maintenance timing, and fragility of the ecological environment), we aim to derive optimal monthly maintenance plans. We develop a multi-objective nonlinear optimization model that comprehensively accounts for minimizing maintenance costs, affected traffic volume and carbon emissions, and maximizing pavement maintenance effectiveness. Utilizing linearization methods, the model is reconstructed into a typical mixed-integer linear programming (MILP) model, enabling it to be solved directly using conventional solvers. We consider five types of decision strategies to reflect the preferences of different decision-makers. Given the uncertainty of maintenance costs, we also utilize the robust optimization method based on the acceptable objective variation range (AOVR) to construct a robust optimization model and discuss the characteristics of optimistic, robust, and pessimistic solutions. The results suggest that different decision strategies show differences in the indicators of maintenance costs, affected traffic volume, carbon emissions, and pavement performance. When multiple decision objectives are comprehensively considered, the indicators are between the maximum and minimum values, which can effectively balance the decision needs of maintenance effectiveness, maintenance timing, and environmental protection. The number of maintenance workers, the requirement of the minimum pavement condition index (PCI), and the annual budget influence the maintenance planning. The obtained robust solution can somewhat overcome the conservative nature of the pessimistic solution. The method proposed in this paper helps address the complexities of pavement maintenance decisions in high-altitude regions and provides guidance for pavement maintenance decisions in such areas.

Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems

A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.

Global Optimization and Quantitative Assessment of Large-Scale Renewables-Based Hydrogen System Considering Various Transportation Modes and Multi-Field Hydrogen Loads

In the past, hydrogen was mostly produced from fossil fuels, causing a certain degree of energy and environmental problems. With the development of low-carbon energy systems, renewable energy hydrogen production technology has developed rapidly and become one of the focuses of research in recent years. However, the existing work is still limited by small-scale hydrogen production systems, and there is a lack of comprehensive research on the whole production-storage-transportation-utilization hydrogen system (PSTUH2S), especially on the modeling of different hydrogen transportation modes and various hydrogen loads in different fields. To make up for these deficiencies, the specific physical and mathematical models of the PSTUH2S are firstly described in this paper, with a full account of large-scale water-electrolytic hydrogen production from renewable power curtailment and grid power, various hydrogen storage and transportation modes, and multi-field hydrogen consumption paths. Furthermore, to achieve the maximum economic, energy, and environmental benefits from the PSTUH2S, a multi-objective nonlinear optimization model is also presented herein and then solved by the hybrid method combining the nonlinear processing method, the CPLEX solver and the piecewise time series production simulation method. Lastly, case studies are conducted against the background of a region in northwest China, where hydrogen consumption capacity in various years is accurately assessed and the potential advantages of the PSTUH2S are demonstrated. As the simulation results show, the power curtailment of renewable energy generation can be reduced by 3.61/11.87/14.72 billion kW·h in 2025/2030/2035, respectively, thus contributing to a 4.98%~10.09% increase in the renewable energy consumption rate and millions of tons of carbon emission reduction in these years. In terms of the total equivalent economic benefits, the proposed method is able to bring about a cost saving of USD 190.44 million, USD 634.66 million, and USD 865.87 million for 2025, 2030, and 2035, respectively.

Biomass-based Brayton-Stirling-AGMD polygeneration for small-scale applications in rural areas

The lack of access to electricity and clean water still affects a substantial proportion of rural areas worldwide, in particular the global south. This paper presents a sustainable polygeneration system that can provide electricity, heat, and drinking water by using agricultural residues in remote rural areas. This polygeneration system consists of a solid biomass-fueled Brayton-Stirling combined cycle system, a boiler, and an air-gap membrane distillation unit. Four different system operation modes were designed to examine the most ideal configurations for maximizing power output, overall efficiency, and/or clean water production, considering a polygeneration system designed for a rural village with daily demands of 13450 kWh electricity and 7.5 m3 drinking water. A thermodynamic analysis are employed to analyze and compare these modes, each operating under steady state conditions. The highest electricity output, up to 160 kW, while the highest clean water is up to 0.7 m3/h. The fuel consumption can reach 0.9 kWh/kg of solid fuel and provide up to 0.0045 m3 of freshwater. In addition, nonlinear multi-objective optimization is used to meet the power demands of typical day in rural areas by varying the polygeneration operation modes and turbine inlet temperature.

Designing a multi-purpose network of sustainable and closed-loop renewable energy supply chain, considering reliability and circular economy

Since renewable energy systems have a limited lifespan and cannot be used after a while, it seems imperative to pay attention to recycling and sustainability in the supply chain network design of these systems. Also, modern power systems have high complexity and a large number of problems that affect the reliability of electricity supply to consumers. Therefore, organizations should consider broader goals, including the maximum use of resources and the minimization of waste, which is known as lean economy. In this research, a multi-objective non-linear forward optimization model has been considered for the design of the supply chain network of photovoltaic and wind systems based on the aspects of stability and taking into account the reliability. Also, adding the reverse flow, in addition to the forward flow, is also considered, which, in addition to economic advantages, also pays attention to environmental and social issues. The objective function includes minimizing all costs and negative environmental effects as well as increasing reliability. In order to convert the multi-objective planning model into a single-objective one, the epsilon method of the enhanced constraint is used. Uncertainty has been considered for all variables (except binary variables) and parameters of demand, intensity of sun radiation and amount of wind speed. Then, the efficiency of the model has been investigated through its implementation on a case study and the results have been obtained. Eventually, the model's efficiency is illustrated by discussing a real-world case, through which prominent managerial results are acquired.

A novel solution methodology for electrical vehicles charging schedule in coordinated with full flexible resources in microgrid

This paper proposes a new model for the day-ahead Electric Vehicle charging schedule in Microgrids (MGs) with flexible resources such as Wind Turbine (WT) and Photovoltaic (PV) electrical power, Combined Heat and Power (CHP), Energy Storage Source (ESS), and load Demand Responses (DR). The proposed Mixed Integer Nonlinear Multi-Objective Optimization (MINMO) model considers uncertainty properties with optimal operation objects. The cost function, and power loss minimization are the proposed model's objects for considering optimal operation objects. This model is solved by a three-level decomposition method in master-sub problem presentation and Binary-Continues PSO algorithm (BC PSO) to quickly calculate the optimal solution. In the first layer, the main constraint of electric vehicle aggregators (EVAs) is satisfied by the binary PSO algorithm. According to the top-layer solution, flexible recourses are managed to satisfy the operation objects by the Bi-level Continues PSO algorithm in the second layer. Then, after converging to the optimum solution of these two layers, Electric Vehicles (EVs) charging stations are solved at the last layer by algebraic equations. Finally, the efficiency of the proposed method is illustrated via its application in IEEE 33-bus MG system. The numerical results show that the proposed solution methodology reduces the runtime of the problem up to 95 % compared to intelligence-based and full Newton–Raphson AC power flow method. Also, numerical results illustrate that considering CHP and DR in addition to the other flexible resources reduces the operation cost and power loss up to 21 % and 5 % respectively. In top of that the minimum total cost for day-ahead EV charging schedule by the proposed model and solution methodology is 578,312.7$.

An optimal approach of pure/mixed CO2 sequestration with producing hydrated natural gas: Physical insights and validation

In this contribution, an optimal approach is developed to sequestrate pure/mixed CO2 by dislodging the hydrated natural gas, the cleanest fossil fuel, thereby catching two birds by one stone. For depicting its intricacies, a transient thermo-kinetic swapping model is developed with considering first time the effect of permeability and water saturation, along with porosity involved in sediments of hydrate reservoir. The formulation takes into account various fundamental issues having practical relevance, like porous particles with uneven size and shape, surface dynamics involved in phase transformation, non-unity reaction order (i.e., nth order), among others. A mixed-integer nonlinear multi-objective sequential optimization (MOSO) problem is articulated within the framework of a robust global optimizer (i.e., nondominated sorting genetic algorithm II) to deal with two conflicting objectives, concerning minimization of absolute average relative deviation and maximization of swapping efficiency. This optimal approach is validated with laboratory and field data, showing its outperformance over the latest models at diverse geological conditions. The proposed model framework is employed for lab-scale cases to identify the optimal guest gas (CO2/N2) ratio that secures the maximum swapping efficiency. Simulation results suggest that the presented theoretical model is rigorous in interpreting these swapping dynamics in hydrates.

Determination of Optimal Locations and Parameters of Passive Harmonic Filters in Unbalanced Systems Using the Multiobjective Genetic Algorithm

This paper discusses the problem of optimal placement and sizing of passive harmonic filters to mitigate harmonics in unbalanced distribution systems. The problem is formulated as a nonlinear multiobjective optimisation problem and solved using the multiobjective genetic algorithm. The performance of the proposed algorithm is tested on unbalanced IEEE 13- and 37-bus three-phase systems. The optimal solutions are obtained based on the following objective functions: 1) minimisation of total harmonic distortion in voltage, 2) minimisation of costs of filters, 3) minimisation of voltage unbalances, and 4) a simultaneous minimisation of total harmonic distortion in voltage, costs of filters, and voltage unbalances. Finally, an analysis of the influence of uncertainties of load powers and changes in system frequency and filter parameters on filter efficiency was performed.

Optimizing tensile strength and energy consumption for FDM through Mixed-Integer Nonlinear Multi-objective optimization and design of experiments

This study presents a methodology for optimizing key parameters of a fused deposition modeling (FDM) printer to minimize energy consumption (EC) while exceeding a specified tensile strength (TS) threshold. Employing Design of Experiments (DoE) with Taguchi and Response Surface analysis, we identify influential parameters affecting TS and EC. A Mixed-Integer Nonlinear Multi-Objective Optimization model is then utilized to balance TS and EC, resulting in optimal parameter values. Validation using fabricated specimens demonstrates less than 5 % error in Tensile Strength and less than 2 % error in Energy Consumption, confirming the efficacy of the proposed methodology.

Research on Detection System of Intelligent Computer Optimization Algorithm for Concrete Mix Ratio Based on Big Data

PLC is used to complete the control function of the concrete proportioning system. The MCGS (Configuration Software Monitor and Control System) is used to realize the real-time monitoring, data management and fault warning of the whole monitoring system. The material feed and PLC control process in the feed system are emphatically introduced. A concrete proportioning design method based on multiple parameters is proposed. The nonlinear multi-objective optimization model of concrete mix ratio was established by stepwise regression analysis and complex optimization method. The problems of narrow range of variables and single form of objective and constraint in traditional linear optimization methods are solved, which makes the selection of optimal index simpler and more flexible. Through the calculation of examples, it is clear that this method can obtain the mixture that meets the use conditions, and can greatly save the experimental work and construction cost.

Multi-objectives transmission expansion planning considering energy storage systems and high penetration of renewables and electric vehicles under uncertain conditions

Transmission expansion planning (TEP) integrating electric vehicles (EVs) and renewable energy sources (RESs) is pivotal for the transition toward cleaner and more sustainable energy systems. One of the biggest challenges in TEP with EVs and RESs is the uncertainty inherent in their behaviors. Managing this uncertainty is critical for ensuring the grid's reliability and resilience, and for facilitating a seamless transition to EVs. A potent method for addressing uncertainties in power systems is the application of a scenario-based approach. However, the efficiency of this approach is contingent upon an increase in the number of representative scenarios, which, in turn, escalates computational time, making solving the TEP problem a crucial task. To tackle these challenges, this paper proposes a multi-objective resilience model for TEP, to advance towards more sustainable energy systems. The model seeks to strike a balance between economic, environmental, and technical considerations by minimizing planning costs, carbon dioxide emissions, and enhancing the voltage profile. Furthermore, the paper proposes a cascaded intelligent strategy to handle uncertainties and reduce computational complexity by reducing the number of representative scenarios without compromising system reliability. The adaptive neuro-inference system is designed to manage long-term uncertainties, while two fuzzy systems are developed to address short-term uncertainties. The problem is formulated as a complex non-linear multi-objective optimization problem. To address this, a hybrid approach combining the mountain gazelle optimizer and the multi-objective salp swarm optimizer is developed to solve the problem. The efficacy of the proposed method is validated on two separate test systems, demonstrating its superiority in maintaining system reliability while reducing computing time by at least 92 % in comparison with the considered traditional methods. The results also highlight the superior performance of the proposed hybrid algorithm compared to existing meta-heuristic algorithms in solving the TEP.

A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification

In recent decades, there has been a surge in demand for the development of renewable energies, leading to extensive research efforts focused on the gasification process. Consequently, a wide range of studies has been conducted to explore different feedstocks for gasification, with particular emphasis on plastic waste. Although a wide range of studies conducted various optimization methods for the gasification process, there was no specific study to employ metaheuristic methods in the field of plastic waste gasification. This study aimed to perform a multi-objective particle swarm optimization (MOPSO) method to solve a multi-objective plastic waste gasification optimization problem for enhancing energetic and exergetic viewpoints. Moreover, exact methods including non-linear optimization and response surface methodology (RSM) were conducted to be compared with the results derived from MOPSO. Pareto-front solutions obtained from MOPSO were ranked using grey relational analysis (GRA) and the optimum responses were 517 kJ/kg, 84 %, and 57 % for lower-heating value, cold gas efficiency, and exergy efficiency, respectively, which were compared to optimum options obtained from multi-objective non-linear optimization and RSM techniques. While the MOPSO model may not have performed as well as other methods in this particular problem, it is important to acknowledge its capabilities. Future research can concentrate on improving the behavior and performance of the MOPSO method when dealing with a larger number of points or when applied to different problem domains.