Nonlinear Multi-objective Optimization Model Research Articles

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$.

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.

Study on the Optimization of Wujiang’s Water Resources by Combining the Quota Method and NSGA-II Algorithm

Recently, the Chinese government has implemented stringent water requirements based on the concept of ‘Basing four aspects on water resources’. However, existing research has inadequately addressed the constraints of water resources on population, city boundaries, land, and production, failing to adequately analyze the interplay between water resource limitations and urban development. Recognizing the interconnectedness between urban water use and economic development, a multi-objective model becomes crucial for optimizing urban water resources. This study establishes a nonlinear multi-objective water resources joint optimization model, aligning with the “Basing four aspects on water resources” requirement to maximize urban GDP and minimize total water use. A genetic algorithm (NSGA-II Algorithm) is applied to solve this complex nonlinear multi-objective model and obtain the Pareto solution set, addressing information loss inherent in the traditional water quota method. The model was tested in Wujiang District, an area located in China’s Jiangsu Province that has been rapidly urbanizing over the past few decades, and yielded 50 non-inferior water resource optimization schemes. The results reveal that the Pareto solution set visually illustrates the competition among objectives and comprehensively displays the interplay between water and urban development. The model takes a holistic approach to consider the relationships between water resources and urban population, land use, and industries, clearly presenting their intricate interdependencies. This study serves as a valuable reference for the rational optimization of water resources in urban development.

Study on Supermarket Replenishment and Pricing Based on Time Series Forecasting Algorithm and Nonlinear Multi-Objective Optimization Model

Study on Supermarket Replenishment and Pricing Based on Time Series Forecasting Algorithm and Nonlinear Multi-Objective Optimization Model

Simultaneous evaluation of criteria and alternatives method-based site selection for solar hydrogen production plant in Inner Mongolia, China

In the context of achieving carbon neutrality, China's demand for renewable energy continues to grow, with the development of solar energy attracting widespread attention. Aiming at the problem that solar energy is not accessible at all times and the storage of excess power, this paper proposes a model for siting a solar hydrogen plant in Inner Mongolia based on Simultaneous Evaluation of Criteria and Alternatives (SECA). Firstly, considering the uniqueness of solar hydrogen production projects (SHPPs), we incorporate the criteria of hydrogen production capacity and local finance into the siting decision model. Secondly, the SECA method is employed to construct a nonlinear multi-objective optimization model, facilitating the direct determination of criterion weights and enhancing decision-making efficiency. Third, the convergence change of the coefficient β in the SECA method is used to rank the candidate cities by solving the optimization model to produce stable results. Finally, this study verifies the validity of the model used through sensitivity and comparative analyses. The results show that Chifeng is the best location for solar hydrogen production considering the three most important factors are hydrogen production capacity (11.7%), average humidity (12.4%) and average temperature (14.46%).

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

In Taiwan, numerous company logistics centers have embraced installing solar photovoltaic power stations (SPPSs) on their rooftops. The primary objective of this study is to expedite the generation of green electricity for sale, bolstering the logistics center’s income and enhancing its environmental, social, and governance (ESG) profile. How can we secure solar photovoltaic power station (SPPS) projects with expedited construction timelines, reduced investment costs, and heightened quality aligned with the long-term ESG objectives? The study applies the critical path method (CPM) to determine the item’s path. Next, the mothed leverages Zimmermann’s mathematical models for nonlinear multi-objectives and Yager’s fuzzy sets to enhance project efficiency, minimizing completion time and cost while maximizing the quality ratio. Subsequently, the project uses Liou and Wang’s defuzzification values and incorporates Dong’s fuzzy to accelerate calculations. In this case, Project HP’s item J, the construction time is reduced from 24.3 to 3.2 days, ensuring that construction quality meets an 85% standard. Item J necessitates expanding the fuzzy cost interval (4549.90, 15,416.65, 26,283.41) (it refers to a scope of possible costs). It becomes evident that construction time plays a pivotal role in controlling costs. For Project HP’s item H, the unit time quality decision ranges from TWD 238,000 to 240,000, to turn into a cost interval of TWD 215,100, 239,000, and 262,900. Consequently, cost transformation transitions from an active to a more passive role, with quality and construction time becoming the driving components. This study uses a fuzzy nonlinear multi-objective model to guide the decision analysis of SPPSs within logistics centers. This strategy enables decision-makers to streamline logistics center operations, ensuring time, cost, and quality (TCQ) alignment during SPPS installation, thereby advancing ESG sustainability goals.

Multi-Objective Job Rotation in Rice Seed Harvesting With Equitable Injury Risk and Cost Allocation

This article presents a non-linear multi-objective optimization model with four different objectives for manual rice seed harvesting, aiming to ensure members' fairness and mutual benefits for a group of rice field owners responsible for seed planting and a group of workers tasked with harvesting rice seeds. The harvesting plan primarily focuses on minimizing the average injury risk to workers and secondarily balances this risk among workers. Simultaneously, the model seeks to minimize and equitably allocate wage costs for rice field owners. Worker characteristics, including age, gender, and body mass index are considered to influence injury risk differentially. The optimal solution involves rotating workers to different rice stalk types in several fields, all within appropriate work and rest periods. This approach serves to prevent musculoskeletal disorders and fatigue among the workers while helping rice field owners reduce their costs. This collaborative planning has the potential to enhance sustainability within the farming community.

A Method to Co-Design Antenna Element and Array Patterns

In this paper, we develop a novel method to design the elements of an antenna array and their feed weights simultaneously. The method is based on formulating the design problem as a non-linear multi-objective optimization model that estimates the realized gain at certain angles as a function of the element-level port signals and impedances, and the array-level weights for the elements. This enables utilization of genetic algorithms to find optimal signals, impedances, and weights for given steering range requirements. As an example, an array consisting of multi-port antenna elements is simulated and modeled with its impedance and radiation matrices. These matrices are used in the calculation of realized gain with the model. The model is then applied as part of the method to find as wide scanning range for the array as possible. The antenna elements are designed such that the multi-port system can be reduced to a single feed with physically realizable matching components and a matching network. The array designed with the proposed method is also compared to a reference antenna array of the same size. Both the simulations and measurements verify that the method can provide substantial improvements in the scanning range as compared to the reference.

Grounding grid corrosion detection based on mini-batch gradient descent and greedy method

To ensure the speed, recall, and precision of the algorithm to solve the algorithm’s measurement failure due to the problem of high underdetermination and the deviation of some outgoing lines from accessible nodes, the ideal resistance method is proposed to diagnose the corrosion of the grounding grid. The information extraction algorithm, a two-way heuristic network resistance diagnosis method, is added. A non-linear multi-objective optimization model of the deviation between the measured potential and the real potential is established. This paper puts forward that the grounding network’s fault diagnosis is analogous to a neural network’s training process, which makes full use of the excellent robustness and rapidity of a neural network training method. Simultaneously, the algorithm adds the retraining method combined with the field excavation in training and proves its feasibility through the Grobner basis codimension theory in algebraic geometry. Through result verification, it is found that the new algorithm can avoid the inversion failure caused by the algorithm failure due to the lack of accessible nodes and the abnormal part of input data at the same time as a fast solution.

A Framework for Online Reverse Auction Based on Market Maker Learning with a Risk-Averse Buyer

The online reverse auction is considered as a new e-commerce approach to purchasing and procuring goods and materials in the supply chain. With the rapid and ever-expanding development of information technology as well as the increasing usage of the Internet around the world, the use of an online reverse auction method to provide the required items by organizations has increased. Accordingly, in this paper, a new framework for the online reverse auction process is provided that takes both sides of the procurement process, namely, buyer and seller. The proposed process is a multiattribute semisealed multiround online reverse auction. The main feature of the proposed process is that an online market maker facilitates the seller’s bidding process by the estimation of the buyer’s scoring function. For this purpose, a multilayer perceptron neural network was used to estimate the scoring function. In this case, in addition to hiding the buyer’s scoring function, sellers can improve their bids using the estimated scoring function and a nonlinear multiobjective optimization model. The NSGA II algorithm has been used to solve the seller model. To evaluate the proposed model, the auction process is simulated by considering three scoring functions (additive, multiplicative, and risk-aversion) and two types of open and semisealed auctions. The simulation results show that the efficiency of the proposed model is not significantly different from the open auction, and in addition, unlike the open auction, the buyer information was not disclosed.

Multi-Objective Optimization for Order Assignment in Food Delivery Industry with Human Factor Considerations

The order assignment in the food delivery industry is of high complexity due to the uneven distribution of order requirements and the large-scale optimization of workforce resources. The delivery performance of employees varies in different conditions, which further exacerbates the difficulty of order assignment optimization. In this research, a non-linear multi-objective optimization model is proposed with human factor considerations in terms of both deteriorating effect and learning effect, in order to acquire the optimal solutions in practice. The objectives comprised the minimization of the operational cost in multiple periods and the workload balancing among multiple employees. The proposed model is further transformed to a standardized mixed-integer linear model by the exploitation of linearization procedures and normalization operations. Numerical experiments show that the proposed model can be easily solved using commercial optimization softwares. The results indicate that the variance of employee performance can affect the entire delivery performance, and significant improvement of workload balancing can be achieved at the price of slight increase of the operational cost. The proposed model can facilitate the decision-making process of order assignment and workforce scheduling in the food delivery industry. Moreover, it can provide managerial insights for other labor-intensive service-oriented industries.

Global path planning and multi-objective path control for unmanned surface vehicle based on modified particle swarm optimization (PSO) algorithm

This paper investigates the novel path navigation method for an unmanned surface vehicle (USV), which is divided into two-stage: global path planning and path control. In the first stage, combined with the travelling salesman problem (TSP), a global path is obtained by maximizing the profit per unit time in multiple task locations. In the second stage, a nonlinear multi-objective optimization model is formulated for the path control between two task locations. In addition, fixed and time-varying currents are also considered for USV motion, which aims to avoid collision and take full advantage of the direction of currents. To solve the problem quickly and accurately, a chaotic and sharing-learning particle swarm optimization (CSPSO) algorithm is developed to solve the extended TSP and the nonlinear multi-objective model. Simulation experiments validate that the proposed hierarchical navigation method, CSPSO algorithm, and collision avoidance rules are effective and justifiable.

Reliability-Centered Maintenance Task Planning for Overhead Electric Power Distribution Networks

In this paper, it is presented an approach to match technically and economically the reliability of electricity distribution networks through an optimization methodology consisting of the mathematical model and metaheuristic solution technique to obtain an optimized plan for efficient management of maintenance tasks. The problem of maintenance tasks is formulated as a mixed dynamic nonlinear multi-objective optimization model, in which costs to perform maintenance tasks on equipment and/or components that make up the electric distribution network are minimized, while they have their reliability maximized. The constraints of this model are the individual and group electricity supply interruption duration and frequency indices, and availability of financial and human resources. The solution of this problem is obtained through a specialized non-dominated sorting genetic algorithm multi-objective metaheuristic, which provides a set of non-dominated solutions very close to the optimal Pareto frontier. Each solution at this frontier represents a maintenance plan able to assist the making decision of the operators in distribution companies for managing the maintenance crews.

Zigzag search for multi-objective optimization considering generation cost and emission

The zigzag search algorithm has been applied in engineering fields, such as oil well placement, with satisfactory results. In this paper, the zigzag search algorithm is introduced, modified with enhancement, and effectively applied to solve an economic emission dispatch problem and to demonstrate its practicability in power systems. The problem is formulated as a non-linear multi-objective optimization model taking energy constraints, generation limits, and transmission constraints into consideration. A set of non-dominant solutions can be obtained to form the Pareto front. Case studies are carried out with the IEEE 30-bus system and IEEE 118-bus system. The results indicate that the proposed zigzag search algorithms have the ability to deal with relevant power system problems. Comparisons are made with algorithms which have been widely used in literatures, such as the genetic algorithm (GA) and particle swarm optimization (PSO). This demonstrates that the zigzag search is easy to implement and is superior to other multi-objective (MO) techniques in both accuracy and efficiency.

Multiobjective Coordinated Scheduling of Energy and Flight for Hybrid Electric Unmanned Aircraft Microgrids

A hybrid electric unmanned aircraft (HEUA) uses the aerial thermal engine and energy storage system (ESS)-driven electric motor to meet the load demand, thus can be viewed as a “mobile multienergy microgrid.” Conventionally, for a given flight mission, only the energy of an HEUA is optimized while the flight speed is fixed; thus, the overall energy efficiency may be limited. This paper aims to coordinately schedule the energy consumption and the flight speed of an HEUA toward optimal economic and environmental objectives. First, a coordinated optimization model is proposed to coordinately schedule the energy consumption (including the power output of the thermal engine and the ESS) and flight speed (i.e., the true air speed) of an HEUA for simultaneously minimizing the fuel consumption (FC) and polluted gas emission (PGE). Second, a decomposition-based solution method is developed to convert the original nonlinear multiobjective optimization model into a bilevel programming model which can be solved iteratively. Simulation results demonstrate that, compared with the conventional single energy scheduling, the proposed coordinated scheduling method can achieve much better performance in terms of FC and PGE.

The optimization of investment strategy for resource utilization and energy conservation in iron mines based on Monte Carlo and intelligent computation

How to improve resource utilization and reduce energy consumption are two challenging tasks in iron mines. The realization of resource utilization and energy conservation goals depends on proper investment strategy on key production processes with relatively high resource loss or energy consumption. However, none of literature have explored the decision-making issue of investment strategy combined with the mining and dressing grades from the perspective of system engineering. Focusing on the entire mine system, this study links the investment decision-making of resource utilization and energy conservation with the determination of the grades combination, and obtains the investment strategies to maximize the goals of resource utilization and energy conservation. A nonlinear multi-objective constrained optimization model is established, and then Monte Carlo simulation and intelligent computation methods are fused to be MC-IO algorithm, to find out the optimal investment strategy and grades combination. Taking DA iron mine in China as an empirical study, five different investment strategies with grades combination are obtained. The results indicate the feasibility and validity of the proposed methodology. This study has provided a scientific and feasible approach for improving resource utilization and energy conservation in iron mines.

Software component evaluation and selection using TOPSIS and fuzzy interactive approach under multiple applications development

In this paper, a two phase approach is proposed for decision-making situation that involves optimal software component evaluation and selection for designing component-based modular software system with multiple applications. In the first phase, components are evaluated using technique for order preference by similarity to ideal solution. In the second phase, a non-linear multi-objective optimization model is developed that facilitates the decision whether “to buy commercial-off-the-shelf components” or “to build in-house components” so that the total score of alternative components is maximized while the overall cost and delivery time of the system are minimized. Many critical parameters such as reliability of various applications, reusability and compatibility of the software components are considered simultaneously in the proposed optimization model. To determine a preferred compromise solution for the multi-objective optimization problem, a fuzzy interactive approach is used. Numerical illustrations based on a small-scale case study are presented to demonstrate usefulness of the proposed optimization model for optimal “build or buy” decisions in real-world applications.

Data envelopment analysis based multi-objective optimization model for evaluation and selection of software components under optimal redundancy

Software developers face the challenge of developing in-time, low cost, high profit and high-quality software to meet competitive requirements and user demands. The software components for the same can be selected either from the available commercial-off-the-shelf repository or developed in-house. In this paper, we propose a data envelopment analysis (DEA) based nonlinear multi-objective optimization model for selecting software components in the presence of optimal redundancy to ensure software reliability. The proposed optimization model integrates both build and/or buy decisions for selection of components. We use DEA technique for evaluating the fitness of software components based upon multiple inputs and outputs provided by various members of the decision group. The overall efficiency score of each software component is obtained from the aggregated information. The proposed optimization model minimizes the total cost of software system and maximizes the total value of purchasing using constraints corresponding to compatibility of selected components, reliability, execution time, and delivery time of the software system. It also provides the information on the testing efforts needed to be performed on in-house developed components. A real-world case study of modular software development is discussed to illustrate the efficiency of the proposed optimization model. To the best of our knowledge, there exists no previous study on integrated optimization model for the software component selection problem involving build and/or buy decisions under optimal redundancy.

Developing a methodology for real-time trading of water withdrawal and waste load discharge permits in rivers

In this paper, a new methodology is proposed for the real-time trading of water withdrawal and waste load discharge permits in agricultural areas along the rivers. Total Dissolved Solids (TDS) is chosen as an indicator of river water quality and the TDS load that agricultural water users discharge to the river are controlled by storing a part of return flows in some evaporation ponds. Available surface water withdrawal and waste load discharge permits are determined using a non-linear multi-objective optimization model. Total available permits are then fairly reallocated among agricultural water users, proportional to their arable lands. Water users can trade their water withdrawal and waste load discharge permits simultaneously, in a bilateral, step by step framework, which takes advantage of differences in their water use efficiencies and agricultural return flow rates. A trade that would take place at each time step results in either more benefit or less diverted return flow. The Nucleolus cooperative game is used to redistribute the benefits generated through trades in different time steps. The proposed methodology is applied to PayePol region in the Karkheh River catchment, southwest Iran. Predicting that 1922.7 Million Cubic Meters (MCM) of annual flow is available to agricultural lands at the beginning of the cultivation year, the real-time optimization model estimates the total annual benefit to reach 46.07 million US Dollars (USD), which requires 6.31 MCM of return flow to be diverted to the evaporation ponds. Fair reallocation of the permits, changes these values to 35.38 million USD and 13.69 MCM, respectively. Results illustrate the effectiveness of the proposed methodology in the real-time water and waste load allocation and simultaneous trading of permits.