Nonlinear Multi-objective Optimization Research Articles

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.

Bio-Inspired Jumping Spider Optimization for Controller Tuning/ Parameter Estimation of an Uncertain Aerodynamic MIMO System

The practical near impossibility of empirical attempts in estimating optimal controller gains makes the use of metaheuristics strategies inevitable to automatically obtain these gains by an iterative, heuristic simulation procedure. The convergence of the gains values to the local or global solutions occur with ease. In designing controllers for the Twin-Rotor MIMO System (TRMS), Jumping Spider Optimization Algorithm (JSOA), a novel neoteric population-based bio-inspired metaheuristic approach is used to obtain optimum values for the Proportional, Integral and Derivative (PID) controllers. With the k,p,i controller gains as the decision variables, the JSOA solution to a nonlinear multi-objective optimization problem subject to some intrinsic constraints spawned optimal values for the controllers’ variables. Counter to other algorithms (deterministic and stochastic) that get caught in local minima, JSOA evolved a solution after searchingly rummaging the entire solution search space in a vectorized fashion for an optimal value. Compared with several other versatile controllers (using GA, PSO, Pattern Search and Simulated Annealing), statistical results obtained showed JSOA technique provided a unique solution and found the gains of the PID controllers, marginally in relation to the others (optimization methods).

Optimal load management of autonomous power systems in conditions of water shortage

The issues of optimizing the operation of micro hydropower plants in conditions of water scarcity, performed by additional connection to the grid of an energy storage system and wind power turbine, as well as optimal load management, are considered. It is assumed that the load of the system is a concentrated autonomous power facility that consumes only active power. The paper presents a rigorous mathematical formulation of the problem, the solution of which corresponds to the minimum cost of an energy storage system and a wind turbine, which allows for uninterrupted supply of electricity to power facilities in conditions of water shortage necessary for the operation of micro hydropower plants (under unfavorable hydrological conditions). The problem is formulated as a nonlinear multi-objective optimization problem to apply metaheuristic stochastic algorithms. At the same time, a significant part of the problem is taken out and framed as a subproblem of linear programming which will make it possible to solve it by a deterministic simplex method that guarantees to find the exact global optimum. This approach will significantly increase the efficiency of solving the entire problem by combining metaheuristic algorithms and taking into account expert knowledge about the problem being solved.

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.

Route Optimization for Hazardous Chemicals Transportation under Time-Varying Conditions

Since accidents of hazardous chemicals transportation will cause serious loss to the surrounding environment and lives and properties, this paper studies the transportation route optimization problem of hazardous chemicals under dynamic time-varying conditions. Combined with the goal of green sustainable development, a multiobjective nonlinear optimization model is constructed to minimize the transportation risk, transportation cost, and carbon emissions generated in the transportation. The model is solved by the improved Fast Non-Dominated Sorting Genetic Algorithm with Elite Strategy (NSGA-II) algorithm. The effectiveness of the model and the algorithm are tested on the Sioux Falls network. The experimental results show that under time-varying conditions, a vehicle’s departure at different times will generate different transportation costs and risks. Therefore, enterprises need to rationally arrange the departure time of vehicles according to the time windows of customer nodes and road conditions. In additio, from the relationship between the optimization objectives, in order to achieve green, sustainable and low-risk transportation, enterprises should first reduce their transportation costs.

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

Highway Alignment Optimization Design Method Based on Multi-Objective Particle Swarm Optimization

Highway alignment design is a nonlinear multi-objective optimization problem. Due to the uncertainty and complexity of the constraints, it is challenging to develop a suitable model for 3D road alignment design. To comprehensively consider the constraints and realize the intelligent design, this study puts forward a novel highway alignment model to optimize the horizontal and vertical alignment design, in which the length utility cost and structure construction cost are projected into the optimization space. Finally, the numerical solution is carried out by MOPSO on MATLAB platform. The results show that this method can effectively solve the problem of highway alignment design under the condition of realizing the highway design specifications, shortening the design cycle, and improving the design quality, which verifies the feasibility of the optimization algorithm for the horizontal and vertical alignment optimization design of highway.

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%).

Efficiency evaluation and nonlinear multi-objective optimization of forestry industry transformation in the Heilongjiang state-owned forest region

With the deepening of the concept of sustainable development of the whole society, protecting forest resources has become a crucial task of the current society. The present forestry industrial structure of Heilongjiang state-owned forest areas has undergone significant changes, and the transformation of the forestry industry has become increasingly prominent. How to deepen the forestry industry transformation and improve its efficiency has become an important research direction in forest areas. This work first analyzes the data envelopment method, and further designs the evaluation method of forestry transformation efficiency in forest areas. Then, the evaluation index system of forestry industry transformation efficiency in Heilongjiang state-owned forest areas is built. The relevant nonlinear multi-objective optimization (MOO) constraints are designed. Relevant data are quoted to evaluate the efficiency of the forestry industry transformation in the Heilongjiang state-owned forest areas. The results show that: (1) During 2015–2021, the average value of the scale, technical, and comprehensive production efficiencies of Heilongjiang state-owned forest areas were 0.765, 0.53, and 0.399, all of which were less than 1. And they were in a relatively ineffective state. (2) The overall industrial transformation of state-owned forest areas was optimistic. The technical efficiency decreased slightly in 2017, while the pure technical efficiency was greater than 1 in 2016 and 2018. The efficiency value increased to the peak by the end of 2021. (3) In the transformation of the forestry industry in state-owned forest areas, the influence of the industrial economy and resource protection subsystems was the first and backward, and the contribution of the social development subsystem was in the middle. (4) In the MOO problem, the forest area should be planned according to the proportion of public welfare, multi-functional, and commercial forests: 35.2%, 38.8%, and 26%, respectively. This work provides an essential reference for protecting forest resources and contributes to the transformation and development of the social forestry industry.

Enhancing the performance of radial distribution systems via optimal integration of electric vehicles

<span lang="EN-US">Electric vehicles (EVs) and their associated charging stations (CSs) are a promising avenue for greenhouse gas reduction and energy security. However, improper location and size of the EV charging station (CSs/EVs) negatively affect the power system. It results in some technical challenges such as increased real power-loss, decreased voltage stability and increased voltage deviation. This paper suggests optimum planning of CSs/EVs locations to conserve voltage, improve power-loss and reduce the effect of CSs/</span><span lang="EN-US">EVs in electrical distribution systems. The multi objective genetic algorithm method (MOGA) is utilized to solve the optimization problem and reduce the impact of the random location of CSs/EVs. <span>The simulations are</span> performed on IEEE 33-bus and IEEE 69-bus radial distribution systems (RDS). In addition, the optimal EV allocation is carried out with two fixed levels of loading from 100% to 150% of the candidate EV load. A comparison between the proposed MOGA technique and other optimization techniques is carried out. The results demonstrated the capability of the proposed technique for optimal placement of CSs/EVs in RDS. </span><span lang="EN-US">Moreover, it is providing an objective value to solve a complex multi-objective nonlinear optimization problem to reduce the total power-loss, improve the voltage profile and extend the voltage stability.</span>

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.

Adaptive surrogate assisted multi-objective optimization approach for highly nonlinear and complex engineering design problems

Despite enormous advances in computer power, computationally costly models impede the use of traditional optimization approaches that must be invoked repeatedly during the optimization process in practical engineering applications. Surrogate models have been found to be a promising endeavor in multi-objective optimization problems involving expensive analysis and simulation processes such as multi-physics modeling and simulation, finite element analysis (FEA), and computational fluid dynamics (CFD. Developing an optimization algorithm that can easily identify the Pareto frontier of highly nonlinear multi-objective optimization problems with less computation cost is the aim of this work. In this paper, an Adaptive Multi-Objective Optimization approach based Surrogate models (AMOS) is developed to reduce computation cost of fitness evaluations and discover the Pareto optima for multi-objective optimization problems with comparable high accuracy. AMOS explores the design space by sampling using LHD to identify promising regions. Then, AMOS exploits the identified promising region by adaptively constructing the most suitable surrogate model, which could be response surface, radial basis, or Kriging surrogates, in the feasible design space based on root mean square error values (RMSE). AMOS stops iterating when a termination criterion is met, and a Pareto frontier is identified based on developed guidance and fitness functions. AMOS has successfully identified the pareto frontier of practical engineering optimization problems with expensive black box functions and significantly reduced the computation cost. The novel method was put to the test utilizing real-world challenges and engineering design examples such vehicle magnetorheological design and wind turbine airfoil geometry.

Fuzzy prediction of the mine's ventilation structure's tunnel air volume

For the problem that it is difficult to accurately measure the air volume in the tunnel where the mine ventilation structure is located. Firstly, the tunnel air volume value is expressed by the interval number, and the air volume value of the tunnel where the ventilation structure is located is obtained by the law of nodal air balance. Then the interval number is transformed into a triangular fuzzy number to represent the tunnel air volume, the generalized induced ordered weighted average operator is introduced, the minimum-maximum closeness is used as the optimal quasi-measure, and the preference coefficient is introduced to transform the multi-objective nonlinear optimization problem into a single-objective optimization problem. And consider the temporal characteristics of the error series and the trend of the error value change for the error correction of air volume prediction error, and construct the interval combination type air volume fuzzy prediction model. Using the air volume data of a mine tunnel in Inner Mongolia, the example calculation of the model shows that the interval combination type prediction method can effectively improve the accuracy of air volume prediction in the tunnel of ventilation structures. Keywods: Error correction, Interval combination type, Interval number, Preference coefficient, Triangular fuzzy number

Three-Dimensional Path Planning of Deep-Sea Mining Vehicle Based on Improved Particle Swarm Optimization

Three-dimensional path planning is instrumental in path decision making and obstacle avoidance for deep-sea mining vehicles (DSMV). However, conventional particle swarm algorithms have been prone to trapping in local optima and have slow convergence rates when applied to underwater robot path planning. In order to secure a safe and economical three-dimensional path for the DSMV from the mining area to the storage base in connection with innovative mining system, this paper proposes a multi-objective optimization algorithm based on improved particle swarm optimization (IPSO) path planning. Firstly, we construct an unstructured seabed mining area terrain model with hazardous obstacles. Consequently, by considering optimization objectives such as the path length, terrain undulation, comprehensive energy consumption, and crawler slippage rate, we convert the path planning problem into a multi-objective optimization problem, constructing a multi-objective optimization mathematical model. Following that, we propose an IPSO algorithm to tackle the multi-objective non-linear optimization problem, which enables global optimization for DSMV path planning. Finally, we conduct a comprehensive set of experiments using the MATLAB simulation platform and compare the proposed method with existing advanced methods. Experimental results indicate that the path planned by the IPSO exhibits superior performance in terms of path length, terrain undulation, energy consumption, and safety.

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the literature.

Three-dimensional path planning for AUVs in ocean currents environment based on an improved compression factor particle swarm optimization algorithm

Three-dimensional path planning for autonomous underwater vehicles (AUVs) in underwater environments is the key to ensuring safe navigation and reliable mission completion. To obtain a safe and smooth three-dimensional path for an AUV in ocean currents and seabed obstacle environments, an improved compression factor particle swarm optimization algorithm is proposed. First, a three-dimensional seabed environment model and Lamb vortex current environment model are constructed. Second, by considering optimization objectives such as travel distance cost, seabed terrain constraints and ocean current constraints, a three-dimensional path planning mathematical model is constructed. Finally, an improved compression factor particle swarm optimization algorithm is proposed and applied to solve the multi-objective nonlinear optimization problem. To verify the optimization performance of the new algorithm, its optimization results are compared with those of other algorithms by minimizing the fitness value. The experimental results reveal that the improved compressed factor particle swarm optimal algorithm has better planning efficiency, path quality, and shorter planning time, which provides a new effective method for path planning of autonomous underwater vehicle.

An infeasible interior-point technique to generate the nondominated set for multiobjective optimization problems

In this paper, an infeasible interior-point technique is proposed to generate the nondominated set of nonlinear multi-objective optimization problems with the help of the direction-based cone method. We derive the proposed method for both convex and nonconvex problems. In order to solve the parametric optimization problems of the cone method, the infeasible interior-point method starts with an initial iterate outside the feasible region, and then gradually reduces the primal and dual infeasibility measures and the objective function value across the iterations with the help of a merit function. Estimates of the reduction of primal and dual infeasibility parameters per iteration are given. The convergence analysis of the method and an estimate of the number of iterations to reach an ϵ-precise solution are also provided. We provide the performance of the proposed methods on a variety of convex and nonconvex multi-objective test problems. Performance comparison between the proposed method and popular existing solvers is provided with respect to two performance measures and the corresponding relative efficiency measures. The reduction of a combined infeasibility measure, as the iterations progress, on the test problems is also shown graphically.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

A Newton-type proximal gradient method for nonlinear multi-objective optimization problems

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method deals with unconstrained convex multi-objective optimization problems. This method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a suitable descent direction. The subproblem uses a quadratic approximation of each smooth function. An Armijo type line search is conducted to find a suitable step length. A sequence is generated using the descent direction and the step length. The global convergence of this method is justified under some mild assumptions. The proposed method is verified and compared with some existing methods using a set of test problems.