Single-objective Optimization Model Research Articles

Research on the Development of the Insurance Industry under Extreme Weather based on a Multi-Objective Optimization Model

In recent years, the global climate has continuously deteriorated, with extreme weather events occurring frequently, which has exerted a huge and even devastating impact on the insurance industry. To address the location planning challenges faced by the insurance industry globally in the context of extreme weather, this papaer initially innovatively employs an ordered induction weighted operator to combine three forecasting models: ARIMA, SVR, and LSTM, thus developing an IASL model to forecast future extreme weather events. Subsequently, by integrating the interests of both insurance companies and property owners, a multi-objective optimization model is established, which is then transformed into a single-objective optimization model using the Method of Distance Functions. Lastly, the model is solved using an improved Firefly Algorithm. This holistic approach is anticipated to offer more effective support for insurance industry planning and risk management in addressing the challenges posed by extreme weather.

Prediction and compensation of stretch-bending springback for L-section profile

This study aimed to achieve one-time stretch-bending forming in an L-shaped profile. Consequently, it focused on two main aspects: springback compensation and process parameter optimization. The process first combined simulation and experimental data, through a Co-Kriging model, facilitating the construction of an approximate model of a profile’s stretch-bending forming. A multi-objective optimization model was then formulated, to minimize springback displacement, deformation, and residual stress. The study employed the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to explore the solution space for optimal combinations in stretch-bending processes. It created a single-objective optimization model to minimize the average positional error across each profile node. Subsequently, a simulated annealing algorithm was used to solve this model, enabling the determination of an optimal die profile, which met the required specifications of the one-time stretch-bending forming process. Moreover, a novel variable compensation factor method was proposed, which accurately determined the optimal compensation factors for each node, thereby enhancing node compensation precision.

Research on Multibeam Bathymetric System Based on Greedy Algorithm and Variable Step Size Traversal Algorithm

Multi-beam bathymetry system is an advanced technology to measure the seabed based on single-beam bathymetry. In this paper, the greedy algorithm and variable step traversal method will be used to establish the mathematical models of coverage width and overlapping rate of adjacent strips of multi-beam sounding, and the best scheme of survey line layout will be designed by establishing the optimization model. According to the established mathematical model of overlap rate, the mathematical model of coverage width of multi-beam sounding in three-dimensional rectangular waters is optimized. Finally, according to the real life, with the overlapping rate of adjacent strips within 10% to 20% as the limiting condition and the minimum total length of survey lines as the objective function, a single-objective optimization model is established. Then, Python is used to solve the problem through greedy algorithm and variable step-size traversal algorithm, and it is found that the included angle of survey line direction in the optimal scheme is 90, and the minimum total length of survey line is 68 nautical miles. Stability analysis is carried out by changing the constraint range of overlap rate.

An adaptive differential evolution algorithm with multi-strategy for solving complex optimization problem

In this paper, an adaptive differential evolution algorithm with multi-strategy, namely ESADE is proposed to solve the premature convergence and high time complexity for complex optimization problem. In the ESADE, the population is divided into several sub-populations after the fitness value of each individual is sorted. Then different mutation strategies are proposed for different populations to balance the global exploration and local optimization. Next, a new self-adaptive strategy is designed adjust parameters to avoid falling into local optimum while the convergence accuracy has reached its maximum value. And a complex airport gate allocation multi-objective optimization model with the maximum flight allocation rate, the maximum near gate allocation rate, and the maximum passenger rate at near gate is constructed, which is divided into several single-objective optimization model. Finally, the ESADE is applied solve airport gate allocation optimization model. The experiment results show that the proposed ESADE algorithm can effectively solve the complex airport gate allocation problem and achieve ideal airport gate allocation results by comparing with the current common heuristic optimization algorithms.

A single-objective optimization model for power systems with the introduction of line-heavy load rate index constraints

The increasing penetration of new energy sources in new power systems has exacerbated the volatility and complexity of power system currents. Grid planning is facing higher challenges. Established grid planning models usually use the upper and lower limits of grid transmission capacity as constraints, but this may lead to long-term heavy load operation of certain lines and increase system risks. Therefore, this paper designs a line-heavy load rate constraint and establishes a single-objective optimization model for grid planning based on this constraint. Example analyses verify the effectiveness of adding line-heavy load rate constraints in planning and the reasonableness of the single-objective optimization model.

Multi-objective optimization and evaluation of hybrid combined cooling, heating and power system considering thermal energy storage

Introducing thermal energy storage (TES) and solar energy effectively reduces fossil fuel consumption and greenhouse gas emissions in combined cooling, heating, and power (CCHP) systems. This study establishes a two-layer optimization framework to obtain the optimal configuration of the CCHP system coupling solar and thermal energy storage. The outer layer uses component sizes as decision variables to optimize the system's annual economic economy, annual carbon dioxide emissions, and annual primary energy consumption; the inner layer uses equipment output as decision variables to optimize the operation and maintenance costs. Firstly, the representative typical scenes were obtained using the k-means algorithm to reduce the computational complexity. Then, the multi-objective chaos optimization (MOCGO) algorithm is combined with mixed-integer linear programming (MILP) to obtain the established optimization model's configuration scheme and optimal operating strategy. TOPSIS is to rank the best Pareto solutions. Finally, a large hotel is a case study. The optimization results indicate that the proposed two-layer optimization model can achieve the optimal configuration scheme and scheduling strategy for hybrid CCHP. Compared to the rule-based multi-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 30.63 %, 37.94 %, and 38.16 % in economic, energy, and environmental performance. Compared with the rule-based single-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 34.95 %, 35.81 %, and 37.55 % in economic, energy, and environmental performance, respectively. In addition, TES can substantially increase the optimal performance of the two-layer optimization model.

3D Path Planning of the Solar Powered UAV in the Urban-Mountainous Environment with Multi-Objective and Multi-Constraint Based on the Enhanced Sparrow Search Algorithm Incorporating the Levy Flight Strategy

In response to practical application challenges in utilizing solar-powered unmanned aerial vehicle (UAV) for remote sensing, this study presents a three-dimensional path planning method tailored for urban-mountainous environment. Taking into account constraints related to the solar-powered UAV, terrain, and mission objectives, a multi-objective trajectory optimization model is transferred into a single-objective optimization problem with weight factors and multi-constraint and is developed with a focus on three key indicators: minimizing trajectory length, maximizing energy flow efficiency, and minimizing regional risk levels. Additionally, an enhanced sparrow search algorithm incorporating the Levy flight strategy (SSA-Levy) is introduced to address trajectory planning challenges in such complex environments. Through simulation, the proposed algorithm is compared with particle swarm optimization (PSO) and the regular sparrow search algorithm (SSA) across 17 standard test functions and a simplified simulation of urban-mountainous environments. The results of the simulation demonstrate the superior effectiveness of the designed improved SSA based on the Levy flight strategy for solving the established single-objective trajectory optimization model.

Power Resource Allocation Algorithm for Dual-Function Radar–Communication System

In this paper, a power allocation algorithm of dual-function radar–communication system with limited power is proposed to obtain better overall system performance measured by the weighted summation of radar signal to interference plus noise ratio (SINR) and communication channel capacity. First, a power allocation model is established to maximize the radar SINR and communication channel capacity with limited transmitted power. Then, the Karush–Kuhn–Tucker (KKT) conditions are used to solve the optimal objective function under the condition that only radar SINR or communication channel capacity is considered, respectively. Finally, the optimal value is combined with the original model and transformed into a single objective optimization model, and the optimal power is obtained by solving the model through the iterative optimization algorithm. Simulation results show that, compared with other power allocation algorithms, the proposed algorithm can achieve better radar-communication integration performance under the same transmit power.

Automated Vegetable Pricing and Replenishment Decisions based on PSO

The main aspects that supermarkets need to consider are the purchase volume and pricing, especially the freshness of vegetable products, so it is more important to determine the daily replenishment volume. This paper divides 251 typical vegetables into 6 categories for the market, collects the daily sales volume, daily sales unit price and cost price and loss rate of each vegetable in a typical supermarket within three years, and formulates replenishment and pricing strategies for the coming week to maximize the operating profit of the supermarket. This article constructs a "cost-plus pricing" model. First, the regression model is used to analyze the relationship between total sales and cost-plus pricing for different vegetable categories. Secondly, using the single-objective optimization model, taking revenue as the objective function, sales volume and cost markup as the decision variables, considering the constraints such as the relationship between total sales and pricing, and solving with particle swarm optimization to find appropriate replenishment and pricing strategies, so as to maximize the revenue of supermarkets in the coming week. Finally, using time series forecasting, the sales volume of each vegetable category in the next week is predicted by using the sales flow of the previous three years, and the replenishment volume obtained by the above optimization model is compared to detect the reliability of the model, and the results show that the reliability of the model results is high.

A study of forest management plans based on single-objective optimization

The global decline in forest area and massive greenhouse gas emissions have increased concern about the scale of forest carbon sinks, but the social value of forests as a source of timber and of forests themselves for tourism is also a focus of attention. The balance between forest carbon sinks and other values becomes a research question in this paper. We propose a forest management plan for forest managers by developing a carbon sink model and a forest management decision model. First, we developed a carbon sequestration model to determine how much carbon dioxide can be sequestered by the forest and its products over time. Then, we developed a single-objective optimization model with the goal of maximizing the amount of carbon sequestered. To develop a forest management plan, we selected six influencing factors: carbon storage, forest trees and their products, biodiversity, soil water storage, climate regulation, and landscape value, and then used hierarchical analysis to determine the influence weights of each factor, and then built a forest management decision model based on the single-objective optimization model. For specific forests, we initialize the model with specific parameters of the influencing factors and determine the transition points so that the model can be suitable for diverse forests and make a targeted management plan.

A chance-constrained programming method with credibility measure for solving the multi-skill multi-mode resource-constrained project scheduling problem

This paper addresses a multi-skilled extension of the multi-mode resource-constrained project scheduling problem (MRCPSP) with preemption of activities and generalized precedence relations under uncertainty. The problem is formulated mathematically as a single objective optimization model to minimize the project makespan. Concerning real-world circumstances, amount of non-renewable resources and availability are considered as interval type-2 fuzzy numbers. Therefore, a type-2 fuzzy chance-constrained programming (TFCP) method is developed to tackle the problem. Four unique characteristics are taken into account in this paper concurrently: (i) multi-skilled resources; (ii) renewable and non-renewable resources; (iii) preemptable activities; and (iv) interval type-2 fuzzy parameters. The existence of these practical contributions causes projects schedule, especially construction projects, to be closer to the real-world conditions. The proposed mathematical model is validated and tested on instances from PSPLIB (j12, j16 and j18) and MMLIB (MM50 and MM100) datasets. In this study, the computational results for the first time demonstrate that the number of preemption points depend heavily on fluctuations of non-renewable resources and number of skills. It is also shown that considering multi-skill renewable resources is an effective factor in project makespan. In J20, there were both a four-unit reduction and increase in the number of preemption points achieving by increasing the average amount of available non-renewable resources by 23 units and decreasing it by 22 units, respectively. Additionally, when seven skills of renewable resources were reduced, the number of preemption points increased by seven units. In this problem instance, project is completed within 28 days considering multi-skill renewable resources, whereas the project makespan is reported 33 days without considering them. Various sensitivity analyses are presented to evaluate the proposed mathematical model and the overall solution approach. Comparative analysis is conducted to compare the schedule in crisp and uncertain conditions. Eventually, the importance of considering multi-skill resources in project scheduling is illustrated compared to not considering them.

Multi-scenario optimization model for operation of inter-basin water transfer-supply systems considering cost–benefit relationships

Abstract The optimized operation of an inter-basin water transfer system is a widely used approach to achieving optimized regional water resource allocation. The costs of water transfers vary considerably, depending on the composition of the water source, the target audience and the route and distance of the transfer. This study proposes a multi-scenario optimization model for the operation of inter-basin water transfer-supply systems that balances the cost–benefit relationships. A two-objective optimization model is first established including minimizing the sum of squared water supply deficits and the cost of water transfers. Three water transfer scenarios are developed for different cost–benefit relationships. Based on these scenarios, the established optimization model is further converted into a single-objective optimization model to avoid the direct calculation of complex water transfer costs. The model is finally solved to obtain water transfer schemes. The proposed model is applied to the eastern route of the South-to-North Water Diversion Project in China. The results show that with a contracted diversion of 60% of the Yangtze River, the reliability of the water supply is 78.2% and the water shortage index is 2.8%, which is a compromise between balancing the water shortage index and the volume and cost of water transfer.

An equilibrium approach towards sustainable operation of a modern coal chemical industrial park

The problem of high water consumption and pollution emission of modern coal chemical industry have received widespread attention in recent years. However, while protecting the environment, the economic interests of coal chemical enterprises also need to be guaranteed. To address this challenge, this paper proposes an equilibrium strategy based on a bi-level multi-objectives model to assist decision-makers in coal chemical industrial parks in making plans for infrastructure investment, wastewater discharge load allocation, and production activities while balancing economic benefits, ecological protection, and energy efficiency promotion. The decision framework describes the hierarchical relationship between the park authority and individual coal chemical companies, and coordinates the conflicts between their different goals. Then, a real case study of Yushen coal chemical industrial park in Shaanxi province, China is presented using a hybrid algorithm named “particle swarm optimization - non-dominated sorting genetic algorithm - II (PSO-NSGA-II)” to solve multi-objectives programming. The research further discusses the final solutions under different preferences of decision-makers with the Subtractive clustering - Multi-criteria tournament decision - Gain analysis method (SC-MTD-GAM), and also compares the results of a single-objective optimization model and multi-objective programming. The results show that the equilibrium strategy of this research can provide a satisfactory consequence for coal chemical industrial parks in terms of integrative management involving the economy, environment and efficiency. Finally, based on a comprehensive discussion, management suggestions are given to help the related decision/policy-makers to develop sustainable management mechanisms.

Combination of different trajectory description approaches improves the trajectory synthesis performance: Validation by a coarse-to-fine method

In the past decade, trajectory synthesis methods seem to reach a bottleneck. These methods occasionally fail when some complex trajectories and linkage configurations are encountered. One important reason is that each trajectory description approach has its limitations. Is it possible to combine these description approaches to obtain better synthesis precision and versatility of different configurations? In this study, a coarse-to-fine optimal method for trajectory synthesis is proposed to verify the above conjecture. This method incorporates a well-designed multi-objective optimization model based on Fourier series (FS) and a single-objective optimization model based on discrete points (DP). FS and DP are selected because they are able to describe the overall shape and local details of the trajectory well, respectibely. In a synthesis problem of a leg mechanism, the method achieves better synthesis accuracy than others and demonstrates the applicability to both complex trajectories and multiple configurations. This work proves that the combination of different trajectory description methods leads to a better synthesis performance, which we believe provides new ideas for developing more efficient trajectory synthesis methods.

Multi-Objective Optimization of Epoxy Resin Adhesive for Pavement Toughened by Self-Made Toughening Agent.

Epoxy resin adhesive for pavement is often insufficient in flexibility and toughness. Therefore, a new type of toughening agent was prepared to overcome this shortcoming. To achieve the best toughening effect of a self-made toughening agent on an epoxy resin adhesive, its ratio to the epoxy resin needs to be optimally selected. A curing agent, a toughening agent, and an accelerator dosage were chosen as independent variables. The epoxy resin's adhesive tensile strength, elongation at break, flexural strength, and flexural deflection were used as response values to establish a single-objective prediction model of epoxy resin mechanical property indexes. Response surface methodology (RSM) was used to determine the single-objective optimal ratio and analyze the effect of factor interaction on epoxy resin adhesive's performance indexes. Based on principal component analysis (PCA), multi-objective optimization was performed using gray relational analysis (GRA) to construct a second-order regression prediction model between the ratio and gray relational grade (GRG) to determine the optimal ratio and to validate it. The results showed that the multi-objective optimization using response surface methodology and gray relational analysis (RSM-GRA) was more effective than the single-objective optimization model. The optimal ratio of epoxy resin adhesive was 100 parts of epoxy resin, 160.7 parts curing agent, 16.1 parts toughening agent, and 3.0 parts accelerator. The measured tensile strength was 10.75 MPa, elongation at break was 23.54%, the bending strength was 6.16 MPa, and the bending deflection was 7.15 mm. RSM-GRA has excellent accuracy for epoxy resin adhesive ratio optimization and can provide a reference for the epoxy resin system ratio optimization design of complex components.

DV-Hop Algorithm Based on Multi-Objective Salp Swarm Algorithm Optimization.

The localization of sensor nodes is an important problem in wireless sensor networks. The DV-Hop algorithm is a typical range-free algorithm, but the localization accuracy is not high. To further improve the localization accuracy, this paper designs a DV-Hop algorithm based on multi-objective salp swarm optimization. Firstly, hop counts in the DV-Hop algorithm are subdivided, and the average hop distance is corrected based on the minimum mean-square error criterion and weighting. Secondly, the traditional single-objective optimization model is transformed into a multi-objective optimization model. Then, in the third stage of DV-Hop, the improved multi-objective salp swarm algorithm is used to estimate the node coordinates. Finally, the proposed algorithm is compared with three improved DV-Hop algorithms in two topologies. Compared with DV-Hop, The localization errors of the proposed algorithm are reduced by 50.79% and 56.79% in the two topology environments with different communication radii. The localization errors of different node numbers are decreased by 38.27% and 56.79%. The maximum reductions in localization errors are 38.44% and 56.79% for different anchor node numbers. Based on different regions, the maximum reductions in localization errors are 56.75% and 56.79%. The simulation results show that the accuracy of the proposed algorithm is better than that of DV-Hop, GWO-DV-Hop, SSA-DV-Hop, and ISSA-DV-Hop algorithms.

Optimizing Emergency Supply Location Selection in Urban Areas: A Multi-Objective Planning Model and Algorithm

The scientific location and layout of emergency material storage and rescue points in urban areas are critical aspects of emergency management. In this study, a multi-objective programming optimization model was constructed based on related theories, incorporating multiple goal combinations with different dimensions according to various disaster scenarios and urban emergency needs. The weight factors of emergency timeliness, economy, and safety were considered, and the multi-objective model optimization problem was transformed into a single-objective comprehensive optimization model problem using the weight method. The analysis decision function was utilized to study the transformation and solution method of the urban emergency rescue point location model. Heuristic optimization algorithms were employed to perform average segmentation calculations on the preset neighborhoods, constantly changing and narrowing the neighborhood range until the algorithm termination conditions were met, approaching the domain range of the optimal solution. Additionally, another precision parameter was utilized to control the accuracy of the final solution neighborhood range. The optimization of emergency vehicle scheduling was used to synergistically solve the problem of reserve rescue point location layout and optimization solution. The results of the example demonstrate the feasibility of constructing a multi-objective model with multiple combinations of different dimensions of objectives and the rationality of the Dijkstra heuristic optimization algorithm used. This study provides multiple methodologies and alternative site selection plans for decision-makers to select the required multi-objective reserve rescue point location model based on different urban disaster situations and their own emergency rescue needs.

Robust Optimization of Energy-Saving Train Trajectories Under Passenger Load Uncertainty Based on p-NSGA-II

Railway electrification has attracted substantial interest in recent years as a key part of the global effort to achieve transport decarbonization. To improve the energy efficiency of train operations, of particular interest is the optimization of train speed trajectories. However, most studies formulate the problem as a single-objective optimization model and do not take into account train mass uncertainty associated with the passenger load variations. This article formulates a biobjective robust optimization model to minimize both the energy consumption and journey time, in which the robustness against the uncertain train mass is considered and viewed as a decision-maker preference. A novel multiobjective optimization algorithm, namely, p-nondominated sorting genetic algorithm-II (NSGA-II), is proposed, incorporating the original NSGA-II and a proposed preference dominance criterion to handle the DM preference. With the proposed p-NSGA-II, not only all solutions will converge to the optimal Pareto front but also solutions with better robustness in the Pareto front will be automatically selected and retained; meanwhile, the spread of the selected solutions is maintained. The effectiveness of the p-NSGA-II to generate a set of performance-robust driving schemes is verified by numerical case studies. The results show that the p-NSGA-II can achieve up to 40.59% robustness improvement compared to the original NSGA-II.

A Two-Stage Optimization Algorithm of the Train Traction Energy Consumption in Urban Rail Transit

The optimization of the train traction energy consumption in urban rail transit is a nonlinear optimization problem, and its solution is a very difficult task. This article focuses on the optimization of train traction energy consumption on the line with multiple stations. First, a single-objective nonlinear energy-saving optimization model is established for a given line and total travel time. Second, a two-stage optimization algorithm is proposed to solve this model. In the first stage, for a given interval and travel time, an optimization model of the traction energy consumption is established by using the distance discretization method. A dichotomous iterative algorithm based on energy consumption is proposed to search the optimal traction energy consumption. By calling this algorithm repeatedly, the energy–time curve of each interval can be obtained. In the second stage, according to these energy–time curves, the total travel time of a train on the line is allocated to each interval one by one in the form of time slices. And finally the optimal travel time and optimal traction energy consumption of the train on each interval are obtained. This method does not need to set the train operation mode sequence in advance but adaptively selects the energy-saving operation mode according to the line constraints and the train parameters. The up-direction from Yizhuang to Tongjinan of the Beijing Metro Yizhuang line in China is selected as the test section. The experimental results demonstrate the effectiveness and computational efficiency of our proposed methods and algorithms. Moreover, the dichotomous iterative algorithm runs so fast that it can be used in real-time driver advisory systems or automatic train operation systems.

Instantaneous cross-correlation function-[formula omitted]-Wigner distribution: Theory and application

To raise the noisy linear frequency-modulated (LFM) signal detection threshold without sacrificing the computing performance, this study employs the well-known τ-Wigner distribution (τ-WD) in extending further the notion of the instantaneous cross-correlation function WD (ICFWD) to the so-called ICF-τ-WD. We extend some essential properties of the ICFWD to those of the ICF-τ-WD. We analyze the computational complexities of the ICFWD and τ-WD, based on which we derive the computational complexity of the ICF-τ-WD. We address an important concern regarding the ICF-τ-WD’s optimal parameters selection for the noisy single component LFM signal processing, in accordance with the output signal-to-noise ratio (SNR) optimization models including the single-objective (expectation-SNR) optimization model and the double-objective (expectation-SNR and variance-SNR) optimization model. We also provide numerical simulations for verifying the advantage of the double-objective optimization model over the single-objective one and the ICF-τ-WD over the ICFWD in the improvement of detection performance.