Multi-objective Optimization Mathematical Model Research Articles

Underground space optimization of smart city based on information processing technology

This study explores the underground space optimization method of smart city based on information processing technology to save space optimization operation time. Taking coordinate of intersection point, radius of intersection point, mileage of vertical slope change point and elevation of slope change point as design variables, taking total cost of underground space construction of smart city as objective function and taking plane, vertical section, horizontal and vertical combination and environmental impact as constraint conditions, a multi-objective optimization mathematical model of underground space of smart city was constructed. Parete genetic algorithm in information processing technology was used to solve the multi-objective optimization mathematical model of the underground space of smart city, realize the automatic search for the optimal scheme of the underground space of smart city, and complete the intelligent optimization process of the underground space construction scheme of smart city. The results show that the method obtained from this study can effectively optimize the underground space of smart city and obtain the optimal subway laying line, save space and optimize operation time and improve the convergence of the method.

Vehicle logistics path optimization based on ant colony and particle hybrid algorithm

In the actual vehicle logistics distribution process, the number of vehicles and the choice of distribution path determine the logistics cost. Aiming at the problem of high logistics cost, this paper establishes a multi-objective vehicle logistics path optimization mathematical model considering the distribution process and the number of vehicles. In order to solve the model, a hybrid ant colony particle swarm optimization algorithm is proposed. The algorithm integrates the particle swarm algorithm into the ant colony algorithm, which makes the ant colony algorithm have the characteristics of “particles”, speeds up the search speed of the ant colony algorithm, and reduces the defect of falling into local convergence. The simulation results show that the path optimization model and its hybrid algorithm have fast convergence, can effectively reduce the distribution process and the number of vehicles, and can reduce a large number of vehicle logistics costs, which provides a valuable reference for the whole vehicle logistics path planning.

A novel tooth surface modification methodology for wide-faced double-helical gear pairs

Aiming to improve the meshing quality of tooth surface and reduce the system vibration, a novel tooth surface modification methodology for the wide-faced double-helical gear pairs is developed in consideration of system flexibility. The quasi-static multi-point contact analysis model for double-helical gear system is established based on the new concept of axial multi-point contact and the substructure technique. The mesh misalignment caused by system flexibility and the compensated tooth surface modification parameters can be determined. Also, a multi-objective optimization mathematical model of tooth surface modification is established in order to reduce the fluctuation of vibration exciting force and improve the load distribution. The Pareto frontier solutions of tooth surface modification parameters are obtained by combining the loaded tooth contact analysis(LTCA) model and the NSGA-II algorithm. The final modified tooth surface for wide-faced double-helical gear pairs is obtained using the combination of compensated tooth surface modification and multi-objective optimization modification. The influences of system flexibility and tooth surface modification on quasi-static behaviors of the wide-faced double-helical gear pairs are discussed.

Reactive scheduling of multiple EOSs under cloud uncertainties: Model and algorithms

Most earth observation satellites (EOSs) are low-orbit satellites equipped with optical sensors that cannot see through clouds. Hence, cloud coverage, high dynamics, and cloud uncertainties are important issues in the scheduling of EOSs. The proactive-reactive scheduling framework has been proven to be effective and efficient for the uncertain scheduling problem and has been extensively employed. Numerous studies have been conducted on methods for the proactive scheduling of EOSs, including expectation, chance-constrained, and robust optimization models and the relevant solution algorithms. This study focuses on the reactive scheduling of EOSs under cloud uncertainties. First, using an example, we describe the reactive scheduling problem in detail, clarifying its significance and key issues. Considering the two key objectives of observation profits and scheduling stability, we construct a multi-objective optimization mathematical model. Then, we obtain the possible disruptions of EOS scheduling during execution under cloud uncertainties, adopting an event-driven policy for the reactive scheduling. For the different disruptions, different reactive scheduling algorithms are designed. Finally, numerous simulation experiments are conducted to verify the feasibility and effectiveness of the proposed reactive scheduling algorithms. The experimental results show that the reactive scheduling algorithms can both improve observation profits and reduce system perturbations.

Slope Stability Analysis Based on Leader Dolphins Herd Algorithm and Simplified Bishop Method

According to the principles of bionics and predatory behavior of dolphins, Leader Dolphin Herd Algorithm (LDHA) was designed, whose performance is also tested on the basis of heuristic algorithm, showing that LDHA is obviously superior to the other algorithms in calculation accuracy and efficiency. The minimum safety factor of sliding surface was taken as the objective function, the recurrence formula of safety factor based on simplified Bishop Method was regarded as constraint condition, a non-linear multi-objective optimization mathematical model used for analyzing slope stability was established. the process of searching slope sliding surface and solving safety factor were designed on account of LDHA. By taking homogeneous slope and layered slope as calculation examples compared to other intelligent algorithms, the results show that the calculation result of LDHA is close to that of Genetic Algorithm and Simulated Annealing Algorithm and improved Genetic Algorithm. Moreover, the LDHA has less iterations and faster convergence rate, and the result is closer to the optimal solution, which indicates the feasibility and practicability of LDHA in solving the minimum stability safety factor.

Research on compound comprehensive energy evaluation and intelligent control optimization

Under the background of increasing energy demand, integrated energy system is an important way to promote the development of clean energy, support the efficient use of energy and energy saving and emission reduction. This paper firstly establishes a comprehensive energy system evaluation index model composed of three sub-models of economy, environment and energy. On the basis of this model, a comprehensive energy multi-objective optimization mathematical model with the lowest total cost, excellent environmental benefits and high comprehensive energy utilization efficiency is established, and the energy supply and demand allocation optimization method based on improved genetic algorithm is adopted for solution. The simulation proves the effectiveness of the proposed optimization model.

Application of the Headstock of CNC Boring Machine for Tractor Engine Cylinder Block Based on Multi-Objective Genetic Algorithm

HighlightsThe headstock of the single-sided horizontal CNC boring machine specializing in processing tractor 6-cylinder engine cylinders is optimized.The constraint conditions such as tooth width and modulus are constructed. The model is optimized by the NSGA algorithm, and the optimization results are good.The optimization results of the NSGA algorithm are compared with the results of the weighted sum method and the GA, which highlights the superiority of the NSGA algorithm.ABSTRACT. The tractor is one of the most frequently used equipment in agricultural production, and its mass production is the general trend. With the continuous advancement of the global industrialization process, the importance of Computer Numerical Control (CNC) machine in the entire industrial production has become more and more prominent, and the application of CNC machine in tractor manufacturing has greatly improved production efficiency. This article takes the headstock of a single-sided horizontal CNC boring machine dedicated to processing tractor 6-cylinder engine cylinders as the research objective, takes the key parameters of the gear train in the headstock as the optimization design variables, constructs constraints, such as modulus, tooth width, etc., establishes a multi-objective optimization mathematical model, uses the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to process the model and obtains the Pareto solution set through multiple iterations. The optimization results show that the volume, center distance and the reciprocal of coincidence degree of the main shaft 1 transmission group are reduced in varying degrees. Finally, it is compared with the weighted sum method and genetic algorithm (GA) to highlight the superiority of NSGA-II. Keywords: Headstock, Multi-optimization, Non-dominated Sorting Genetic Algorithm II, Tractor cylinder.

A multi-objective genetic algorithm for assembly planning and supplier selection with capacity constraints

This study evaluates the supplier selection problem encountered when using multiple assembly plants with production capacity constraints to produce multiple products. It also applies assembly sequence planning (ASP) and assembly task assignment to production planning for the overall supply chain to determine optimal supplier combinations and production resource allocation. A multi-objective optimization mathematical model was constructed and a modified multi-objective algorithm was used to solve the optimization model. Developed on the basis of the nondominated sorting genetic algorithm II (NSGA-II), this modified algorithm incorporates an algorithmic and determination mechanism involving the greatest number of following tasks and the longest task time when initial solutions are generated. This increases the efficiency of solutions derived from the NSGA-II, here referred to as the W-NSGA2. The W-NSGA2 is then applied to the actual case of a faucet assembly task, and solutions derived by the W-NSGA2 are compared with those derived by the NSGA-II and the nondominated sorting particle swarm optimizer (NSPSO). Results show that the W-NSGA2 yields better solutions.

An optimal service selection approach for service-oriented business collaboration using crowd-based cooperative computing

Crowd-based cooperative computing (CBCC) emerges as a new computing paradigm, the core issue of which is the effective management and the coordinated use of crowd resources, including Internet users, application services, and smart devices. The service-oriented architecture (SOA) provides interoperability among crowd resources to support service-oriented business collaboration (SOBC). To address such a common issue of the coordinated use of crowd resources for SOBC, this paper studies a collaborative service computing model by considering the competition and cooperation among crowd resources. Then, a multi-objective optimization mathematical model is established for optimal service selection (OSS). Specifically, the methodology is resorted to an improved particle swarm optimization (IPSO) algorithm to find suitable collaborative services that optimally balance the quality of service (QoS) and synergy effect (SE). Furthermore, a flexible rescheduling strategy is presented for faulty services. The experimental results show that the proposed methodology is effective and feasible to obtain better-quality solutions for fulfilling the SOBC.

Optimization design of gear reducer based on multi-attribute decision making and reliability sensitivity

In order to solve the complexity and implicitness of lightweight optimization of the gear reducer, this paper constructs a multi-objective reliability optimization mathematical model of the gear reducer. and to obtain multi-objective Pareto solution, artificial intelligence algorithm is used to optimize structural parameters. Then, through repeatedly changing the structural parameters of the reducer, the experimental simulation analysis is carried out to obtain the maximum working stress. Based on the idea of the weight reduction and miniaturization, the stress state and reliability index values under different structural parameters are compared and analyzed. In order to determine the optimal solution of structural parameters, multi-attribute decision theory is used to determine the solution. Finally, in order to effectively reveal the inherent variation of attribute values and decision results and quantitatively reflect the impact of various structural parameters on system reliability, reliability sensitivity analysis of the gear reducer is carried out by the response surface-Monte Carlo and DPS methods. Thereby, an optimized structure that meets the safety reliability and the appropriate economy is obtained, and this study produces a balanced and improved optimized design that is coordinated with cost, quality, volume, safety and stability.

Cloud Manufacturing Service Composition Optimization with Improved Genetic Algorithm

Aiming at the problems in which there exists collocation between services and manufacturing tasks, multiobjective cloud manufacturing service composition optimization seldom considers the synergy degree of composite cloud services and the complexity of service composition, so a novel service composition optimization approach, called improved genetic algorithm based on entropy (IGABE), is put forward. First, the mathematical expressions of service collocation degree, composition synergy degree, composition entropy, and their related influence factors of the service composition are analyzed, and their definitions and calculation methods are given. Then, a multiobjective cloud manufacturing service composition optimization mathematical model is established. Moreover, crossover and mutation operators are improved by introducing normal cloud model theory and piecewise function, and improved roulette selection method is used to perform the selection operation. And the fitness function of the proposed IGABE is designed by combining Euclidean deviation with angular deviation. Finally, the manufacturing task of a wheeled cleaning robot is exemplified to verify the correctness of the proposed multiobjective optimization model for cloud manufacturing service composition and the effectiveness of the proposed algorithm, compared with Standard Genetic Algorithm (SGA), Hybrid Genetic Algorithm (HGA), and Cloud-entropy Enhanced Genetic Algorithm (CEGA). The studied results show that IGABE converges faster than SGA and HGA and can analyze and reflect the content difference expressed by the objective functions of service composition scheme and its approximation degree to the corresponding dimensions of the ideal point vector more comprehensively than CEGA. As such, the optimal service composition obtained by IGABE algorithm can better meet the complex needs of users.

Multi-objective optimization method for spectrum allocation in cognitive heterogeneous wireless networks

In a multi-heterogeneous network dense deployment and convergence environment, the cognitive radio technology dynamically utilizes the idle spectrum resources of each primary network, which can effectively improve the data transmission rate and system capacity, and is also a key technology of the next generation wireless communication network. However, how to efficiently and reasonably select the network and allocate idle spectrum resources to meet the low cost and large traffic demand of users is a difficult problem in the case of dynamic coupling with multiple heterogeneous primary networks overlapping coverage and diversified user requirements. In this paper, with the goal of maximizing the total bandwidth and minimizing the total cost, a multi-objective optimization mathematical model for network selection and idle spectrum allocation is established in the context of comprehensive consideration of the difference of spectrum resource attributes of different primary networks in the network domain and the diversification of secondary user requirements in the user domain, and the complexity of the problem is analyzed. Based on this, two kinds of technical paths to solve the complex network selection and spectrum allocation problem are applied in this paper. The first is the simplification method. By analyzing the relationship between optimization objectives and constraints, simplification method simplifies the objective function and constraints of the mathematical model and transforms the complex allocation problem into a standard form of the 01 programming problem. The second is the intelligent optimization algorithm. By improving the traditional multi-objective optimization algorithm Non-dominated Sorting Genetic Algorithm II (NSGA-II), an improved NSGA-II(INSGA-II) method is proposed, which combines the interference constraints of the primary network and the service quality requirements of the secondary users into the objective value evaluation of NSGA-II algorithm, while making the decision selection on the optimal solution set to select a compromise solution. Finally, the performance of this two methods is compared and analyzed through experiments. The experimental results show that the simplified method has higher efficiency advantages, and the INSGA-II algorithm can often meet the user’s service requirements at a lower cost, especially the cost priority strategy.

A N–N optimization model for logistic resources allocation with multiple logistic tasks under demand uncertainty

It is challenging to make an optimal allocation scheme for multiple paralleling logistics tasks match suitable resources in collaborative logistics network (CLN) due to the uncertainty. In this paper, we propose a multi-objective optimization mathematical model to solve the N–N task-resource assignment (TRA) problem in CLN under demand uncertainty. Chance constraint in the model is used to indicate demand uncertainty, and resource leveling is considered in the execution of multiple paralleling logistics tasks scheduling. A hybrid heuristic algorithm based on genetic algorithm and tabu search is presented to solve the N–N TRA model. The experimental results demonstrate that the proposed model can promisingly describe the TRA problem, and the hybrid heuristic algorithm can achieve superior result about the size of uncertainty degree on allocation scheme.

Bi-level Multi-objective Environmental Economic Dispatch with Wind Farm

A bi-level multi-objective environmental economic dispatch model with wind farms is established based on decomposition coordination principle and users’ side resources. Considering the level of system load and users’ satisfaction degree, a multi-objective optimization mathematical model was established to determine fitting load of the system and time sharing price. Considering the randomness of wind power output, a multi-objective environmental economic dispatch model is established to determine the generation plan. A hybrid universal gravitation algorithm and tabu search algorithm is proposed to solve the model. The optimal scheduling scheme is determined by the method of approximate ideal solution based on entropy weight. Simulation results show that: Considering the influence of resources of source side in the scheduling process not only can improve load level of the system operation, the satisfaction of using electricity and absorptive capacity of wind power, but also can effectively in reduce the generation costs and pollution emissions.

Multi-objective Optimization of Cloud Manufacturing Service Composition with Cloud-Entropy Enhanced Genetic Algorithm

To consider the service-matching degree, the composition harmony degree, and the service composition complexity in cloud manufacturing service composition optimization problems, a new composition optimization approach, called cloud-entropy enhanced genetic algorithm (CEGA), is put forward to solve such problems with multi-objectives. The definitions of service-matching degree, composition harmony degree, and cloud-entropy and the corresponding calculation methods are given. A multi-objective optimization mathematical model of cloud manufacturing service composition is built. The manufacturing task of AGV (automated guided vehicle) is taken as an example to verify the proposed CEGA algorithm on the established composition model. The studied result shows that CEGA converges faster than a standard genetic algorithm with shorter time.

Green supply chain design: A mathematical modeling approach based on a multi-objective optimization model

Increasing levels of industrialization of developed nations associated with globalization trends have been creating new challenges to supply chain management (SCM). For decades, the main focus of SCM has been on efficient ways of managing the flows through complex networks of supplier, producers and customers. More recently, and as a result of the exponential increase of energy and materials consumption rates of energy and materials, sustainable development arise as an urgent issue and new approaches to SCM are required to incorporate environmental and economic concerns in the design of supply chains. In this paper, a new green supply chain (GSC) design approach has been proposed to deal with the trade-offs between environmental and financial issues in order to reduce negative impacts on the environment caused by the increasing levels of industrialization. The new approach incorporates a closed loop network to accommodate the reprocessing paradigm of disposal products and a multi-objective optimization mathematical model to minimize overall costs and carbon dioxide emissions when setting the supply chain. Optimization process is performed using three scalarization approaches, namely weighted sum method, weighted Tchebycheff and augmented weighted Tchebycheff. Computational results are analyzed to identify the advantages and drawbacks of each approach. The model was tested in a case study and results allowed to identify the capability of the model to deal with the trade-offs between the costs and environmental issues as well as to identify its main limitation when addressing real size problems.

DYNAMIC MULTIOBJECTIVE OPTIMIZATION OF A COMPRESSOR-DRIVEN ADSORPTION SYSTEM BY ITERATIVE DYNAMIC PROGRAMMING

A compressor-driven adsorption refrigeration system that uses graphite-BaCl2 composite adsorbent/ammonia as a working pair has been investigated through dynamic optimization. The main purposes of this work were to obtain the optimal volume flow rate profile with the optimal cycle time and to improve the COP and SCP of this system simultaneously. A general dynamic multiobjective optimization mathematical model has been presented, and then shrinked to a single goal dynamic optimization problem by the weighted sum method. Because the cycle time was not specified, a normalized time variable was introduced and the cycle time was divided into a set of time stages of variable length. In order to solve this mathematical model, the iterative dynamic programming algorithm was adopted by a parallel program, and the effectiveness of this algorithm has also been verified. The optimal volume flow rate firstly keeps its maximum, and then drops to a relatively moderate value which rises slowly with time and reaches its minimum at the end of the cycle. As the weight of COP increases, the optimal volume flow rate control profile approaches the lower bounds and the optimal cycle time gradually gets longer.

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.

Matching Study of Hydraulic Torque Converter and Engine Based on Genetic Algorithm

According to the multiple matching principles of hydraulic torque converter and engine, a multi-objective optimization mathematical model is established. Genetic Algorithm is used to optimize the matching mathematical model, because the search process is not easy to fall into local optimum. The matching example of YJSW315 type hydraulic torque converter and WD615.67G3-28 type engine is optimized. The design variables’ optimization results are obtained and the figure of optimization results is shown. The matching evaluation indicators of automobile power performance and economy are compared before and after optimization. We can find out that maximum output of hydraulic torque converter torque, highly effective rotational speed range, highly effective torque range, average power output of full working condition range and efficient working condition range are all increased, at the same time, average fuel consumption rate of full working condition range and efficient working condition range are decreased. In accordance with the optimization results, we can see that GA can be used to optimize the matching of engine and hydraulic torque converter.

Research on Ceramic Manufacturing for Creating and Solving Ceramic Formulations Model

This paper describes some theories on basic designing optimization problem, and then establishes the multi-objective optimization mathematical model of ceramic blank. It transforms the ceramic formulation problem in real-world into a mathematical algorithm problem. It also provides a good theoretical basis for a computer to process ceramic formulation. Finally, we transforms the ceramic blank problem from mathematical problem into matrix equation, solving the quality percentage of each ingredient in the formulation program, which has achieved some good results to a certain extent, but still requires further study.