Efficient Multi-objective Optimization Method Research Articles

Multi-objective optimization of electrical discharge machining parameters using particle swarm optimization

This manuscript presents an efficient multi-objective optimization method based on using particle swarm optimization together with a desirability function that can be applied where the response variables may have an opposite behavior and where the range of variation of the independent variables as well as those of the responses are subjected to constraints, which has a great deal of industrial interest. For example, maintaining roughness and dimensional tolerances within a tolerance range is determined by the design requirements of the manufactured parts (shape errors, microgeometry errors, etc.) and these requirements must be met in the manufacture of parts. It is demonstrated that it is possible to obtain optimal results in the ranges of variation considered for the independent variables, with regard to those obtained by experimentation. Similarly, models based on Adaptive Network-based Fuzzy Inference Systems are used to solve the problem that may arise from the inadequate fitting of the regression models. Thus, thanks to this present study a fast and efficient method is available for the multiple-optimization of response variables, subject to constraints on both response and independent variables, which are obtained from experiments and modelled by means of soft computing techniques. Furthermore, it is also demonstrated that it is possible to obtain technology tables for various manufacturing processes, which is of great interest from a technological point of view so as to obtain the most suitable processing conditions.

Thermodynamic Multi-Field Coupling Optimization of Microsystem Based on Artificial Intelligence

An efficient multi-objective optimization method of temperature and stress for a microsystem based on particle swarm optimization (PSO) was established, which is used to map the relationship between through-silicon via (TSV) structural design parameters and performance objectives in the microsystem, and complete optimization temperature, stress and thermal expansion deformation efficiently. The relationship between the design and performance parameters is obtained by a finite element method (FEM) simulation model. The neural network is built and trained in order to understand the mapping relationship. Then, the design parameters are iteratively optimized using the PSO algorithm, and the FEM results are used to verify the efficiency and reliability of the optimization methods. When the optimization target of peak temperature, bump temperature, TSV temperature, maximum stress and maximum thermal deformation are set as 100 °C, 55 °C, 35 °C, 180 Mpa and 12 μm, the optimization results are as follows: the peak temperature is 97.90 °C, the bump temperature is 56.01 °C, the TSV temperature is 31.52 °C, the maximum stress is 247.4 Mpa and the maximum expansion deformation is 11.14 μm. The corresponding TSV structure design parameters are as follows: the radius of TSV is 10.28 μm, the pitch is 65 μm and the thickness of SiO2 is 0.83 μm. The error between the optimization result and the target temperature is 2.1%, 1.8%, 9.9%, 37.4% and 7.2% respectively. The PSO method has been verified by regression analysis, and the difference between the temperature and deformation optimization results of the FEM method is not more than 3%. The stress error has been analyzed, and the reliability of the developed method has been verified. While ensuring the accuracy of the results, the proposed optimization method reduces the time consumption of a single simulation from 2 h to 70 s, saves a lot of time and human resources, greatly improves the efficiency of the optimization design of microsystems, and has great significance for the development of microsystems.

Multi-objective optimization of building energy performance and indoor thermal comfort by combining artificial neural networks and metaheuristic algorithms

During the last few years, multi-objective optimization processes have become one of the main challenges for energy efficiency in buildings. In this work, a new efficient multi-objective optimization method, based on the Building Performance Optimization (BPO) technique, has been developed to improve the indoor thermal comfort and energy performance of residential buildings, i.e. a Moroccan ground floor + first floor (GFFF) house located in Marrakech region (5th climatic zone according to the Thermal Building Code in Morocco). The most influential design variables have been well explored in order to find the optimal trade-off between these two objectives. Indeed, this technique is based on the integration of Artificial Neural Networks (ANNs), in particular Multilayer Feedforward Neural Networks (MFNN), coupled with the most commonly used metaheuristic algorithms, i.e. Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Genetic Algorithm (MOGA), in order to minimize computation time as much as possible. The TRNSYS software was used to establish the various dynamic thermal simulations required to create the database, from which the ANNs were able to set up their learning. The results show that this methodology is being used successfully, leading to different proposed solutions in terms of building envelope design. However, only the solutions using MOPSO are finally retained, as they have shown the greatest desired performance compared to the others. Thus, the thermal needs, particularly those for heating and cooling, have been significantly reduced to 74.52% of the total, while improving the indoor thermal comfort by 4.32% compared to the base design. Finally, we strongly recommend this methodology to the different actors in this field, including designers, engineers, architects, engineering offices, etc., when several objectives need to be contrasted while simultaneously considering several design variables.

An efficient multi-objective optimization method based on the adaptive approximation model of the radial basis function

Considering the high computational cost caused by solving multi-objective optimization (MOO) problems, an efficient multi-objective optimization method based on the adaptive approximation model is developed. Firstly, the Latin hypercube design (LHD) is employed for obtaining the initial sample points. Secondly, initial approximation models of objective functions and constraints are established by using the radial basis function (RBF). For ensuring the accuracy of the approximation models, the reverse shape parameter analysis method (RSPAM) is proposed to obtain improved approximation models. Thirdly, the micro multi-objective genetic algorithm (μMOGA) is adopted to solve the Pareto optimal set and the local-densifying approximation method is also applied to strengthen the ability of solving accurate Pareto optimal sets. Finally, the effectiveness and practicability of the proposed method is demonstrated by two numerical examples and two engineering examples.

Driving-Cycle-Oriented Design Optimization of a Permanent Magnet Hub Motor Drive System for a Four-Wheel-Drive Electric Vehicle

The electrical drive system is crucial to the drive performance and safety of electric vehicles (EVs). In contrast to the traditional two-wheel-driven EVs, the hub motor four-wheel-drive system can steer the vehicle by controlling the torque and speed of each wheel independently, yielding a very simple distributed drivetrain with high efficiency and reliability. This article presents a system-level design optimization method for a permanent magnet hub motor drive system for a campus patrol EV based on a practical driving cycle. An outer rotor permanent-magnet synchronous hub motor (PMSHM) and an improved model predicate current control are proposed for the drive system. Due to the lack of reducers, the direct-drive PMSHM needs to face more complex working conditions and design constraints. In the implementation, the motor design requirements are obtained through the collection of practical EV driving cycles on the campus. Based on these requirements, two models are proposed as the preliminary designs for the PMSHM. To improve their performance, an efficient multiobjective optimization method is employed to the motor considering different operational conditions. The finite-element model and thermal network model are employed to verify the performance of the optimized PMSHM. An optimal design scheme is selected by comparing the comprehensive performance of the two optimized motors. In addition, a duty-cycle model predictive current control is adopted to drive the motor. Finally, a prototype is developed and tested, and the experimental results are presented.

Multi-objective optimization design for windows and shading configuration considering energy consumption and thermal comfort: A case study for office building in different climatic regions of China

As a large energy-consuming part of the envelope, windows and shading system play a significant role in building savings. Once established in the primary design stage, it is difficult to make changes later, especially for high-rise buildings with large areas of glass. Moreover, strongly influenced by solar radiation, the configuration of windows and shading system conflicts with each other in terms of energy consumption and indoor comfort, the optimal configuration of windows and shading system under different climatic regions has not been well solved at yet. This paper proposes an easy-operation, useful, and efficient multi-objective optimization method, using a smart optimization algorithm NSGA-II in combination with DesignBuilder energy simulation software, especially beneficial for non-programming designers. In this research, a typical high-rise office building with a large area window has been selected as a case study. Building orientation, the configuration of windows and shading system, including materials for each layer of the double-layer window, installation angle and depth of overhangs have been taken into consideration, aiming to minimize the heating, cooling, lighting energy consumption and discomfort hours, and to find the mutual relationship between each other. A set of Pareto solutions can be obtained after optimization, and the most recommended variable parameters of windows and shading system in four cities representing severe cold climate, cold climate, hot summer and cold winter climate, and hot summer and warm winter climate can be identified, respectively. Besides, Pareto optimal solutions can give designers different scheme choices based on preferences, which are of great significance to provide guidance and suggestion for designers in the early design of buildings.

Effective optimization on Bump inlet using meta-model multi-objective particle swarm assisted by expected hyper-volume improvement

This paper presents an efficient multi-objective optimization method, focusing on aerodynamic optimization of a diverterless supersonic inlet (DSI) in transonic and supersonic flight conditions. The DSI inlet, through scrutinizing the Bump shape has potential to attain greater aerodynamic performance on exit plane of inlet. However, the high cost of computational fluid dynamic (CFD) simulations raises a significant challenge in the DSI optimization process. In order to obtain solution set in few numbers of objective function calls, a meta-model multi-objective particle swarm optimization (MOPSO) method is proposed based on a self-adaptive Kriging surrogate model, and applied to solve this kind of costly black-box optimization problem. The Kriging model is updated by using a dynamic expected hyper-volume improvement (EHVI) sample metric, which is developed by analyzing disadvantages of the original sample criterion. With the help of the dynamic sample metric, simulation results show that the surrogate-based MOPSO algorithm can obtain plenty enough non-dominated solutions and achieve high precision in the approximation of the Pareto front. In terms of DSI inlet optimization, the bump shape is parameterized by free form deformation (FFD) method, and the total pressure distortions of inlet exit plane are treated as two minimization objectives under transonic and supersonic flight conditions. A well distributed non-dominated solution set is generated by the proposed algorithm within the context of a small call number of cost evaluations, and optimized inlet configurated by the selected solution has better aerodynamic characteristics compared with the initial inlet.

An Efficient Multi-Objective Optimization Method for Use in the Design of Marine Protected Area Networks

An efficient connectivity-based method for multi-objective optimisation applicable to the design of marine protected area networks is described. Multi-objective network optimisation highlighted previously unreported step changes in the structure of optimal subnetworks for protection associated with minimal changes in cost or benefit functions. This emphasises the desirability of performing a full, unconstrained, multi-objective optimisation for marine spatial planning. Brute force methods, examining all possible combinations of protected and unprotected sites for a network of sites, are impractical for all but the smallest networks as the number of possible networks grows as 2^m, where m is the number of sites within the network. A metaheuristic method based around Markov Chain Monte Carlo methods is described which searches for the set of Pareto optimal networks (or a good approximation thereto) given two separate objective functions, for example for network quality or effectiveness, population persistence, or cost of protection. The optimisation and search methods are independent of the choice of objective functions and can be easily extended to more than two functions. The speed, accuracy and convergence of the method under a range of network configurations are tested with model networks based on an extension of random geometric graphs. Examination of two real-world marine networks, one designated for the protection of the stony coral Lophelia pertusa, the other a hypothetical man-made network of oil and gas installations to protect hard substrate ecosystems, demonstrates the power of the method in finding multi-objective optimal solutions for networks of up to 100 sites. Results using network average shortest path as a proxy for population resilience and gene flow within the network supports the use of a conservation strategy based around highly connected clusters of sites.

An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model

Compared with the interval model, the ellipsoidal convex model can describe the correlation of the uncertain parameters through a multidimensional ellipsoid, and whereby excludes extreme combination of uncertain parameters and avoids over-conservative designs. In this paper, we attempt to propose an efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model. Firstly, each uncertain objective function is transformed into deterministic optimization problem by using nonlinear interval number programming (NINP) method and a possibility degree of interval number is applied to deal with the uncertain constraints. The penalty function method is suggested to transform the uncertain optimization problem into deterministic non-constrained optimization problem. Secondly, the approximation model based on radial basis function (RBF) is applied to improve computational efficiency. For ensuring the accuracy of the approximation models, a local-densifying approximation technique is suggested. Then, the micro multi-objective genetic algorithm (μMOGA) is used to optimize design parameters in the outer loop and the intergeneration projection genetic algorithm (IP-GA) is used to treat uncertain vector in the inner loop. Finally, two numerical examples and an engineering example are investigated to demonstrate the effectiveness of the present method.

An efficient multi-objective optimization method for water quality sensor placement within water distribution systems considering contamination probability variations

Water quality security within water distribution systems (WDSs) has been an important issue due to their inherent vulnerability associated with contamination intrusion. This motivates intensive studies to identify optimal water quality sensor placement (WQSP) strategies, aimed to timely/effectively detect (un)intentional intrusion events. However, these available WQSP optimization methods have consistently presumed that each WDS node has an equal contamination probability. While being simple in implementation, this assumption may do not conform to the fact that the nodal contamination probability may be significantly regionally varied owing to variations in population density and user properties. Furthermore, the low computational efficiency is another important factor that has seriously hampered the practical applications of the currently available WQSP optimization approaches. To address these two issues, this paper proposes an efficient multi-objective WQSP optimization method to explicitly account for contamination probability variations. Four different contamination probability functions (CPFs) are proposed to represent the potential variations of nodal contamination probabilities within the WDS. Two real-world WDSs are used to demonstrate the utility of the proposed method. Results show that WQSP strategies can be significantly affected by the choice of the CPF. For example, when the proposed method is applied to the large case study with the CPF accounting for user properties, the event detection probabilities of the resultant solutions are approximately 65%, while these values are around 25% for the traditional approach, and such design solutions are achieved approximately 10,000 times faster than the traditional method. This paper provides an alternative method to identify optimal WQSP solutions for the WDS, and also builds knowledge regarding the impacts of different CPFs on sensor deployments.

Multi-Objective Optimization of Node-Based Spacecraft Radiator Design

An efficient multi-objective optimization method is proposed for node-based spacecraft radiator design. In contrast to a conventional manual approach to node-based radiator design with a thermal model, the proposed approach finds an optimum design solution for radiator node combinations through an optimization algorithm. The important parameters of radiator design are radiator size and topology, represented by discrete binary design variables allocated to each node division in the candidate radiator region. The optimization problem is formulated as a multi-objective problem with two or more objectives to minimize the number of radiator nodes and temperature margins of unit boxes, and a genetic algorithm suitable for multi-objective optimization is used. A small thermal model (verification thermal model) was developed to verify the proposed multi-objective optimization of the node-based spacecraft radiator design method, and test problems for this thermal model were defined. The numerical optimal solutions for test problems show good agreement with the analytic optimal solutions. Therefore, the applicability and feasibility of the multi-objective optimization of node-based spacecraft radiator design method to practical radiator design were confirmed.

Efficient Multi-objective Optimization Method for the Mixed-model-line Assembly Line Design Problem

This paper presents a mathematical model and an adaptation of the Strength Pareto Evolutionary Algorithm II (SPEA2) for the Mixed-Model Assembly Line balancing and equipment selection problem. The SPEA2 was enriched with a task and equipment reassignment procedure and aims at supporting the planners to find better solutions in the earliest phases of a production system planning project.

Optimization of astronaut landing position based on micro multi-objective genetic algorithms

In this paper, an efficient multi-objective optimization method for the optimization of astronaut landing position is presented. The finite element model is employed to simulate the airdrop process and the design variables are determined by Sobol sensitivity method. The approximation models of landing impact are constructed by the Radial Basis Functions with the samples which are obtained from the design of experiments. The micro multi-objective genetic algorithm is employed to search for the Pareto optimal solutions of the problem. According to the optimal astronaut landing position, the engineers could design airdrop protection devices to ensure the safety of astronauts.

An efficient multi-objective optimization method for black-box functions using sequential approximate technique

Multi-objective optimization problems in practical engineering usually involve expensive black-box functions. How to reduce the number of function evaluations at a good approximation of Pareto frontier has been a crucial issue. To this aim, an efficient multi-objective optimization method based on a sequential approximate technique is suggested in this paper. In each iteration, according to the prediction of radial basis function with a micro multi-objective genetic algorithm, an extended trust region updating strategy is adopted to adjust the design region, a sample inheriting strategy is presented to reduce the number of new function evaluations, and then a local-densifying strategy is proposed to improve the accuracy of approximations in concerned regions. At the end of each iteration, the obtained actual Pareto optimal points are stored in an external archive and are updated as the iteration process. The effect of the present method is demonstrated by eight test functions. Finally, it is employed to perform the structure optimization of a vehicle door.

An Efficient Multi-Objective Optimization Method for Complicated Vehicle Random Vibration

In this paper, a new approach is proposed and addressed for designing vehicle suspension systems based on the scheme of multi-objective programming. For complicated vehicle random vibration, a linear model is used to describe the dynamic behavior of vehicles running on randomly profiled roads. The road irregularity is regarded as a Gaussian random process. Pesudo excitation method has been used to solve the dynamic responses. And a Kriging model is introduced to build the approximate mapping relationship between the design variables and the responses. Optimal solutions are derived by means of the method of centers for structural optimization with multiple objectives. Numerical examples are given, and compared with other optimization methods.

Fuzzy preference based Interactive Fuzzy Physical Programming and its application in multi-objective optimization

Interactive Fuzzy Physical Programming (IFPP) developed in this paper is a new efficient multi-objective optimization method, which retains the advantages of physical programming while considering the fuzziness of the designer's preferences. The fuzzy preference function is introduced based on the model of linear physical programming, which is used to guide the search for improved solutions by interactive decision analysis. The example of multi-objective optimization design of the spindle of internal grinder demonstrates that the improved preference conforms to the subjective desires of the designer.

Optimum tire contour design using systematic stom and neural network

An efficient multi-objective optimization method is presented making use of neural network and a systematic satisficing trade-off method (STOM), in order to simultaneously improve both maneuverability and durability of tire. Objective functions are defined as follows: the sidewall-carcass tension distribution for the former performance while the belt-edge strain energy density for the latter. A back-propagation neural network model approximates the objective functions to reduce the total CPU time required for the sensitivity analysis using finite difference scheme. The satisficing trade-off process between the objective functions showing the remarkably conflicting trends each other is systematically carried out according to our aspiration-level adjustment procedure. The optimization procedure presented is illustrated through the optimum design simulation of a representative automobile tire. The assessment of its numerical merit as well as the optimization results is also presented.