Using multi-population intelligent genetic algorithm to find the pareto-optimal parameters for a nano-particle milling process

Nano-particle materials have been widely applied in many industries and the wet-type mechanical milling process is a popular powder technology to produce the nano-particles. Since the milling process involves a number of process parameters and the multi-objective quality criteria, it is very important to set the optimal milling process parameters in order to achieve the desired multiple quality criteria. In this study, a new multi-objective evolutionary algorithm (MOEA), called the multi-population intelligent genetic algorithm (MPIGA), is proposed to find the optimal process parameters for the nano-particle milling process. In the new method, the orthogonal array (OA) experiment is first applied to obtain the analytic data of the milling process. Then the response surface method (RSM) is applied to model the nano-particle milling process and to determine the objective (fitness) value. The generalized Pareto-based scale-independent fitness function (GPSIFF) is then used to evaluate the Pareto solutions. Finally, the MPIGA is proposed to find the Pareto-optimal solutions. The results show that the integrated MPIGA approach can generate the Pareto-optimal solutions for the decision maker to determine the optimal parameters and to achieve the desired product qualities for a nano-particle milling process.     

A novel multi-objective immune algorithm with a decomposition-based clonal selection

In recent years, a number of multi-objective immune algorithms (MOIAs) have been proposed as inspired by the information processing in biologic immune system. Since most MOIAs encourage to search around some boundary and less-crowded areas using the clonal selection principle, they have been validated to show the effectiveness on tackling various kinds of multi-objective optimization problems (MOPs). The crowding distance metric is often used in MOIAs as a diversity metric to reflect the status of population’s diversity, which is employed to clone less-crowded individuals for evolution. However, this kind of cloning may encounter some difficulties when tackling some complicated MOPs (e.g., the UF problems with variable linkages). To alleviate the above difficulties, a novel MOIA with a decomposition-based clonal selection strategy (MOIA-DCSS) is proposed in this paper. Each individual is associated to one subproblem using the decomposition approach and then the performance enhancement on each subproblem can be easily quantified. Then, a novel decomposition-based clonal selection strategy is designed to clone the solutions with the larger improvements for the subproblems, which encourages to search around these subproblems. Moreover, differential evolution is employed in MOIA-DCSS to strength the exploration ability and also to improve the population’s diversity. To evaluate the performance of MOIA-DCSS, twenty-eight test problems are used with the complicated Pareto-optimal sets and fronts. The experimental results validate the superiority of MOIA-DCSS over four state-of-the-art multi-objective algorithms (i.e., NSLS, MOEA/D-M2M, MOEA/D-DRA and MOEA/DD) and three competitive MOIAs (i.e., NNIA, HEIA, and AIMA).     

A novel hybrid multi-objective immune algorithm with adaptive differential evolution

In this paper, we propose a novel hybrid multi-objective immune algorithm with adaptive differential evolution, named ADE-MOIA, in which the introduction of differential evolution (DE) into multi-objective immune algorithm (MOIA) combines their respective advantages and thus enhances the robustness to solve various kinds of MOPs. In ADE-MOIA, in order to effectively cooperate DE with MOIA, we present a novel adaptive DE operator, which includes a suitable parent selection strategy and a novel adaptive parameter control approach. When performing DE operation, two parents are respectively picked from the current evolved and dominated population in order to provide a correct evolutionary direction. Moreover, based on the evolutionary progress and the success rate of offspring, the crossover rate and scaling factor in DE operator are adaptively varied for each individual. The proposed adaptive DE operator is able to improve both of the convergence speed and population diversity, which are validated by the experimental studies. When comparing ADE-MOIA with several nature-inspired heuristic algorithms, such as NSGA-II, SPEA2, AbYSS, MOEA/D-DE, MIMO and D²MOPSO, simulations show that ADE-MOIA performs better on most of 21 well-known benchmark problems.     

A multi-objective artificial physics optimization algorithm based on ranks of individuals

This paper proposes a multi-objective artificial physics optimization algorithm based on individuals’ ranks. Using a Pareto sorting based technique and incorporating the concept of neighborhood crowding degree, evolutionary individuals in the search space are evaluated at first. Then each individual is assigned a unique serial number in terms of its performance, which affects the mass of the individual. Thereby, the population evolves towards the direction of the Pareto-optimal front. Synchronously, the presented approach has good diversity, such that the population is spread evenly on the Pareto front. Results of simulation on a number of difficult test problems show that the proposed algorithm, with less evolutionary generations, is able to find a better spread of solutions and better convergence near the true Pareto-optimal front compared to classical multi-objective evolutionary algorithms (NSGA, SPEA, MOPSO) and to simple multi-objective artificial physics optimization algorithm.     

Optimal placement of distributed generation units in distribution systems via an enhanced multi-objective particle swarm optimization algorithm

This paper deals with the optimal placement of distributed generation （DG） units in distribution systems via an enhanced multi-objective particle swarm optimization （EMOPSO） algorithm. To pursue a better simulation of the reality and provide the designer with diverse alternative options, a multi-objective optimization model with technical and operational con- straints is constructed to minimize the total power loss and the voltage fluctuation of the power system simultaneously. To enhance the convergence of MOPSO, special techniques including a dynamic inertia weight and acceleration coefficients have been inte- grated as well as a mutation operator. Besides, to promote the diversity of Pareto-optimal solutions, an improved non-dominated crowding distance sorting technique has been introduced and applied to the selection of particles for the next iteration. After verifying its effectiveness and competitiveness with a set of well-known benchmark functions, the EMOPSO algorithm is em- ployed to achieve the optimal placement of DG units in the IEEE 33-bus system. Simulation results indicate that the EMOPSO algorithm enables the identification of a set of Pareto-optimal solutions with good tradeoff between power loss and voltage sta- bility. Compared with other representative methods, the present results reveal the advantages of optimizing capacities and loca- tions of DG units simultaneously, and exemplify the validity of the EMOPSO algorithm applied for optimally placing DG units.     

A novel evolutionary root system growth algorithm for solving multi-objective optimization problems

This paper proposes a novel multi-objective root system growth optimizer (MORSGO) for the copper strip burdening optimization. The MORSGO aims to handle multi-objective problems with satisfactory convergence and diversity via implementing adaptive root growth operators with a pool of multi-objective search rules and strategies. Specifically, the single-objective root growth operators including branching, regrowing and auxin-based tropisms are deliberately designed. They have merits of appropriately balancing exploring & exploiting and self-adaptively varying population size to reduce redundant computation. The effective multi-objective strategies including the fast non-dominated sorting and the farthest-candidate selection are developed for saving and retrieving the Pareto optimal solutions with remarkable approximation as well as uniform spread of Pareto-optimal solutions. With comprehensive evaluation against a suit of benchmark functions, the MORSGO is verified experimentally to be superior or at least comparable to its competitors in terms of the IGD and HV metrics. The MORSGO is then validated to solve the real-world copper strip burdening optimization with different elements. Computation results verifies the potential and effectiveness of the MORSGO to resolve complex industrial process optimization.     

基于Pareto的多目标优化免疫算法

免疫算法具有搜索效率高、避免过早收敛、群体优化、保持个体多样性等优点。将其应用于多目标优化问题,建立了一种新型的基于Pareto的多目标优化免疫算法(MOIA)。算法中,将优化问题的可行解对应抗体,优化问题的目标函数对应抗原,Pareto最优解被保存在记忆细胞集中,并利用有别于聚类的邻近排挤算法对其进行不断更新,进而获得分布均匀的Pareto最优解。文章最后,对MOIA算法与文献[3]中SPEA算法进行仿真,通过比较两者的收敛性和分布性,得到了MOIA优于SPEA的结论。     

Elite-guided multi-objective artificial bee colony algorithm

Multi-objective optimization has been a difficult problem and a research focus in the field of science and engineering. This paper presents a novel multi-objective optimization algorithm called elite-guided multi-objective artificial bee colony (EMOABC) algorithm. In our proposal, the fast non-dominated sorting and population selection strategy are applied to measure the quality of the solution and select the better ones. The elite-guided solution generation strategy is designed to exploit the neighborhood of the existing solutions based on the guidance of the elite. Furthermore, a novel fitness calculation method is presented to calculate the selecting probability for onlookers. The proposed algorithm is validated on benchmark functions in terms of four indicators: GD, ER, SPR, and TI. The experimental results show that the proposed approach can find solutions with competitive convergence and diversity within a shorter period of time, compared with the traditional multi-objective algorithms. Consequently, it can be considered as a viable alternative to solve the multi-objective optimization problems.     

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

There is an ever increasing need to use optimization methods for thermal design of data centers and the hardware populating them. Airflow simulations of cabinets and data centers are computationally intensive and this problem is exacerbated when the simulation model is integrated with a design optimization method. Generally speaking, thermal design of data center hardware can be posed as a constrained multi-objective optimization problem. A popular approach for solving this kind of problem is to use Multi-Objective Genetic Algorithms (MOGAs). However, the large number of simulation evaluations needed for MOGAs has been preventing their applications to realistic engineering design problems. In this paper, details of a substantially more efficient MOGA are formulated and demonstrated through a thermal analysis simulation model of a data center cabinet. First, a reduced-order model of the cabinet problem is constructed using the Proper Orthogonal Decomposition (POD). The POD model is then used to form the objective and constraint functions of an optimization model. Next, this optimization model is integrated with the new MOGA. The new MOGA uses a “kriging” guided operation in addition to conventional genetic algorithm operations to search the design space for global optimal design solutions. This approach for optimal design is essential to handle complex multi-objective situations, where the optimal solutions may be non-obvious from simple analyses or intuition. It is shown that in optimizing the data center cabinet problem, the new MOGA outperforms a conventional MOGA by estimating the Pareto front using 50% fewer simulation calls, which makes its use very promising for complex thermal design problems. Recommended by: Monem Beitelmal     

Knowledge-based integrated product design framework towards sustainable low-carbon manufacturing

With a global challenge on the serious ecological problems, low-carbon manufacturing aiming to reduce carbon emission and resource consumption is gaining the ever-increasing attention. Due to the significant impact on the product lifecycle, low-carbon product design is considered as an effective and attractive approach to improve the eco-market trade-off of electromechanical products. Existing low-carbon product design approaches focus on solving specific low-carbon problems, and how to explore and navigate the integrative design space considering low-carbon and knowledge in a holistic perspective is rarely discussed. In response, this paper proposes a knowledge-based integrated product design framework to support low-carbon product development. An ontology-based knowledge modelling approach is put forward to represent the multidisciplinary design knowledge to facilitate knowledge sharing and integration. Subsequently, a function–structure synthesis approach based on case-based reasoning is presented to narrow down the design space to generate suitable design solutions for achieving desired functions. A multi-objective mathematical model is established, and the multi-objective particle swarm optimization is adopted to solve the low-carbon product optimization. Furthermore, a decision-making ranking approach based on the closeness degree is employed to prioritize the potential solutions from Pareto set. Finally, a case study of low-carbon product design of hydraulic machine is demonstrated to show the effectiveness.     

A surrogate-assisted evolutionary algorithm based on the genetic diversity objective

In this work, a novel surrogate-assisted memetic algorithm is proposed which is based on the preservation of genetic diversity within the population. The aim of the algorithm is to solve multi-objective optimization problems featuring computationally expensive fitness functions in an efficient manner. The main novelty is the use of an evolutionary algorithm as global searcher that treats the genetic diversity as an objective during the evolution and uses it, together with a non-dominated sorting approach, to assign the ranks. This algorithm, coupled with a gradient-based algorithm as local searcher and a back-propagation neural network as global surrogate model, demonstrates to provide a reliable and effective balance between exploration and exploitation. A detailed performance analysis has been conducted on five commonly used multi-objective problems, each one involving distinct features that can make the convergence difficult toward the Pareto-optimal front. In most cases, the proposed algorithm outperformed the other state-of-the-art evolutionary algorithms considered in the comparison, assuring higher repeatability on the final non-dominated set, deeper convergence level and higher convergence rate. It also demonstrates a clear ability to widely cover the Pareto-optimal front with larger percentage of non-dominated solutions if compared to the total number of function evaluations.     

Convergence analysis of a self-adaptive multi-objective evolutionary algorithm based on grids

Evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms, especially with self-adaption, are relatively scarce. This paper analyzes the convergence properties of a self-adaptive (μ+1)-algorithm. The convergence of the algorithm is defined, and general convergence conditions are studied. Under these conditions, it is proven that the proposed self-adaptive (μ+1)-algorithm converges in probability or almost surely to the Pareto-optimal front.     

Optimizing green production strategies: An integrated approach

Selection of green production strategy is a critical but difficult task due to the fact that it affects not only green benefits, but also production economy. The problem is essentially multi-objective and involves dynamic and uncertain conditions. This study focused on an integrated approach to improve the analysis and facilitate decision-making process. Discrete-event simulation model was developed to capture production flow and decision logic under real world conditions. A multi-objective genetic algorithm (MOGA), combined with improving heuristics, was developed to search the best solutions (Pareto optimums). The two modules are integrated to work in evolutionary cycles to achieve the optimization. Experiments were designed and carried out via a prototype system developed to verify and validate proposed concepts, including sensitivity analysis of related model parameters.     

A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems

This paper proposes a self-organized speciation based multi-objective particle swarm optimizer (SS-MOPSO) to locate multiple Pareto optimal solutions for solving multimodal multi-objective problems. In the proposed method, the speciation strategy is used to form stable niches and these niches/subpopulations are optimized to search and maintain Pareto-optimal solutions in parallel. Moreover, a self-organized mechanism is proposed to improve the efficiency of the species formulation as well as the performance of the algorithm. To maintain the diversity of the solutions in both the decision and objective spaces, SS-MOPSO is incorporated with the non-dominated sorting scheme and special crowding distance techniques. The performance of SS-MOPSO is compared with a number of the state-of-the-art multi-objective optimization algorithms on fourteen test problems. Moreover, the proposed SS-MOSPO is also employed to solve a real-life problem. The experimental results suggest that the proposed algorithm is able to solve the multimodal multi-objective problems effectively and shows superior performance by finding more and better distributed Pareto solutions.     

A memetic algorithm for bi-objective integrated forward/reverse logistics network design

Logistics network design is a major strategic issue due to its impact on the efficiency and responsiveness of the supply chain. This paper proposes a model for integrated logistics network design to avoid the sub-optimality caused by a separate, sequential design of forward and reverse logistics networks. First, a bi-objective mixed integer programming formulation is developed to minimize the total costs and maximize the responsiveness of a logistics network. To find the set of non-dominated solutions, an efficient multi-objective memetic algorithm is developed. The proposed solution algorithm uses a new dynamic search strategy by employing three different local searches. To assess the quality of the novel solution approach, the quality of its Pareto-optimal solutions is compared to those generated by an existing powerful multi-objective genetic algorithm from the recent literature and to exact solutions obtained by a commercial solver.     

Optimizing the IC wire bonding process using a neural networks/genetic algorithms approach

A critical aspect of wire bonding is the quality of the bonding strength that contributes the major part of yield loss to the integrated circuit assembly process. This paper applies an integrated approach using a neural networks and genetic algorithms to optimize IC wire bonding process. We first use a back-propagation network to provide the nonlinear relationship between factors and the response based on the experimental data from a semiconductor manufacturing company in Taiwan. Then, a genetic algorithms is applied to obtain the optimal factor settings. A comparison between the proposed approach and the Taguchi method was also conducted. The results demonstrate the superiority of the proposed approach in terms of process capability.     

A multi-objective scatter search for a dynamic cell formation problem

Cellular manufacturing system—an important application of group technology (GT)—has been recognized as an effective way to enhance the productivity in a factory. Consequently, a multi-objective dynamic cell formation problem is presented in this paper, where the total cell load variation and sum of the miscellaneous costs (machine cost, inter-cell material handling cost, and machine relocation cost) are to be minimized simultaneously. Since this type of problem is NP-hard, a new multi-objective scatter search (MOSS) is designed for finding locally Pareto-optimal frontier. To demonstrate the efficiency of the proposed algorithm, MOSS is compared with two salient multi-objective genetic algorithms, i.e. SPEA-II and NSGA-II based on some comparison metrics and statistical approach. The computational results indicate the superiority of the proposed MOSS compared to these two genetic algorithms.     

Multi-Objective Particle Swarm Optimization with time variant inertia and acceleration coefficients

In this article we describe a novel Particle Swarm Optimization (PSO) approach to multi-objective optimization (MOO), called Time Variant Multi-Objective Particle Swarm Optimization (TV-MOPSO). TV-MOPSO is made adaptive in nature by allowing its vital parameters (viz., inertia weight and acceleration coefficients) to change with iterations. This adaptiveness helps the algorithm to explore the search space more efficiently. A new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non-dominated fronts, while retaining at the same time the convergence to the Pareto-optimal front. TV-MOPSO has been compared with some recently developed multi-objective PSO techniques and evolutionary algorithms for 11 function optimization problems, using different performance measures.     

Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction

This study investigates the coupling effects of objective-reduction and preference-ordering schemes on the search efficiency in the evolutionary process of multi-objective optimization. The difficulty in solving a many-objective problem increases with the number of conflicting objectives. Degenerated objective space can enhance the multi-directional search toward the multi-dimensional Pareto-optimal front by eliminating redundant objectives, but it is difficult to capture the true Pareto-relation among objectives in the non-optimal solution domain. Successive linear objective-reduction for the dimensionality-reduction and dynamic goal programming for preference-ordering are developed individually and combined with a multi-objective genetic algorithm in order to reflect the aspiration levels for the essential objectives adaptively during optimization. The performance of the proposed framework is demonstrated in redundant and non-redundant benchmark test problems. The preference-ordering approach induces the non-dominated solutions near the front despite enduring a small loss in diversity of the solutions. The induced solutions facilitate a degeneration of the Pareto-optimal front using successive linear objective-reduction, which updates the set of essential objectives by excluding non-conflicting objectives from the set of total objectives based on a principal component analysis. Salient issues related to real-world problems are discussed based on the results of an oil-field application.     

机组短期负荷环境／经济调度多目标混合优化

环境/经济短期负荷调度主要由调度周期内的最优机组组合和负荷环境/经济分配组成,本文将变权重多目标进化算法与混沌局部优化相结合形成混合优化算法应用到电站机组环境/经济运行多目标优化问题中,在混合多目标优化算法中采用组合结构基因,其中机组基因用于机组组合全局粗寻优,参数基因用于负荷分配局部优化,基因修正与罚函数结合解决约束问题．通过对优秀个体进行基于线性搜索的混沌局部优化,可加快收敛速度和降低计算时间．实例仿真结果说明所提出的算法能获得较好分布的Pareto优化解．