NSGA-Ⅱ求解多目标优化综合精度的研究

多目标过程综合可归结为1个多目标混合整数非线性规划(MOMINLP),主要有2大类求解技术:多目标数学规划法和以多目标遗传算法(MOGA)为代表的进化算法.MOGA能并行处理多个目标,鲁棒性强,近年来得到长足发展.但由于无法从理论上保证得到问题的真正非劣解,应用受到了一定限制.本文应用多目标遗传算法NSGA-Ⅱ对废料最少问题进行求解,得到近似非劣解集.提出1个逐步插值算法,对近似解集中的点依次进行筛选,给出了所选点的搜索目标函数的构造方法,并应用SQP法对其寻优,得到真正的非劣解.将精确解与近似解进行比较表明,NSGA-Ⅱ的求解精度较高,绝大部分近似解的最大可能误差不超过3%,可为实际工程中的初步决策提供依据.     

多目标遗传算法在人脸识别中的应用

多目标遗传算法MOGA是求解多目标优化问题的有效工具，因而在求解实际问题中得到了越来越广泛的应用。但是，不同的实际问题有不同的要求及不同的约束条件，因此在求解实际问题时需要对算法的遗传操作做出改进，以满足不同问题的需要。本文就是多目标遗传算法在人脸识别中的具体应用。     

解决多目标优化问题的几种进化算法的比较研究

进化算法具有适于解决多目标优化问题的特性,近来一直用于求解此类问题。群体智能优化算法是一种基于群体智能的进化算法,通过简单个体的交互表现出高度智能,大大增强了解决和处理优化问题的能力。分析了遗传算法、粒子群算法和混洗蛙跳算法的具体流程,比较了这三种进化算法的优劣。     

基于双重特征空间的人脸识别

多目标遗传算法(MOGA)是求解多目标优化问题的有效工具,因而在求解实际问题中得到越来越广泛的应用.PCA是一种基于二阶统计的最小均方误差意义上的最优维数压缩技术,PCA方法所抽取特征的各分量之间是统计不相关的.在人脸识别的实际应用中,将多目标遗传算法引入到PCA所生成的特征空间的优化中,提出基于双重特征空间的人脸识别算法.通过对剑桥ORL库实验表明,该方法与传统的PCA相比,识别率得到明显提高.     

基于改进的遗传算法的多目标优化问题研究

研究多目标优化算法问题,针对传统的多目标优化算法由于计算复杂度非常高,难以获得令人满意的解等问题,在图论和遗传算法基础上,提出了一种改进的遗传算法求解多目标优化方法。首先采用二进制编码表示最小树问题,然后采用深度优先搜索算法进行图的连通性判断,给出了一种新的适应度函数,以提高算法执行速度和进化效率。最后仿真结果表明,与经典的Prim算法和Kruskal算法相比,新算法复杂度较低,并能在第一次遗传进化过程中获得一批最小生成树,适合于解决不同类型的多目标最小树问题。     

基于改进多目标差分进化算法的诺西肽发酵过程优化

诺西肽发酵存在着产量较低和生产效率不高的问题, 多目标优化是解决此类问题的有效途径. 将差分进化算法引入多目标优化, 构建了改进的多目标差分进化算法((IDEMO). 根据Pareto优劣等级和拥挤距离对种群进行选择操作, 并引入自适应变异算子和棍沌迁移算子以改善算法性能. 在诺西肽分批发酵动力学模型的基础上建立了多目标优化的模型, 并利用IDEMO对此优化问题进行了求解, 优化结果表明了算法的有效性.     

一种求解旅行商问题的进化多目标优化方法

为了克服传统小生境(Niching)策略中的参数设置难题,提出一种求解旅行商问题的进化多目标优化方法:建立以路径长度和平均离群距离为目标的双目标优化模型,利用改进非支配排序遗传算法(NSGAII)进行求解.为了在全局探索能力与局部开发能力之间保持平衡,算法中采用一种使路径长度相同的可行解互不占优的评价策略,并通过一种新的离散差分进化算子和简化的2-Opt策略生成候选解.与已有算法的数值试验结果比较表明,求解旅行商问题(TSP)的改进非支配排序遗传算法(NSGAII-TSP)能够更好地保持种群多样性,从而克服局部最优解的吸引并具有更鲁棒的全局探索能力.通过借助特殊的个体评价策略,所提出的算法可以更好地进行全局优化,甚至同时得到多个全局最优解.     

多目标进化算法研究进展

进化算法具有本质上并行、不需要求导或其他辅助知识、一次运行产生多个解和简单易于实现等优点，被视为求解多目标优化问题的有效方法，目前已经形成了各种不同的多目标进化算法（MOEA）。本文首先回顾了多目标进化算法的研究起源，给出了多目标优化问题的数学描述；其次，详细分析了第一代多目标进化算法，其主要特征是简单易于实现，包括NSGA、NPGA、MOGA等，并指出这一代算法研究的成绩与不足；然后，对第二代多目标进化算法作了全面分析，指出其特征是强调效率，以精英保留策略为实现机制，且对SPEA、PAES、NSGAⅡ、NPGA2、PESA、Micro-GA等方法进行分析比较，还对这一代的研究作了总结；最后，对多目标进化算法的研究趋势作了展望和预测。     

多线路准快速公交调度优化及混合遗传禁忌算法仿真

针对多线路准快速公交社会效益及企业运营效益最大化的多目标调度问题建立了优化模型。根据问题的特点设计了组合优化调度问题的混合遗传—禁忌算法,结合深圳市龙岗区公交调查数据对该模型进行了验证,计算结果及分析表明该算法比遗传算法及禁忌算法在求解此类问题时有更高的效率。     

多类型物流配送优化策略研究

研究多类型物流配送优化问题。物流中货物的配装以及送货的线路优化是物流配送的核心难点问题。对目前常见的物流配送过程中优化调度算法进行比较,分析了物流配送抽象流程,阐述了半启发式的遗传算法,以求取优化配送效率、降低算法的时间和空间复杂度为目标,建立了多类型物流配送整数线性规划模型,并设计了相关求解算法。将自适应遗传算法的多类型物流配送优化策略应用到实际物流配送过程中进行仿真,处理结果进行科学评价。通过实例的应用,验证了提出算法的可行性和高效性。     

Strategies for multiobjective genetic algorithm development: Application to optimal batch plant design in process systems engineering

This work deals with multiobjective optimization problems using Genetic Algorithms (GA). A MultiObjective GA (MOGA) is proposed to solve multiobjective problems combining both continuous and discrete variables. This kind of problem is commonly found in chemical engineering since process design and operability involve structural and decisional choices as well as the determination of operating conditions. In this paper, a design of a basic MOGA which copes successfully with a range of typical chemical engineering optimization problems is considered and the key points of its architecture described in detail. Several performance tests are presented, based on the influence of bit ranging encoding in a chromosome. Four mathematical functions were used as a test bench. The MOGA was able to find the optimal solution for each objective function, as well as an important number of Pareto optimal solutions. Then, the results of two multiobjective case studies in batch plant design and retrofit were presented, showing the flexibility and adaptability of the MOGA to deal with various engineering problems.     

Multi-objective GA with fuzzy decision making for security enhancement in power system

Power system security enhancement is a major concern in the operation of power system. In this paper, the task of security enhancement is formulated as a multi-objective optimization problem with minimization of fuel cost and minimization of FACTS device investment cost as objectives. Generator active power, generator bus voltage magnitude and the reactance of Thyristor Controlled Series Capacitors (TCSC) are taken as the decision variables. The probable locations of TCSC are pre-selected based on the values of Line Overload Sensitivity Index (LOSI) calculated for each branch in the system. Multi-objective genetic algorithm (MOGA) is applied to solve this security optimization problem. In the proposed GA, the decision variables are represented as floating point numbers in the GA population. The MOGA emphasize non-dominated solutions and simultaneously maintains diversity in the non-dominated solutions. A fuzzy set theory-based approach is employed to obtain the best compromise solution over the trade-off curve. The proposed approach has been evaluated on the IEEE 30-bus and IEEE 118-bus test systems. Simulation results show the effectiveness of the proposed approach for solving the multi-objective security enhancement problem.     

Multiple Objective Genetic Algorithms for Path-planning Optimization in Autonomous Mobile Robots

This paper describes the use of a genetic algorithm (GA) for the problem of offline point-to-point autonomous mobile robot path planning. The problem consists of generating “valid” paths or trajectories, for an Holonomic Robot to use to move from a starting position to a destination across a flat map of a terrain, represented by a two-dimensional grid, with obstacles and dangerous ground that the Robot must evade. This means that the GA optimizes possible paths based on two criteria: length and difficulty. First, we decided to use a conventional GA to evaluate its ability to solve this problem (using only one criteria for optimization). Due to the fact that we also wanted to optimize paths under two criteria or objectives, then we extended the conventional GA to implement the ideas of Pareto optimality, making it a multi-objective genetic algorithm (MOGA). We describe useful performance measures and simulation results of the conventional GA and of the MOGA that show that both types of GAs are effective tools for solving the point-to-point path-planning problem.     

Ensemble component selection for improving ICA based microarray data prediction models

Independent component analysis (ICA) has been widely used to tackle the microarray dataset classification problem, but there still exists an unsolved problem that the independent component (IC) sets may not be reproducible after different ICA transformations. Inspired by the idea of ensemble feature selection, we design an ICA based ensemble learning system to fully utilize the difference among different IC sets. In this system, some IC sets are generated by different ICA transformations firstly. A multi-objective genetic algorithm (MOGA) is designed to select different biologically significant IC subsets from these IC sets, which are then applied to build base classifiers. Three schemes are used to fuse these base classifiers. The first fusion scheme is to combine all individuals in the final generation of the MOGA. In addition, in the evolution, we design a global-recording technique to record the best IC subsets of each IC set in a global-recording list. Then the IC subsets in the list are deployed to build base classifier so as to implement the second fusion scheme. Furthermore, by pruning about half of less accurate base classifiers obtained by the second scheme, a compact and more accurate ensemble system is built, which is regarded as the third fusion scheme. Three microarray datasets are used to test the ensemble systems, and the corresponding results demonstrate that these ensemble schemes can further improve the performance of the ICA based classification model, and the third fusion scheme leads to the most accurate ensemble system with the smallest ensemble size.     

Improving multi-objective genetic algorithms with adaptive design of experiments and online metamodeling

Applications of multi-objective genetic algorithms (MOGAs) in engineering optimization problems often require numerous function calls. One way to reduce the number of function calls is to use an approximation in lieu of function calls. An approximation involves two steps: design of experiments (DOE) and metamodeling. This paper presents a new approach where both DOE and metamodeling are integrated with a MOGA. In particular, the DOE method reduces the number of generations in a MOGA, while the metamodeling reduces the number of function calls in each generation. In the present approach, the DOE locates a subset of design points that is estimated to better sample the design space, while the metamodeling assists in estimating the fitness of design points. Several numerical and engineering examples are used to demonstrate the applicability of this new approach. The results from these examples show that the proposed improved approach requires significantly fewer function calls and obtains similar solutions compared to a conventional MOGA and a recently developed metamodeling-assisted MOGA.     

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     

Embedding linear programming in multi objective genetic algorithms for reducing the size of the search space with application to leakage minimization in water distribution networks

This paper shows how embedding a local search algorithm, such as the iterated linear programming (LP), in the multi-objective genetic algorithms (MOGAs) can lead to a reduction in the search space and then to the improvement of the computational efficiency of the MOGAs. In fact, when the optimization problem features both continuous real variables and discrete integer variables, the search space can be subdivided into two sub-spaces, related to the two kinds of variables respectively. The problem can then be structured in such a way that MOGAs can be used for the search within the sub-space of the discrete integer variables. For each solution proposed by the MOGAs, the iterated LP can be used for the search within the sub-space of the continuous real variables. An example of this hybrid algorithm is provided herein as far as water distribution networks are concerned. In particular, the problem of the optimal location of control valves for leakage attenuation is considered. In this framework, the MOGA NSGAII is used to search for the optimal valve locations and for the identification of the isolation valves which have to be closed in the network in order to improve the effectiveness of the control valves whereas the iterated linear programming is used to search for the optimal settings of the control valves. The application to two case studies clearly proves the reduction in the MOGA search space size to render the hybrid algorithm more efficient than the MOGA without iterated linear programming embedded.     

On improving multiobjective genetic algorithms for design optimization

This paper presents some improvements to Multi-Objective Genetic Algorithms (MOGAs). MOGA modifies certain operators within the GA itself to produce a multiobjective optimization technique. The improvements are made to overcome some of the shortcomings in niche formation, stopping criteria and interaction with a design decision-maker. The technique involves filtering, mating restrictions, the idea of objective constraints, and detecting Pareto solutions in the non-convex region of the Pareto set. A step-by-step procedure for an improved MOGA has been developed and demonstrated via two multiobjective engineering design examples: (i) two-bar truss design, and (ii) vibrating platform design. The two-bar truss example has continuous variables while the vibrating platform example has mixed-discrete (combinatorial) variables. Both examples are solved by MOGA with and without the improvements. It is shown that MOGA with the improvements performs better for both examples in terms of the number of function evaluations.     

Entropy-based multi-objective genetic algorithm for design optimization

Obtaining a fullest possible representation of solutions to a multiobjective optimization problem has been a major concern in Multi-Objective Genetic Algorithms (MOGAs). This is because a MOGA, due to its very nature, can only produce a discrete representation of Pareto solutions to a multiobjective optimization problem that usually tend to group into clusters. This paper presents a new MOGA, one that aims at obtaining the Pareto solutions with maximum possible coverage and uniformity along the Pareto frontier. The new method, called an Entropy-based MOGA (or E-MOGA), is based on an application of concepts from the statistical theory of gases to a baseline MOGA. Two demonstration examples, the design of a two-bar truss and a speed reducer, are used to demonstrate the effectiveness of E-MOGA in comparison to the baseline MOGA.     

基于遗传算法的数码问题求解

在人工智能研究中，数码问题常被用来作为一些搜索算法的测试实例。数码问题的搜索空间巨大，对于24数码问题，目前最好的启发式搜索算法找到最优解(最少移动步数)通常也至少需要2．25小时^[1]。遗传算法具有简单、通用、鲁棒性强的特点，适合于在复杂而庞大的搜索空间中寻找最优解。该文给出了求解该问题的遗传算法，并针对遗传算法容易过早收敛的问题，对传统遗传算法进行了改进。通过用多个随机生成的]5数码和24数码问题作为测试实例，本算法均在较短的时间内找到了问题的解，从而证明了算法的有效性。