The improvement research on multi-objective optimization algorithm based on non-dominated sorting

多目标优化问题（MOP）在许多科学研究和工程设计当中普遍存在，此类问题求解十分复杂但又十分重要。尽管传统多目标优化算法已经有了长足的发展，但遗存的问题依然很多，需要改进。 进化多目标优化算法将传统方法中的加权策略改为以种群为单位的进化策略，取得了更理想的优化的效果，NSGA-II就是其中的佼佼者。在此次研究中本人在NSGA-II的基础上提出了一种基于随机交叉算子、变异算子的算法RCVO-NSGA-II（RandomCrossVariationOperator-nondominatedsortinggeneticalgorithmII）用于解多目标优化问题。RCVO-NSGA-II随机采用模拟...Multiobjective optimization problem is common existing in many scientific researches and engineering design and the solution of this kind of problem is very complicated and important. Although the development of the traditional multi-objective optimization algorithm have made great progress, but a lot of problems are need to be improved. Evolutionary multi-objective optimization algorithm change ...学位：工程硕士院系专业：信息科学与技术学院_工程硕士(计算机技术)学号：X201222101

Optimization of a Quantum Cascade Laser Operating in the Terahertz Frequency Range Using a Multiobjective Evolutionary Algorithm

A quantum cascade (QC) laser is a specific type of semiconductor laser that operates through principles of quantum mechanics. In less than a decade QC lasers are already able to outperform previously designed double heterostructure semiconductor lasers. Because there is a genuine lack of compact and coherent devices which can operate in the far-infrared region the motivation exists for designing a terahertz QC laser. A device operating at this frequency is expected to be more efficient and cost effective than currently existing devices. It has potential applications in the fields of spectroscopy, astronomy, medicine and free-space communication as well as applications to near-space radar and chemical/biological detection. The overarching goal of this research was to find QC laser parameter combinations which can be used to fabricate viable structures. To ensure operation in the THz region the device must conform to the extremely small energy level spacing range from ~10-15 meV. The time and expense of the design and production process is prohibitive, so an alternative to fabrication was necessary. To accomplish this goal a model of a QC laser, developed at Worchester Polytechnic Institute with sponsorship from the Air Force Research Laboratory Sensors Directorate, and the General Multiobjective Parallel Genetic Algorithm (GenMOP), developed at the Air Force Institute of Technology, were integrated to form a computer simulation which stochastically searches for feasible solutions

A Multipopulation Coevolutionary Strategy for Multiobjective Immune Algorithm

How to maintain the population diversity is an important issue in designing a multiobjective evolutionary algorithm. This paper presents an enhanced nondominated neighbor-based immune algorithm in which a multipopulation coevolutionary strategy is introduced for improving the population diversity. In the proposed algorithm, subpopulations evolve independently; thus the unique characteristics of each subpopulation can be effectively maintained, and the diversity of the entire population is effectively increased. Besides, the dynamic information of multiple subpopulations is obtained with the help of the designed cooperation operator which reflects a mutually beneficial relationship among subpopulations. Subpopulations gain the opportunity to exchange information, thereby expanding the search range of the entire population. Subpopulations make use of the reference experience from each other, thereby improving the efficiency of evolutionary search. Compared with several state-of-the-art multiobjective evolutionary algorithms on well-known and frequently used multiobjective and many-objective problems, the proposed algorithm achieves comparable results in terms of convergence, diversity metrics, and running time on most test problems

A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms

The Effects of Using Chaotic Map on Improving the Performance of Multiobjective Evolutionary Algorithms

Chaotic maps play an important role in improving evolutionary algorithms (EAs) for avoiding the local optima and speeding up the convergence. However, different chaotic maps in different phases have different effects on EAs. This paper focuses on exploring the effects of chaotic maps and giving comprehensive guidance for improving multiobjective evolutionary algorithms (MOEAs) by series of experiments. NSGA-II algorithm, a representative of MOEAs using the nondominated sorting and elitist strategy, is taken as the framework to study the effect of chaotic maps. Ten chaotic maps are applied in MOEAs in three phases, that is, initial population, crossover, and mutation operator. Multiobjective problems (MOPs) adopted are ZDT series problems to show the generality. Since the scale of some sequences generated by chaotic maps is changed to fit for MOPs, the correctness of scaling transformation of chaotic sequences is proved by measuring the largest Lyapunov exponent. The convergence metric γ and diversity metric Δ are chosen to evaluate the performance of new algorithms with chaos. The results of experiments demonstrate that chaotic maps can improve the performance of MOEAs, especially in solving problems with convex and piecewise Pareto front. In addition, cat map has the best performance in solving problems with local optima

ETEA: A euclidean minimum spanning tree-Based evolutionary algorithm for multiobjective optimization

© the Massachusetts Institute of TechnologyAbstract The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in the space, where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based Evolutionary Algorithm (ETEA) to solve multiobjective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically in ETEA, four strategies are introduced: 1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; 2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; 3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; 4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/K001310/1, and the National Natural Science Foundation of China under Grant 61070088

Service Consistency in Vehicle Routing

This thesis studies service consistency in the context of multi-period vehicle routing problems (VRP) in which customers require repeatable services over a planning horizon of multiple days. Two types of service consistency are considered, namely, driver consistency and time consistency. Driver consistency refers to using the fewest number of different drivers to perform all of the visits required by a customer over a planning horizon and time consistency refers to visiting a customer at roughly the same time on each day he/she needs service. First, the multi-objective consistent VRP is defined to explore the trade-offs between the objectives of travel cost minimization and service consistency maximization. An improved multi-objective optimization algorithm is proposed and the impact of improving service consistency on travel cost is evaluated on various benchmark instances taken from the literature to facilitate managerial decision making. Second, service consistency is introduced for the first time in the literature to the periodic vehicle routing problem (PVRP). In the PVRP, customers may require multiple visits over a planning horizon, and these visits must occur according to an allowable service pattern. A service pattern specifies the days on which the visits required by a customer are allowed to occur. A feasible service pattern must be determined for each customer before vehicle routes can be optimized on each day. Various multi-objective optimization approaches are implemented to evaluate their comparative competitiveness in solving this problem and to evaluate the impact of improving service consistency on the total travel cost. Third, a branch-and-price algorithm is developed to solve the consistent vehicle routing problem in which service consistency is enforced as a hard constraint. In this problem, the objective is to minimize the total travel cost. New constraints are devised to enhance the original mixed integer formulation of the problem. The improved formulation outperforms the original formulation regarding CPLEX solution times on all benchmark instances taken from the literature. The proposed branch-and-price algorithm is shown to be able to solve instances with more than fourteen customers more efficiently than either the existing mixed integer formulation or the one we propose in this paper

A Pareto-Based Adaptive Variable Neighborhood Search for Biobjective Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup Time

Different from most researches focused on the single objective hybrid flowshop scheduling (HFS) problem, this paper investigates a biobjective HFS problem with sequence dependent setup time. The two objectives are the minimization of total weighted tardiness and the total setup time. To efficiently solve this problem, a Pareto-based adaptive biobjective variable neighborhood search (PABOVNS) is developed. In the proposed PABOVNS, a solution is denoted as a sequence of all jobs and a decoding procedure is presented to obtain the corresponding complete schedule. In addition, the proposed PABOVNS has three major features that can guarantee a good balance of exploration and exploitation. First, an adaptive selection strategy of neighborhoods is proposed to automatically select the most promising neighborhood instead of the sequential selection strategy of canonical VNS. Second, a two phase multiobjective local search based on neighborhood search and path relinking is designed for each selected neighborhood. Third, an external archive with diversity maintenance is adopted to store the nondominated solutions and at the same time provide initial solutions for the local search. Computational results based on randomly generated instances show that the PABOVNS is efficient and even superior to some other powerful multiobjective algorithms in the literature