从局部极小到全局最优

所有控制决策问题本质上均可归结为优化问题,但大部分存在多极小,因此如何摆脱局部极小以实现全局最优一直是理论界和工程界关注的热点课题。文章总结了若干全局优化技术的机制和特点,包括模拟退火、进化计算、禁忌搜索、变邻域搜索、噪声方法、巢分区、混沌搜索、隧道方法、平滑技术、混合算法等,力求为优化研究人员了解全局优化技术和开发高效算法提供指导。     

类搜索算法

提出利用类结构驱动的群体进化计算方法——类搜索算法(CSA).CSA在个体间构造簇类形态的虚拟连接关系,并通过对类组织的结构和类搜索过程进行动态调节来优化模拟进化系统的计算状态,提高群体的搜索效率.介绍了CSA的基本模型,并基于CSA融合进化算子与差分计算机制设计出数值优化算法CSA/DE.对多个典型高纬函数和复杂混合函数的仿真实验结果说明,CSA/DE是一种对高纬连续问题高效、稳定的搜索优化方法.该工作一方面验证了CSA的可行性和有效性;另一方面则显示:基于类搜索模型可有效融合异构且具有不同计算特性的搜索机制,形成对待求解问题更具针对性且协调性更佳的搜索计算方法.这为高性能优化算法的设计提供了一条新的途径.     

Preference-based evolutionary multi-objective optimization in ship weather routing

In evolutionary multi-objective optimization (EMO) the aim is to find a set of Pareto-optimal solutions. Such approach may be applied to multiple real-life problems, including weather routing (WR) of ships. The route should be optimal in terms of passage time, fuel consumption and safety of crew and cargo while taking into account dynamically changing weather conditions. Additionally it must not violate any navigational constraints (neither static nor dynamic). Since the resulting non-dominated solutions might be numerous, some user support must be provided to enable the decision maker (DM) selecting a single “best” solution. Commonly, multi-criteria decision making methods (MCDM) are utilized to achieve this goal with DM’s preferences defined a posteriori. Another approach is to apply DM’s preferences into the very process of finding Pareto-optimal solutions, which is referred to as preference-based EMO. Here the Pareto-set is limited to those solutions, which are compliant with the pre-configured user preferences. The paper presents a new tradeoff-based EMO approach utilizing configurable weight intervals assigned to all objectives. The proposed method has been applied to ship WR problem and compared with a popular reference point method: r-dominance. Presented results prove applicability and competitiveness of the proposed method to solving multi-objective WR problem.     

Hybrid genetic algorithms and line search method for industrial production planning with non-linear fitness function

Many engineering, science, information technology and management optimization problems can be considered as non-linear programming real-world problems where all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non-linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers, which was represented by logistic membership functions using the hybrid evolutionary optimization approach. To explore the applicability of the present study, a numerical example is considered to determine the production planning for the decision variables and profit of the company.     

Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

In this paper, we propose and investigate a new category of neurofuzzy networks—fuzzy polynomial neural networks (FPNN) endowed with fuzzy set-based polynomial neurons (FSPNs) We develop a comprehensive design methodology involving mechanisms of genetic optimization, and genetic algorithms (GAs) in particular. The conventional FPNNs developed so far are based on the mechanisms of self-organization, fuzzy neurocomputing, and evolutionary optimization. The design of the network exploits the FSPNs as well as the extended group method of data handling (GMDH). Let us stress that in the previous development strategies some essential parameters of the networks (such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables) being available within the network are provided by the designer in advance and kept fixed throughout the overall development process. This restriction may hamper a possibility of developing an optimal architecture of the model. The design proposed in this study addresses this issue. The augmented and genetically developed FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNNs. The GA-based design procedure being applied at each layer of the FPNN leads to the selection of the most suitable nodes (or FSPNs) available within the FPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gFPNN is quantified through experimentation in which we use a number of modeling benchmarks—synthetic and experimental data being commonly used in fuzzy or neurofuzzy modeling. The obtained results demonstrate the superiority of the proposed networks over the models existing in the references.     

约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

Clustering Search for the Berth Allocation Problem

This work presents a new approach to the Berth Allocation Problem (BAP) for ships in ports. Due to the increasing demand for ships carrying containers, the BAP can be considered as a major optimization problem in marine terminals. In this paper, the BAP is considered as dynamic and modeled in discrete case and we propose a new alternative to solve it. The proposed alternative is based on applying the Clustering Search (CS) method using the Simulated Annealing (SA) for solutions generation. The CS is an iterative method which divides the search space in clusters and it is composed of a metaheuristic for solutions generation, a grouping process and a local search heuristic. The computational results are compared against recent methods found in the literature.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space.     

Illustration of fairness in evolutionary multi-objective optimization

It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present illustrative examples to point out situations, where the right mechanism can speed up the optimization process significantly. We also indicate drawbacks for the use of fairness by presenting instances, where the optimization process is slowed down drastically.     

Evolutionary natural frequency optimization of thin plate bending vibration problems

This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.     

Structured parameter optimization method for the radial basis function-based state-dependent autoregressive model

An off-line structured nonlinear parameter optimization method (SNPOM) for accelerating the computational convergence of parameter estimation of the radial basis function-based state-dependent autoregressive (RBF-AR) model is proposed. Using the method, all the parameters of the RBF-AR model may be optimized automatically and simultaneously. The proposed method combines the advantages of the Levenberg-Marquardt algorithm in nonlinear parameter optimization and the least-squares method in linear parameter estimation. Case studies on two complex time series and a nonlinear chemical reaction process show that the proposed parameter optimization method exhibits significantly accelerated convergence when compared with the classic version of the Levenberg-Marquardt algorithm, and to some hybrid algorithms such as the evolutionary programming algorithm.     

粒子群算法在多船避碰决策中的应用

多船避碰是船舶避碰中最复杂的问题,也是船舶自动避碰方法研究中的难点之一.对许多学者的多船避碰研究进行分析,将最近会遇距离DCPA、最近会遇时间TCPA、两船距离、相对距离、本船转向角等作为基本评判参数,利用雷达进行一系列的观测,获得避让要素,建立碰撞危险度的评价模型.应用粒子群算法找出最优的解决方案,得出最优转向避碰幅度解.该方法不仅有助于解决多船会遇情况下的本船最优转向角度值,而且也有助于多船避碰决策系统的智能化设计与开发.     

Coordinated optimized scheduling of locks and transshipment in inland waterway transportation using binary NSGA‐II

Traffic congestion in inland waterways caused by insufficient throughput capacity of locks has become a compelling problem in developed inland shipping countries. In order to avoid excessive time wasted in waiting for lock service, it is suggested that some types of cargoes should be unloaded at the quays and transported by road/train to their destinations, which is called water–land transshipment. By this means, the ships are divided into two groups that either pass the lock or are transshipped at the quays, engendering the lock and water–land transshipment co‐scheduling (LWTC) problem. This paper focuses on the LWTC, where the roll‐on roll‐off ships, passenger ships, and general cargo ships that can be transshipped and other ships that can only pass the lock are considered in a lock‐quay co‐scheduling system. The LWTC problem is decomposed into an outer‐layer main 0‐1 optimization problem and two inner‐layer subproblems: lock scheduling and berth allocation. A multiobjective optimization model is proposed for the LWTC problem based on its two‐layer structure. To solve the LWTC problem, a hybrid heuristic method is proposed, where a modified binary nondominated sorting genetic algorithm II is proposed to solve the main problem, and the two subproblems are solved by specific heuristics. The proposed model and hybrid method are tested on instances extracted from historical data of traffic at Three Gorges Dam, the results of which demonstrate the feasibility of the model and the superiority of the proposed hybrid heuristic method over other comparisons.     

An interactive evolutionary multi-objective optimization and decision making procedure

With the advent of efficient techniques for multi-objective evolutionary optimization (EMO), real-world search and optimization problems are being increasingly solved for multiple conflicting objectives. During the past decade of research and application, most emphasis has been spent on finding the complete Pareto-optimal set, although EMO researchers were always aware of the importance of procedures which would help choose one particular solution from the Pareto-optimal set for implementation. This is also one of the main issues on which the classical and EMO philosophies are divided on. In this paper, we address this long-standing issue and suggest an interactive EMO procedure which will involve a decision-maker in the evolutionary optimization process and help choose a single solution at the end. This study uses many year’s of research on EMO and would hopefully encourage both practitioners and researchers to pay more attention in viewing the multi-objective optimization as a aggregate task of optimization and decision-making.     

进化算法在复杂网络中的应用综述

复杂网络作为现今科学研究中的一个热点学科,在过去20年里得到了巨大的发展.现实中大量的复杂的交互系统,比如互联网、交通运输网、神经网络等都可以抽象为复杂网络,以进行系统的分析和研究.进化算法作为优化工具应用于复杂网络的不同领域的各个任务中,如网络社团结构的检测任务、网络动力学中的鲁棒性优化任务、网络传播中关键节点的搜寻任务等.本文首先对复杂网络和进化算法相关的基础知识进行了全面的概述,重点讨论了复杂网络中目标优化的研究进展,针对不同任务对优化目标及其具体应用展开了详细介绍,同时,对算法的性能评价指标进行了概述.此外,本文通过一系列实验展示了单/多目标优化算法在复杂网络优化问题上的性能表现,以及部分目标之间的相关性关系.最后对复杂网络中优化问题未来的研究动向进行了展望,为今后研究人员开展进化计算和复杂网络相结合的相关研究提供一些思路.     

Truss topology optimization for mass and reliability considerations—co-evolutionary multiobjective formulations

The paper presents an approach for simultaneous optimization of structural mass and reliability in discrete truss structures. In addition to member sizing, the selection of an optimal topology from a pre-specified ground structure is a feature of the proposed methodology. To allow for a global search, optimization is performed using a multiobjective evolutionary algorithm. System reliability is based on a recently developed computational approach that is efficient and could be integrated within the framework of an evolutionary optimization process. The presence of multiple allowable topologies in the optimization process was handled through co-evolution in competing subpopulations. A unique feature of the algorithm is an automatic reunification of these populations using hypervolume measure-based indicator as reunification criterion to attain greater search efficiency. Numerical experiments demonstrate the computational advantages of the proposed method. These advantages become more pronounced for large-scale optimization problems, where the standard evolutionary approach fails to produce the desired results.     

离散粒子群优化算法求解旅行商问题

在优化领域,粒子群算法适用于求解连续优化问题,而在离散优化上的应用还相对较少。本文在介绍基本粒子群优化算法的基础上,分析了粒子群优化算法在经典旅行商问题 中的应用性能及粒子群算法求解旅行商问题的相关操作。使用Ulysses等标准TSP测试数据进行了相关实验,并通过不同的参数设置对实验结果进行了性能分析和比较。     

一类基于物种迁移优化的进化算法

借鉴自然界中的物种迁移机制,提出一类基于物种迁移优化的进化算法．该算法是根据生态系统中物种分布的迁移模型而提出的一种优化算法．参考其他智能算法的思想,通过物种迁移实现信息交换和共享,从而完成进化过程．讨论了物种迁移优化算法的基本原理和实现过程,同时进行一些基准函数的性能测试．实验结果表明所提出的算法是有效的,具有一定的参考和应用价值．