Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).     

A parallel double-level multiobjective evolutionary algorithm for robust optimization

Robust optimization is a popular method to tackle uncertain optimization problems. However, traditional robust optimization can only find a single solution in one run which is not flexible enough for decision-makers to select a satisfying solution according to their preferences. Besides, traditional robust optimization often takes a large number of Monte Carlo simulations to get a numeric solution, which is quite time-consuming. To address these problems, this paper proposes a parallel double-level multiobjective evolutionary algorithm (PDL-MOEA). In PDL-MOEA, a single-objective uncertain optimization problem is translated into a bi-objective one by conserving the expectation and the variance as two objectives, so that the algorithm can provide decision-makers with a group of solutions with different stabilities. Further, a parallel evolutionary mechanism based on message passing interface (MPI) is proposed to parallel the algorithm. The parallel mechanism adopts a double-level design, i.e., global level and sub-problem level. The global level acts as a master, which maintains the global population information. At the sub-problem level, the optimization problem is decomposed into a set of sub-problems which can be solved in parallel, thus reducing the computation time. Experimental results show that PDL-MOEA generally outperforms several state-of-the-art serial/parallel MOEAs in terms of accuracy, efficiency, and scalability.     

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms, the fitness of an individual requires a quantitative measure. This paper proposes a self-adaptive linear evolutionary algorithm (ALEA) in which we introduce a novel strategy for evaluating individual’s relative strengths and weaknesses. Based on this strategy, searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ‘good’ individuals of the performance for a multiobjective optimization application, regardless of original space complexity. This is considered as our main contribution. In addition, the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase, namely, crossover and mutation. Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective, and provides good performance in terms of uniformity and diversity of solutions.     

多宇宙并行量子多目标进化算法

提出了一种新的基于量子计算的多目标进化算法,即多宇宙并行量子多目标进化算法。算法中将所有的量子个体按给定的拓扑结构分成多个独立子种群,划分为多个宇宙;采用目标个体均匀分配原则和动态调整旋转角机制对各宇宙量子个体进行演化;宇宙之间采用最佳移民操作来交换信息,设计最优个体保留方案以便各宇宙共享全局信息,提高算法的执行效率。该算法用于多目标0/1背包问题的仿真结果表明：新方法能够找到接近Pareto最优前端的更好的解,同时维持解分布的均匀性。     

A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.     

多目标混沌差分进化算法

将差分进化算法用于多目标优化问题,提出了多目标混沌差分进化算法(CDEMO).该算法利用混沌序列初始化种群,并用混沌备用种群进行替换操作.该操作不仅起到了维持非劣最优解集均匀性的作用,而且增强了算法的搜索功能.对CDEMO的性能进行研究,数值实验结果表明了CDEMO的有效性.     

Incentive mechanism for selfish nodes in wireless sensor networks based on evolutionary game

A Wireless Sensor Network (WSN) is made up of a mass of nodes with the character of self-organizing, multi-hop and limited resources. The normal operation of the network calls for cooperation among the nodes. However, there are some nodes that may choose selfish behavior when considering their limited resources such as energy, storage space and so on. The whole network will be paralyzed and unable to provide the normal service if most of the nodes do not forward data packages and take selfish actions in the network. In this paper, we adopt a dynamic incentive mechanism which suits wireless sensor networks based on the evolutionary game. The mechanism emphasizes the nodes adjust strategies forwardly and passively to maximize the fitness, making the population in the wireless sensor network converge to a cooperative state ultimately and promoting the selfish nodes cooperating with each other such that the network could offer normal service. The theoretical analysis and simulation results show that the proposed model has better feasibility and effectiveness.     

基于博弈分析的自动协商系统

自动协商作为一个热点已经研究了很多年。大多数研究工作都着重于研究独立协商应用的抽象和理论模型,而对于实际算法的应用性只做了很少的工作。主要提出了一种基于博弈论的比较有效的协商模型来解决协商中的冲突。在该模型中利用遗传算法进行策略优化,而利用另外一个算法对已有的No-Fear-of-Deviation（NFD）算法进行了改进。     

多目标遗传算法求解认知无线电性能优化问题

认知无线电的性能优化是一个动态多目标优化问题。现有的Bio-CR模型基于遗传算法优化认知无线电的性能,它使用线性加权方法将此多目标优化问题简化为了一个单目标优化问题。针对Bio-CR很难确定每个适应度函数的权值和容易漏掉一些最优解的问题,提出了基于多目标遗传算法的认知无线电性能优化算法CREA。CREA能够根据信道条件和用户服务需求的变化动态地调整传输参数以优化性能,不仅克服了Bio-CR的两个缺点,而且通过保存计算结果进一步减少了遗传算法的运行次数。CREA首先根据信道条件的变化动态确定一组适应度函数,然后运行多目标遗传算法获得一个Pareto-optimal set,最后根据用户服务需求从中选出一个最满意解,并通知认知无线电更新自己的传输参数。Matlab仿真实验证明了CREA的正确性和有效性。     

Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. In this paper, we focus on multi-criteria human resource allocation for solving multistage combinatorial optimization problem. Hence we tackle this problem via a multistage decision-making model. A multistage decision-making model is similar to a complex problem solving, in which a suitable sequence of decisions is to be found. The task can be interpreted as a series of interactions between a decision maker and an outside world, at each stage of which some decisions are available and their immediate effect can be easily computed. Eventually, goals would be reached due to the found of optimized variables. In order to obtain a set of Pareto solutions efficiently, we propose a multiobjective hybrid genetic algorithm (mohGA) approach based on the multistage decision-making model for solving combinatorial optimization problems. According to the proposed method, we apply the mohGA to seek feasible solutions for all stages. The effectiveness of the proposed algorithm was validated by its application to an illustrative example dealing with multiobjective resource allocation problem.     

一种基于个体密度估算的多目标优化演化算法

通过在目标空间中利用目标本身信息估算个体k最近邻距离之和,作为个体的密度信息,根据个体的密度信息对群体中过剩的非劣解进行逐个去除,以便更好地维护解的多样性,由此给出了一种基于个体密度估算的多目标优化演化算法IDEMOEA。用这个算法对几个典型的多目标优化函数进行测试。测试结果表明,算法IDEMOEA求解多目标优化问题是行之有效的。     

基于精英选择和个体迁移的多目标遗传算法

提出基于遗传算法求解多目标优化问题的方法,将多目标问题分解成多个单目标优化问题,用遗传算法分别在每个单目标种群中并行搜索.在进化过程中的每一代,采用精英选择和个体迁移策略加快多个目标的并行搜索,提出了控制Pareto最优解数量并保持个体多样性的有限精度法,同时还提出了多目标遗传算法的终止条件.数值实验说明所提出的算法能较快地找到一组分布广泛且均匀的Pareto最优解.     

一种基于佳点集原理的约束优化进化算法

提出一种基于佳点集理论解决约束优化问题的进化算法.它将实分圆域中均匀分布的佳点映射到求解问题的搜索空间,使得所构造的个体能在搜索空间内分布比采用随机方式更加均匀,并引进预交叉机制来平衡佳点取点个数与算法搜索能力之间的矛盾.新算法的遗传算子基于佳点技术构造,精度不受空间维数的限制,有利于高维优化问题.对6个标准测试函数的数值实验结果验证了新算法的通用性、有效性和稳健性.     

Large-scale parallelization of the Borg multiobjective evolutionary algorithm to enhance the management of complex environmental systems

The Borg MOEA is a self-adaptive multiobjective evolutionary algorithm capable of solving complex, many-objective environmental systems problems efficiently and reliably. Water and environmental resources problems pose significant computational challenges due to their potential for large Pareto optimal sets, the presence of disjoint Pareto-optimal regions that arise from discrete choices, multi-modal suboptimal regions, and expensive objective function calculations. This work develops two large-scale parallel implementations of the Borg MOEA, the master–slave and multi-master Borg MOEA, and applies them to a highly challenging risk-based water supply portfolio planning problem. The performance and scalability of both implementations are compared on up to 16384 processors. The multi-master Borg MOEA is shown to scale efficiently on tens of thousands of cores while dramatically improving the reliability of attaining high-quality solutions. Our results dramatically expand the scale and scope of complex environmental systems that can be addressed using many-objective evolutionary optimization.     

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.     

基于NSGA-II算法的电容称重传感器抗偏载能力的优化

为了满足在保证电容称重传感器最小识别极距变化的同时达到提高其抗偏载能力的要求,对传感器进行了多目标优化的研究。分析计算了电容称重传感器力学性能与结构参数之间的关系,建立了以其导向性能和抗弯性能为优化目标的1/1000g精度电容称重传感器的多目标优化模型。应用Isight优化软件中的改进型非支配解遗传（NSGA-II）算法得到电容称重传感器的Pareto最优解集,并通过有限元验证了优化结果的准确性。研究表明,在保证电容称重传感器最小识别极距变化的前提下,极大地屏蔽了偏载对电容精度的影响,结果具有很强的实用性。     

一种基于群智能的快速多目标优化算法

粒子群优化算法是一种典型的仿真群智能的算法。探讨了利用粒子群算法求解多目标优化问题,为了提高算法速度,采用了几何Pareto选择算法作为文档算法,用多方向搜索的办法寻找极端点。实验表明：该算法得到的解的数量多,速度快并且近似前沿的程度比较高。     

基于演化博弈的拟态防御策略优化

网络空间拟态防御是近些年出现的一种主动防御理论,以异构冗余和动态反馈机制不断调整执行环境来抵抗攻击。然而,面对黑客的多样化攻击手段,仅凭借拟态防御抵抗攻击是不安全的。为了增强系统的安全防御能力,本文在目前已有的防御系统基础上提出更为合理的防御选取方法。将有限理性的演化博弈引入到拟态防御中,构建了由攻击者、防御者和合法用户组成的三方演化博弈模型,并提出了最优防御策略求解方法。该博弈模型利用复制动态方程得到了演化稳定策略。仿真实验结果表明,系统通过执行推理的演化稳定策略可以降低损失,遏制攻击方的攻击行为,对拟态防御系统中防御策略选取和安全性增强具有一定的借鉴意义。     

容迟网络中基于演化博弈的合作行为

针对容迟网络中节点由于资源有限而表现出来的自私特性,为改善网络中节点的合作行为,进而提高网络的整体性能,提出一种基于演化博弈(EGT)的节点合作行为促进机制。首先,采用囚徒困境模型建立节点与其邻居博弈的收益矩阵;其次,基于度中心性定义节点的社会权威性;进一步地,在节点策略更新规则时考虑社会权威的影响,选择当前邻居中社会权威较高的节点进行模仿学习;最后,在机会网络环境仿真器上基于真实的动态网络拓扑数据进行仿真实验。仿真结果表明,与随机选择邻居的费米(Fermi)更新规则相比,考虑社会权威的更新规则能够更好地促进节点合作行为的涌现,进而提升网络的整体性能。     

Finding optimal strategies in a multi-period multi-leader–follower Stackelberg game using an evolutionary algorithm

Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the other. Despite a number of studies on handling bilevel optimization problems, these problems still remain a challenging territory, and existing methodologies are able to handle only simple problems with few variables under assumptions of continuity and differentiability. In this paper, we consider a special case of a multi-period multi-leader–follower Stackelberg competition model with non-linear cost and demand functions and discrete production variables. The model has potential applications, for instance in aircraft manufacturing industry, which is an oligopoly where a few giant firms enjoy a tremendous commitment power over the other smaller players. We solve cases with different number of leaders and followers, and show how the entrance or exit of a player affects the profits of the other players. In the presence of various model complexities, we use a computationally intensive nested evolutionary strategy to find an optimal solution for the model. The strategy is evaluated on a test-suite of bilevel problems, and it has been shown that the method is successful in handling difficult bilevel problems.