A robust fuzzy multi-objective location-routing problem for hazardous waste under uncertain conditions

Industrialization and population growth have been accompanied by many problems such as waste management worldwide. Waste management and reduction have a vital role in national management. The presents study represents a multi-objective location-routing problem for hazardous wastes. The model was solved using Non dominated Sorting Genetic Algorithm-II, Multi-Objective Particle Swarm Optimization, Multi-Objective Invasive Weed Optimization, Pareto Envelope-based Selection Algorithm, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer algorithms. The findings revealed that the Multi-Objective Invasive Weed Optimization algorithm was the best and the most efficient among the algorithms used in this study. Obtaining income from the incineration of the wastes and reducing the risk of COVID-19 infection are the first innovation of the present study, which considered in the presented model. The second innovation is that uncertainty was considered for some of the crucial parameters of the model while the robust fuzzy optimization model was applied. Besides, the model was solved using several meta-heuristic algorithms such as Multi-Objective Invasive Weed Optimization, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer, which were rarely used in literature. Eventually, the most efficient algorithm was identified by comparing the considered algorithms.

     

Biasing Bayesian Optimization Algorithm using Case Based Reasoning

Studies show that application of the prior knowledge in biasing the Estimation of Distribution Algorithms (EDAs), such as Bayesian Optimization Algorithm (BOA), increases the efficiency of these algorithms significantly. One of the main advantages of the EDAs over other optimization algorithms is that the former provides a trail of probabilistic models of candidate solutions with increasing quality. Some recent studies have applied these probabilistic models, obtained from previously solved problems in biasing the BOA algorithm, to solve the future problems. In this paper, in order to improve the previous works and reduce their disadvantages, a method based on Case Based Reasoning (CBR) is proposed for biasing the BOA algorithm. Herein, after running BOA for solving optimization problems, each problem, the corresponding solution, as well as the last Bayesian network obtained from the BOA algorithm, will be stored as an entry in the case-base. Upon introducing a new problem, similar problems from the case-base are retrieved and the last Bayesian networks of these solved problems are combined according to the degree of their similarity with the new problem; hence, a compound Bayesian network is constructed. The compound Bayesian network is sampled and the initial population for the BOA algorithm is generated. This network will be applied efficiently for biasing future probabilistic models during the runs of BOA for the new problem. The proposed method is tested on three well-known combinatorial benchmark problems. Experimental results show significant improvements in algorithm execution time and quality of solutions, compared to previous methods.     

Automatic parameter tuning for Evolutionary Algorithms using a Bayesian Case-Based Reasoning system

The widespread use and applicability of Evolutionary Algorithms is due in part to the ability to adapt them to a particular problem-solving context by tuning their parameters. This is one of the problems that a user faces when applying an Evolutionary Algorithm to solve a given problem. Before running the algorithm, the user typically has to specify values for a number of parameters, such as population size, selection rate, and probability operators.This paper empirically assesses the performance of an automatic parameter tuning system in order to avoid the problems of time requirements and the interaction of parameters. The system, based on Bayesian Networks and Case-Based Reasoning methodology, estimates the best parameter setting for maximizing the performance of Evolutionary Algorithms. The algorithms are applied to solve a basic problem in constraint-based, geometric parametric modeling, as an instance of general constraint-satisfaction problems.The experimental results demonstrate the validity of the proposed system and its potential effectiveness for configuring algorithms.     

P2P case storage and retrieval with an unspecified ontology

Traditional approaches for similarity-based retrieval of structured data, such as Case-Based Reasoning (CBR), have been largely implemented using centralized storage systems. In such systems, when the cases contain both numeric and free-text attributes, similarity-based retrieval cannot exploit standard speedup techniques based on multi-dimensional indexing, and the retrieval is implemented by an exhaustive comparison of the case to be solved with the whole set of stored cases. In this work, we review current research on Peer-to-Peer (P2P) and distributed CBR techniques and propose a novel approach for storage of the case-base in a decentralized Peer-to-Peer environment using the notion of Unspecified Ontology to improve the performance of the case retrieval stage and build CBR systems that can scale up to large case-bases. We develop an algorithm for efficient retrieval of approximated most-similar cases, which exploits inherent characteristics of the unspecified ontology in order to improve the performance of the case retrieval stage in the CBR problem solving cycle. The experiments show that the algorithm successfully retrieves cases close to the most-similar cases, while reducing the number of cases to be compared. Hence, it improves the performance of the retrieval stage. Moreover, the distributed nature of our approach eliminates the computational bottleneck and single point of failure of the centralized storage systems.     

SP-MEC算法的收敛性分析

进化算法求解多目标优化问题具有独特的优势。SP-MEC是一种新的利用思维进化算法(MEC)解决多目标优化问题的算法,数值实验结果验证了它的可行性与有效性。文章利用概率论的基本理论对其收敛性进行分析,提出局部Pareto最优解集、局部Pareto最优态集及趋同过程产生的序列强收敛的概念,证明了在满足一定条件下趋同过程产生的序列强收敛于局部Pareto最优态集。     

基于多策略融合的混合多目标蝗虫优化算法

为提高蝗虫优化算法（GOA）求解多目标问题的性能,提出一种基于多策略融合的混合多目标蝗虫优化算法（HMOGOA）。首先,利用Halton序列建立初始种群,保证种群在初始阶段具有均匀分布和较高多样性;然后,通过差分变异算子引导种群变异,促进种群向优势个体移动同时进行更大范围寻优;最后,利用自适应权重因子根据种群优化情况动态调整算法全局搜索和局部寻优能力,提高优化效率及解集质量。选取7个典型函数进行实验测试,并将HMOGOA与多目标蝗虫优化、多目标粒子群（MOPSO）、基于分解的多目标进化（MOEA/D）及非支配排序遗传算法（NSGA Ⅱ）对比分析。实验结果表明,该算法避免了其他四种算法的局部最优问题,明显提高了解集分布均匀性和分布广度,具有更好的收敛精度和稳定性。     

基于多策略融合的混合多目标蝗虫优化算法

为提高蝗虫优化算法（GOA）求解多目标问题的性能，提出一种基于多策略融合的混合多目标蝗虫优化算法（HMOGOA）。首先，利用Halton序列建立初始种群，保证种群在初始阶段具有均匀分布和较高多样性；然后，通过差分变异算子引导种群变异，促进种群向优势个体移动同时进行更大范围寻优；最后，利用自适应权重因子根据种群优化情况动态调整算法全局搜索和局部寻优能力，提高优化效率及解集质量。选取7个典型函数进行实验测试，并将HMOGOA与多目标蝗虫优化、多目标粒子群（MOPSO）、基于分解的多目标进化（MOEA/D）及非支配排序遗传算法（NSGA Ⅱ）对比分析。实验结果表明，该算法避免了其他四种算法的局部最优问题，明显提高了解集分布均匀性和分布广度，具有更好的收敛精度和稳定性。     

改进的排序变异多目标差分进化算法

针对多目标差分进化算法在求解问题时收敛速度慢和均匀性欠佳的问题,提出了一种改进的排序变异多目标差分进化算法（MODE-IRM）。该算法将参与变异的三个父代个体中的最优个体作为基向量,提高了排序变异算子的求解速度;另外,算法采用反向参数控制方法在不同的优化阶段动态调整参数值,进一步提高了算法的收敛速度;最后,引入了改进的拥挤距离计算公式进行排序操作,提高了解的均匀性。采用标准多目标优化问题ZDTl~ZDT4,ZDT6和DTLZ6~DTLZ7进行仿真实验:MODE-IRM在总体性能上均优于MODE-RMO和PlatEMO平台上的MOEA/D-DE、RM-MEDA以及IM-MOEA;在世代距离（GD）、反向世代距离（IGD）和间隔指标（SP）性能度量指标方面,MODE-IRM在所有优化问题上的均值和方差均明显小于MODE-RMO。实验结果表明MODE-IRM在收敛性和均匀性指标上明显优于对比算法。     

基于CBR-GA的建筑块重组*

为了解决遗传算法（GA）中好的建筑块被破坏的问题,提出基于CBRGA的建筑块重组方法。首先反复运行简单的遗传算法找到多个局部最优解,并选择多个不同的局部最优解构建案例库;然后应用差异化学习方法产生新案例,有效解决了GA中随机交叉对建筑块破坏的问题;最后通过4阶欺骗问题验证了新算法的可行性。     

Integrating both Wikis and XML with case bases to facilitate case base development and maintenance

Case-based reasoning (CBR), as a promising technology for problem solving and decision support, has drawn considerable attention during the last 20 years. As CBR systems become more frequently deployed in real-world situations and as large-scale case-bases become more commonly used in practice, the development and maintenance of the case-base becomes critical to CBR practitioners. In reality, adding cases to a case-base and updating cases in a case-base can be troublesome and time-consuming processes. It has become increasingly important for CBR practitioners to be able to implement an efficient way to develop and maintain the case base. However, techniques for case-base development and maintenance (such as adding cases and updating cases) have not received enough attention and are often neglected by CBR researchers. This paper discusses Wikis and XML (specifically, the Office Open XML format) and proposes an integrated approach to facilitate case-base development and maintenance in adding cases and in updating cases.     

Measuring the convergence and diversity of CDAS Multi-Objective Particle Swarm Optimization Algorithms: A study of many-objective problems

The interest for many-objective optimization has grown due to the limitations of Pareto dominance based Multi-Objective Evolutionary Algorithms when dealing with problems of a high number of objectives. Recently, some many-objective techniques have been proposed to avoid the deterioration of these algorithms' search ability. At the same time, the interest in the use of Particle Swarm Optimization (PSO) algorithms in multi-objective problems also grew. The PSO has been found to be very efficient to solve multi-objective problems (MOPs) and several Multi-Objective Particle Swarm Optimization (MOPSO) algorithms have been proposed. This work presents a study of the behavior of MOPSO algorithms in many-objective problems. The many-objective technique named control of dominance area of solutions (CDAS) is used on two Multi-Objective Particle Swarm Optimization algorithms. An empirical analysis is performed to identify the influence of the CDAS technique on the convergence and diversity of MOPSO algorithms using three different many-objective problems. The experimental results are compared applying quality indicators and statistical tests.     

Learning adaptation knowledge to improve case-based reasoning

Case-Based Reasoning systems retrieve and reuse solutions for previously solved problems that have been encountered and remembered as cases. In some domains, particularly where the problem solving is a classification task, the retrieved solution can be reused directly. But for design tasks it is common for the retrieved solution to be regarded as an initial solution that should be refined to reflect the differences between the new and retrieved problems. The acquisition of adaptation knowledge to achieve this refinement can be demanding, despite the fact that the knowledge source of stored cases captures a substantial part of the problem-solving expertise. This paper describes an introspective learning approach where the case knowledge itself provides a source from which training data for the adaptation task can be assembled. Different learning algorithms are explored and the effect of the learned adaptations is demonstrated for a demanding component-based pharmaceutical design task, tablet formulation. The evaluation highlights the incremental nature of adaptation as a further reasoning step after nearest-neighbour retrieval. A new property-based classification to adapt symbolic values is proposed, and an ensemble of these property-based adaptation classifiers has been particularly successful for the most difficult of the symbolic adaptation tasks in tablet formulation.     

Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization

Due to the novelty of the Grey Wolf Optimizer (GWO), there is no study in the literature to design a multi-objective version of this algorithm. This paper proposes a Multi-Objective Grey Wolf Optimizer (MOGWO) in order to optimize problems with multiple objectives for the first time. A fixed-sized external archive is integrated to the GWO for saving and retrieving the Pareto optimal solutions. This archive is then employed to define the social hierarchy and simulate the hunting behavior of grey wolves in multi-objective search spaces. The proposed method is tested on 10 multi-objective benchmark problems and compared with two well-known meta-heuristics: Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) and Multi-Objective Particle Swarm Optimization (MOPSO). The qualitative and quantitative results show that the proposed algorithm is able to provide very competitive results and outperforms other algorithms. Note that the source codes of MOGWO are publicly available at http://www.alimirjalili.com/GWO.html.     

A comparative study of Multi-Objective Ant Colony Optimization algorithms for the Time and Space Assembly Line Balancing Problem

Assembly lines for mass manufacturing incrementally build production items by performing tasks on them while flowing between workstations. The configuration of an assembly line consists of assigning tasks to different workstations in order to optimize its operation subject to certain constraints such as the precedence relationships between the tasks. The operation of an assembly line can be optimized by minimizing two conflicting objectives, namely the number of workstations and the physical area these require. This configuration problem is an instance of the TSALBP, which is commonly found in the automotive industry. It is a hard combinatorial optimization problem to which finding the optimum solution might be infeasible or even impossible, but finding a good solution is still of great value to managers configuring the line. We adapt eight different Multi-Objective Ant Colony Optimization (MOACO) algorithms and compare their performance on ten well-known problem instances to solve such a complex problem. Experiments under different modalities show that the commonly used heuristic functions deteriorate the performance of the algorithms in time-limited scenarios due to the added computational cost. Moreover, even neglecting such a cost, the algorithms achieve a better performance without such heuristic functions. The algorithms are ranked according to three multi-objective indicators and the differences between the top-4 are further reviewed using statistical significance tests. Additionally, these four best performing MOACO algorithms are favourably compared with the Infeasibility Driven Evolutionary Algorithm (IDEA) designed specifically for industrial optimization problems.     

Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville–Thermalito complex

This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville–Thermalito Complex (OTC) – a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation–storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California.     

多约束集群目标下武器-目标分配问题

面对未来作战中高密度、多方位的集群智能体,传统点对点饱和攻击已不是最佳策略,可通过选择合适的武器类型和作用点实现火力覆盖,达到武器数量小于目标数量的最大杀伤效果。综合考虑安全目标、毁伤门限、偏好指派等作战需求,首先,建立了多约束多目标武器-目标分配（CMWTA）数学模型;其次,设计了约束违反值的计算方法,并采用个体编码、检测修复和约束支配相结合的方式处理多约束;最后,设计了针对多目标武器-目标分配模型的收敛性度量指标,并基于多目标进化算法（MOEA）框架进行了仿真分析。其中在进化算法框架对比中,SPEA2下的Pareto集合容量主要分布于[21,25]区间内,NSGA-Ⅱ下的Pareto集合容量主要分布于[16,20],而MOEA/D下的Pareto集合容量均小于16;在修复算法验证中,修复算法将三种进化算法框架的Convergence指标提升了20%以上,且可将Pareto解集中不可行解的比例保持在0%。实验结果表明,在求解CMWTA模型中,SPEA2算法框架在分布性和收敛性上优于NSGA-Ⅱ和MOEA/D算法框架,且所提修复算法有效地提高了进化算法对非支配可行解的求解效率。     

一个SPEA改进算法及其收敛性分析

SPEA是一种多目标优化算法。与其它多目标进化算法相比,SPEA算法具有设置参数少、解在空间分布均匀等优点。本文引入多点交叉和Cauchy变异对SPEA算法的收敛速度进行了改进,并对其收敛性进行了分析,文中给出的仿真算例证实了改进方法的有效性。     

多目标进化算法测试问题的设计与分析

为了有效检测多目标优化进化算法的性能,从3个方面进行多目标优化测试问题的设计,即约束条件、最优解分布的均匀性、算法逼近Pareto最优前沿的难度,采用NSGA-Ⅱ算法对这些测试问题进行仿真实验,并将算法求得的最优解可视化。结果显示,测试问题能够有效检测算法在上述3方面的性能。     

混合分散搜索的进化多目标优化算法

在进化多目标优化算法中,种群的多样性、对目标空间的搜索能力及算法的鲁棒性直接影响算法的收敛能力和解集的分散性。针对这些问题,提出了一种混合分散搜索的进化多目标优化算法(SSMOEA)。SSMOEA在混合分散搜索算法架构的同时,重新设计其多样性的选取策略,并引入协同进化机制。此外,为了提高算法的自适应性和鲁棒性,采用了一种新颖的自适应多交叉算子选择方法。SSMOEA与经典的多目标进化算法SPEA2、NSGA-Ⅱ和MOEA/D在12个基准测试函数上的对比结果表明,SSMOEA不仅在求得的Pareto最优解集的宽广性、均匀性和逼近性上有明显优势,而且算法的鲁棒性也有明显的提高。     

Hierarchical case-based reasoning integrating case-based anddecompositional problem-solving techniques for plant-control softwaredesign

Case based reasoning (CBR) is an artificial intelligence technique that emphasises the role of past experience during future problem solving. New problems are solved by retrieving and adapting the solutions to similar problems, solutions that have been stored and indexed for future reuse as cases in a case-base. The power of CBR is severely curtailed if problem solving is limited to the retrieval and adaptation of a single case, so most CBR systems dealing with complex problem solving tasks have to use multiple cases. The paper describes and evaluates the technique of hierarchical case based reasoning, which allows complex problems to be solved by reusing multiple cases at various levels of abstraction. The technique is described in the context of Deja Vu, a CBR system aimed at automating plant-control software design