改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

Differential evolution with generalized differentials

In this paper, we study the mutation operation of the differential evolution (DE) algorithm. In particular, we propose the differential of scaled vectors, called the ‘generalized differential’, as opposed to the existing scaled differential vector in the mutation of DE. We derive the probability distribution of points generated by the mutation with ‘generalized differentials’. We incorporate a vector-projection-based exploratory method within the new mutation scheme. The vector projection is not mandatory and it is only invoked if trial points continue to be unsuccessful. An algorithm is then proposed which implements the mutation strategy based on the difference of the scaled vectors as well as the vector projection technique. A numerical study is carried out using a set of 50 test problems, many of which are inspired by practical applications. Numerical results suggest that the new algorithm is superior to DE.     

Differential evolution with preferential crossover

We study the mutation operation of the differential evolution algorithm. In particular, we study the effect of the scaling parameter of the differential vector in mutation. We derive the probability density function of points generated by mutation and thereby identify some drawbacks of the scaling parameter. We also visualize the drawbacks using simulation. We then propose a crossover rule, called the preferential crossover rule, to reduce the drawbacks. The preferential crossover rule uses points from an auxiliary population set. We also introduce a variable scaling parameter in mutation. Motivations for these changes are provided. A numerical study is carried out using 50 test problems, many of which are inspired by practical applications. Numerical results suggest that the proposed modification reduces the number of function evaluations and cpu time considerably.     

Differential evolution with multi-constraint consensus methods for constrained optimization

Constrained optimization is an important research topic that assists in quality planning and decision making. To solve such problems, one of the important aspects is to improve upon any constraint violation, and thus bring infeasible individuals to the feasible region. To achieve this goal, different constraint consensus methods have been introduced, but no single method performs well for all types of problems. Hence, in this research, for solving constrained optimization problems, we introduce different variants of the Differential Evolution algorithm, with multiple constraint consensus methods. The proposed algorithms are tested and analyzed by solving a set of well-known bench mark problems. For further improvements, a local search is applied to the best variant. We have compared our algorithms among themselves, as well as with other state of the art algorithms. Those comparisons show similar, if not better performance, while also using significantly lower computational time.     

Differential evolution for dynamic environments with unknown numbers of optima

This paper investigates optimization in dynamic environments where the numbers of optima are unknown or fluctuating. The authors present a novel algorithm, Dynamic Population Differential Evolution (DynPopDE), which is specifically designed for these problems. DynPopDE is a Differential Evolution based multi-population algorithm that dynamically spawns and removes populations as required. The new algorithm is evaluated on an extension of the Moving Peaks Benchmark. Comparisons with other state-of-the-art algorithms indicate that DynPopDE is an effective approach to use when the number of optima in a dynamic problem space is unknown or changing over time.     

Differential evolution algorithms using hybrid mutation

Differential evolution (DE) has gained a lot of attention from the global optimization research community. It has proved to be a very robust algorithm for solving non-differentiable and non-convex global optimization problems. In this paper, we propose some modifications to the original algorithm. Specifically, we use the attraction-repulsion concept of electromagnetism-like (EM) algorithm to boost the mutation operation of the original differential evolution. We carried out a numerical study using a set of 50 test problems, many of which are inspired by practical applications. Results presented show the potential of this new approach.     

Differential evolution for sequencing and scheduling optimization

This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.     

Differential evolution framework for big data optimization

During the last two decades, dealing with big data problems has become a major issue for many industries. Although, in recent years, differential evolution has been successful in solving many complex optimization problems, there has been research gaps on using it to solve big data problems. As a real-time big data problem may not be known in advance, determining the appropriate differential evolution operators and parameters to use is a combinatorial optimization problem. Therefore, in this paper, a general differential evolution framework is proposed, in which the most suitable differential evolution algorithm for a problem on hand is adaptively configured. A local search is also employed to increase the exploitation capability of the proposed algorithm. The algorithm is tested on the 2015 big data optimization competition problems (six single objective problems and six multi-objective problems). The results show the superiority of the proposed algorithm to several state-of-the-art algorithms.     

Constrained evolution processes and emergence of organized diversity

In a previous work on perturbation theory in population dynamics, we showed several plausible situations of preservation of the biodiversity. We give now an improved version of the method exhibiting a phenomenon of emergence of structured diversity. We display several (plausible in ethological or sociological contexts) examples of small modifications of the demographic equations that are emergent, that is, they lead to a limit state (the attractor) where the ‘spectators’ (i.e. to the individuals not concerned with the modification) vanish. In other words, even if the modification involves only a small number of individuals initially, the final pattern involves all the individuals. This behavior is easily understood in cases when the modification is concerned with some kind of symbiotic behavior, as it induces an advantage with respect to the ‘spectators’. But the phenomenon is very much general; we give examples of emergence in other contexts, involving predator/pray relations or other entangled relations, including an experimentally known example of subspecies of Escherichia coli. Copyright © 2015 John Wiley & Sons, Ltd.     

On the evolution of an intelligent maintenance optimization system

In this paper the author reviews the development of an intelligent maintenance optimization system over the past 16 years. The paper starts with discussion of the initial motivation behind developing the system and the designs of the early versions of a computer program to access maintenance history data and provide an analysis. The concept behind this system was gradually developed to incorporate a rule base for the selection of a suitable model for preventive maintenance (PM) scheduling and then to a fully developed knowledge-based system for decision support. The need to incorporate case-based reasoning thus creating a hybrid system that can learn with use in addition to using elicited knowledge from experts is discussed. The experience with system validation with two versions of the system is analysed. The paper also reviews the extensive fundamental work on developing appropriate PM models that can deal with real data patterns. Finally, the scope for future development is presented.     

Differential evolution algorithm-based parameter estimation for chaotic systems

Parameter estimation for chaotic systems is an important issue in nonlinear science and has attracted increasing interests from various research fields, which could be essentially formulated as a multidimensional optimization problem. As a novel evolutionary computation technique, differential evolution algorithm (DE) has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. However, to the best of our knowledge, there is no published work on DE for estimating parameters of chaotic systems. In this paper, a DE approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of DE. Moreover, the effect of population size on the optimization performances is investigated as well.     

Differential invariants of the one-dimensional quasi-linear second-order evolution equation

We consider evolution equations of the form u_t = f(x, u, u_x)u_xx + g(x, u, u_x) and u_t = u_xx + g(x, u, u_x). In the spirit of the recent work of Ibragimov [Ibragimov NH. Laplace type invariants for parabolic equations. Nonlinear Dynam 2002;28:125–33] who adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups, we apply the method to these equations. We show that the first class admits one differential invariant of order two, while the second class admits three functional independent differential invariants of order three. We use these invariants to determine equations that can be transformed into the linear diffusion equation.     

Memetic self-adaptive evolution strategies applied to the maximum diversity problem

The maximum diversity problem consists in finding a subset of elements which have maximum diversity between each other. It is a very important problem due to its general aspect, that implies many practical applications such as facility location, genetics, and product design. We propose a method based on evolution strategies with local search and self-adaptation of the parameters. For all time limits from 1 to 300 s as well as for time to converge to the best solutions known, this method leads to better results when compared to other state-of-the-art algorithms.     

Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.     

Degradation-based burn-in with preventive maintenance

As many products are becoming increasingly more reliable, traditional lifetime-based burn-in approaches that try to fail defective units during the test require a long burn-in duration, and thus are not effective. Therefore, we promote the degradation-based burn-in approach that bases the screening decision on the degradation level of a burnt-in unit. Motivated by the infant mortality faced by many Micro-Electro-Mechanical Systems (MEMSs), this study develops two degradation-based joint burn-in and maintenance models under the age and the block based maintenances, respectively. We assume that the product population comprises a weak and a normal subpopulations. Degradation of the product follows Wiener processes with linear drift, while the weak and the normal subpopulations possess distinct drift parameters. The objective of joint burn-in and maintenance decisions is to minimize the long run average cost per unit time during field use by properly choosing the burn-in settings and the preventive replacement intervals. An example using the MEMS devices demonstrates effectiveness of these two models.     

Differential properties of solutions of evolution variational inequalities in the theory of plasticity

We study the differential properties of weak solutions of evolution variational inequalities in the theory of flow of elastoplastic media with hardening. We consider the two most popular models of hardening—isotropic and kinematic. The differential properties studied depend on the nature of the hardening. In the case of isotropic hardening great smoothness of the distributed load is required, and in this situation the result is the same for the stress tensor—it belongs to the class L (0,T;W _2,loc ¹ ).Bibliography: 10 titles. Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 153–173.     

Differential amplifier with transistors

Zusammenfassung In Differentialverstärkern mit Transistoren erhält man die beste Unterdrückung eines Gleichtaktsignals, wenn der gemeinsame Emitterwiderstand etwa den Werth ₂₁/2h ₂₂ annähert. Ein grösserer Emitterwiderstand hat eine Phasenkehr des Gleichtaktsignals am Ausgang zur Folge, was in Verstärkern mit Rückführungen (zur besseren Unterdrückung dieses Signals) Stabilitätsschwierigkeiten zur Folge haben kann.     

Mean-risk analysis with enhanced behavioral content

We study a mean-risk model derived from a behavioral theory of Disappointment with multiple reference points. One distinguishing feature of the risk measure is that it is based on mutual deviations of outcomes, not deviations from a specific target. We prove necessary and sufficient conditions for strict first and second order stochastic dominance, and show that the model is, in addition, a Convex Risk Measure. The model allows for richer, and behaviorally more plausible, risk preference patterns than competing models with equal degrees of freedom, including Expected Utility (EU), Mean–Variance (M-V), Mean-Gini (M-G), and models based on non-additive probability weighting, such as Dual Theory (DT). In asset allocation, the model allows a decision-maker to abstain from diversifying in a positive expected value risky asset if its performance does not meet a certain threshold, and gradually invest beyond this threshold, which appears more acceptable than the extreme solutions provided by either EU and M-V (always diversify) or DT and M-G (always plunge). In asset trading, the model provides no-trade intervals, like DT and M-G, in some, but not all, situations. An illustrative application to portfolio selection is presented. The model can provide an improved criterion for mean-risk analysis by injecting a new level of behavioral realism and flexibility, while maintaining key normative properties.