Packing non-identical circles within a rectangle with open length

Packing non-identical circles inside a rectangle witnesses a wide range of industrial applications. However, the non-convex constraints in this problem make it intractable using exact analytical approaches. Even via heuristic methods, the solution time for industrial-scale instances sometimes is too long to be acceptable. This article aims to challenge the existing methods for the benchmark instances. The most significant contributions of this work are: firstly, we proposed three types of packing positions for selection and used human intelligence to convert an arbitrary circle sequence into a feasible compact layout; secondly, diverse position selection criteria have been tested, and it is found that the criterion commonly used in the literature is not the best; thirdly, the traditional genetic algorithm is adapted with lower crossover rate but higher mutation rate particularly, and a minor-adjustment operator with the purpose of exploring the neighborhood of the current best solutions is introduced.     

Stability of discrete-time positive evolution operators on ordered Banach spaces and applications

In this paper we discuss stability problems for a class of discrete-time evolution operators generated by linear positive operators acting on certain ordered Banach spaces. Our approach is based upon a new representation result that links a positive operator with the adjoint operator of its restriction to a Hilbert subspace formed by sequences of Hilbert–Schmidt operators. This class includes the evolution operators involved in stability and optimal control problems for linear discrete-time stochastic systems. The inclusion is strict because, following the results of Choi, we have proved that there are positive operators on spaces of linear, bounded and self-adjoint operators which have not the representation that characterize the completely positive operators. As applications, we introduce a new concept of weak-detectability for pairs of positive operators, which we use to derive sufficient conditions for the existence of global and stabilizing solutions for a class of generalized discrete-time Riccati equations. Finally, assuming weak-detectability conditions and using the method of Lyapunov equations we derive a new stability criterion for positive evolution operators.     

Induced aggregation operators in the VIKOR method and its application in material selection

In this paper, a hybrid decision making approach integrating induced aggregation operators into VIKOR is proposed for tackling multicriteria problems with conflicting and noncommensurable (different units) criteria. For doing so, we develop a new distance aggregation operator called the induced ordered weighted averaging standardized distance (IOWASD) operator. It is an aggregation operator that provides a wide range of standardized distance measures between the maximum and the minimum by using the induced OWA (IOWA) operator. The main advantage of the IOWA-based VIKOR (IOWA-VIKOR) is that it is able to reflect the complex attitudinal character of the decision maker by using order inducing variables and provide much more complete information for decision making. We also studied some of the IOWASD’s main properties and different particular cases and further generalized it by using the induced generalized OWA (IGOWA) operator. Finally, we apply the integrated IOWA-VIKOR method in a multi-criteria decision making problem regarding the selection of materials and the results are compared for different types of standardized distance aggregation operators.     

Evolutionary algorithms for production planning problems with setup decisions

Production planning problems with setup decisions, which were formulated as mixed integer programmes (MIP), are solved in this study. The integer component of the MIP solution is determined by three evolution algorithms used in this study. Firstly, a traditional genetic algorithm (GA) uses conventional crossover and mutation operators for generating new chromosomes (solutions). Secondly, a modified GA uses not only the conventional operators but also a sibling operator, which stochastically produces new chromosomes from old ones using the sensitivity information of an associated linear programme. Thirdly, a sibling evolution algorithm uses only the sibling operator to reproduce. Based on the experiments done in this study, the sibling evolution algorithm performs the best among all the algorithms used in this study.     

An improved NSGA-III algorithm based on elimination operator for many-objective optimization

Due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance schemes in the environmental selection, the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to handle many-objective optimization problems. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the uniformly distributed reference points to significantly promote population diversity, but the convergence based on the Pareto-dominance relation could still be enhanced. For this purpose, an improved NSGA-III algorithm based on elimination operator (NSGA-III-EO) is proposed. In the proposed algorithm, the elimination operator first identifies the reference point with maximum niche count and then employs the penalty-based boundary intersection distance to rank the individuals associated with it. To this end, the selection scheme is used to remove the worse individuals rather than to select the superior individuals. The proposed NSGA-III-EO is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art MOEAs. Additionally, it is also tested on constrained problems having a large number of objectives and shows good performance.     

Theoretical and Experimental Study of Crossover Operators of Genetic Algorithms

This paper is concerned with crossover operators for genetic algorithms (GAs) which are used to solve problems based on real numbers. First, a classification of the operators is introduced, dividing crossover into a vector-level and a variable-level operator. The theoretical study of variable-level operators for binary coded GAs leads to the discovery of two properties, which are used to define certain characteristics of crossover operators used by real-number encoded GAs. For variable-level operators, the experimental distributions of the offspring variables of given pairs of parent variables are then found. Finally, an experimental comparison of crossover operator performance is carried out.     

一类双曲型方程的Huygens原理

通过双曲型方程的Hadamard基本解理论,将Huygens算子识别问题转化为双曲型方程的系数满足的关系,找出了更多的Huygens算子,从而推广了Stellmacher的结果,并解析了Veselov和Berest给出的一类Huygens算子与Stellmacher算子的关系．     

Quaternionic triangular linear operators

Triangular operators are an essential tool in the study of nonselfadjoint operators that appear in different fields with a wide range of applications. Although the development of a quaternionic counterpart for this theory started at the beginning of this century, the lack of a proper spectral theory combined with problems caused by the underlying noncommutative structure prevented its real development for a long time. In this paper, we give criteria for a quaternionic linear operator to have a triangular representation, namely, under which conditions such operators can be represented as a sum of a diagonal operator with a Volterra operator. To this effect, we investigate quaternionic Volterra operators based on the quaternionic spectral theory arising from the S-spectrum. This allow us to obtain conditions when a non-selfadjoint operator admits a triangular representation.     

Simultaneously Applying Multiple Mutation Operators in Genetic Algorithms

The mutation operation is critical to the success of genetic algorithms since it diversifies the search directions and avoids convergence to local optima. The earliest genetic algorithms use only one mutation operator in producing the next generation. Each problem, even each stage of the genetic process in a single problem, may require appropriately different mutation operators for best results. Determining which mutation operators should be used is quite difficult and is usually learned through experience or by trial-and-error. This paper proposes a new genetic algorithm, the dynamic mutation genetic algorithm, to resolve these difficulties. The dynamic mutation genetic algorithm simultaneously uses several mutation operators in producing the next generation. The mutation ratio of each operator changes according to evaluation results from the respective offspring it produces. Thus, the appropriate mutation operators can be expected to have increasingly greater effects on the genetic process. Experiments are reported that show the proposed algorithm performs better than most genetic algorithms with single mutation operators.     

A differential evolution algorithm with cooperative coevolutionary selection operation for high-dimensional optimization

Although different kinds of evolutionary algorithms (EAs) have been designed and achieved great success on many optimization problems, they are usually limited to some small-scale problems, e.g. with less than 100 decision variables, which may be quite small comparing to the requirements of real-world applications. Therefore, scaling EAs to large size problems have attracted more and more interest. Conventional EAs mimic the seemingly random natural processes by which species evolve. These evolution processes are slow or inefficient. Now, genetic engineering has enabled man to increase both the yields and quality of some crops fast by modifying some part of their genome precisely. In this paper, inspired by the ideas of the genetic engineering, we designed a local selection operator by decomposing the high-dimensional problem into some subcomponents and assigning a local fitness function to evaluate each subcomponent. Then a new differential evolution (DE) is proposed by inserting the local selection operator into the framework of DE. Numerical experiments were carried out to evaluate the performance of the new algorithm on a large number of benchmark functions. The results show that the new algorithm is effective and efficient for high-dimensional optimization.     

Analysis of crossovers and selections in a coarse-grained parallel genetic algorithm

The parallel genetic algorithms (PGA) have been developed for combinatorial optimization problems, and its parallel efficiencies have been investigated on a specific problem. These investigations were concerned with how to design a topology and the determination of the optimum setting for parameters (for example, size of subpopulations, migration interval, and so on) rather than the effectiveness of genetic operators. This paper investigates a relation between the parallel efficiency of the coarse-grained PGA and genetic (crossover and selection) operators for the traveling salesman problem on an MIMD parallel computer. The following genetic operators are considered: improved edge recombination (IERX), distance preserving (DPX), and complete subtour exchange (CSEX) crossovers, and two selection operators, which have relatively high selection pressures. Computational results indicate that the parallel efficiency is significantly affected by the difference of crossovers rather than the selections, and the PGA with CSEX gives better properties.     

The role of crossover operator in the genetic optimization of magnetic models

The Ising model, introduced almost 100 years ago by Wilhelm Lenz and Ernst Ising, is the formalism still popular as a tool to describe magnetic properties of a wide class of materials. Among many issues which arise when using this model there exist problems related to the process of finding minimum energy of the system. Since these problems are NP-hard, optimizations can either be performed for some approximated cases or be the subject of global optimization techniques. In this paper we present an analysis of the effect of different crossover operators on the efficiency of genetic algorithm used to minimize energy in the Ising model. Although it is not a benchmark tool, we hope it may be interesting as a testing tool.     

A memetic algorithm for the orienteering problem with hotel selection

In this paper, a memetic algorithm is developed to solve the orienteering problem with hotel selection (OPHS). The algorithm consists of two levels: a genetic component mainly focuses on finding a good sequence of intermediate hotels, whereas six local search moves embedded in a variable neighborhood structure deal with the selection and sequencing of vertices between the hotels. A set of 176 new and larger benchmark instances of OPHS are created based on optimal solutions of regular orienteering problems. Our algorithm is applied on these new instances as well as on 224 benchmark instances from the literature. The results are compared with the known optimal solutions and with the only other existing algorithm for this problem. The results clearly show that our memetic algorithm outperforms the existing algorithm in terms of solution quality and computational time. A sensitivity analysis shows the significant impact of the number of possible sequences of hotels on the difficulty of an OPHS instance.     

A variant of forward-backward splitting method for the sum of two monotone operators with a new search strategy

In this paper, we propose variants of Forward-Backward splitting method for finding a zero of the sum of two operators. A classical modification of Forward-Backward method was proposed by Tseng, which is known to converge when the forward and the backward operators are monotone and with Lipschitz continuity of the forward operator. The conceptual algorithm proposed here improves Tseng’s method in some instances. The first and main part of our approach, contains an explicit Armijo-type search in the spirit of the extragradient-like methods for variational inequalities. During the iteration process, the search performs only one calculation of the forward-backward operator in each tentative of the step. This achieves a considerable computational saving when the forward-backward operator is computationally expensive. The second part of the scheme consists in special projection steps. The convergence analysis of the proposed scheme is given assuming monotonicity on both operators, without Lipschitz continuity assumption on the forward operator.     

An efficient grouping genetic algorithm for U-shaped assembly line balancing problems with maximizing production rate

U-type assembly line is one of the important tools that may increase companies’ production efficiency. In this study, two different modeling approaches proposed for the assembly line balancing problems have been used in modeling type-II U-line balancing problems, and the performances of these models have been compared with each other. It has been shown that using mathematical formulations to solve medium and large size problem instances is impractical since the problem is NP-hard. Therefore, a grouping genetic and simulated annealing algorithms have been developed, and a particle swarm optimization algorithm is adapted to compare with the proposed methods. A special crossover operator that always obtains feasible offspring has been suggested for the proposed grouping genetic algorithm. Furthermore, a local search procedure based on problem-specific knowledge was applied to increase the intensification of the algorithm. A set of well-known benchmark instances was solved to evaluate the effectiveness of the proposed and existing methods. Results showed that while the mathematical formulations can only be used to solve small size instances, metaheuristics can obtain high quality solutions for all size problem instances within acceptable CPU times. Moreover, grouping genetic algorithm has been found to be superior to the other methods according to the number of optimal solutions, or deviations from the lower bound values.     

Multi-scale modelling of sandwich structures using the Arlequin method Part I: Linear modelling

The paper presents an Arlequin based multi-scale method for studying problems related to the mechanical behaviour of sandwich composite structures. Towards this end, different models are mixed and glued to each other. Several coupling operators are tested in order to assess the usefulness of the proposed approach. A new coupling operator is proposed and tested on the different glued Arlequin zones. A free–clamped sandwich beam with soft core undergoing a concentrated effort on the free edge is used as a typical example (benchmark) in the validation procedure. Numerical simulations were conducted as the preliminary evaluation of the various coupling operators and the discrepancies between local and global models in the gluing zone have been addressed with sufficient care.     

Krill herd: A new bio-inspired optimization algorithm

In this paper, a novel biologically-inspired algorithm, namely krill herd (KH) is proposed for solving optimization tasks. The KH algorithm is based on the simulation of the herding behavior of krill individuals. The minimum distances of each individual krill from food and from highest density of the herd are considered as the objective function for the krill movement. The time-dependent position of the krill individuals is formulated by three main factors: (i) movement induced by the presence of other individuals (ii) foraging activity, and (iii) random diffusion. For more precise modeling of the krill behavior, two adaptive genetic operators are added to the algorithm. The proposed method is verified using several benchmark problems commonly used in the area of optimization. Further, the KH algorithm is compared with eight well-known methods in the literature. The KH algorithm is capable of efficiently solving a wide range of benchmark optimization problems and outperforms the exciting algorithms.     

Some approximation properties by a class of bivariate operators

Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.     

基于遗传算法的固定起讫点危险品配送路线优化

为科学选择危险品配送路线,保障运输安全,将传统TSP(Travelling SalesmanProblem)问题加以推广和延伸,建立以路段交通事故率、路侧人口密度、环境影响因子和路段运输费用为指标的固定起讫点危险品配送路线优化模型.以遗传算法基本框架为基础,引入新的遗传算子,构建了可用于实现模型的多目标遗传算法.实例仿真表明,所建模型和算法在求解固定起讫点危险品配送路线优化问题中有较好的实用性.     

博弈的统计演化分析

首先定义了具有确定分布的随机环境中的基于适应度的平均选择算子,然后证明了主体战略集上的任一概率密度在平均选择算子的迭代过程中收敛于平均适应度函数的最大集上的某一分布,然后就多主体的博弈问题定义了平均选择算子,并以此为基础证明了平均选择算子的不动点就是博弈的纳什均衡.