Non-parametric stochastic subset optimization utilizing multivariate boundary kernels and adaptive stochastic sampling

The implementation of NP-SSO (non-parametric stochastic subset optimization) to general design under uncertainty problems and its enhancement through various soft computing techniques is discussed. NP-SSO relies on iterative simulation of samples of the design variables from an auxiliary probability density, and approximates the objective function through kernel density estimation (KDE) using these samples. To deal with boundary correction in complex domains, a multivariate boundary KDE based on local linear estimation is adopted in this work. Also, a non-parametric characterization of the search space at each iteration using a framework based on support vector machine is formulated. To further improve computational efficiency, an adaptive kernel sampling density formulation is integrated and an adaptive, iterative selection of the number of samples needed for the KDE implementation is established.     

Innovative seismic design optimization with reliability constraints

Performance-Based Design (PBD) methodologies is the contemporary trend in designing better and more economic earthquake-resistant structures where the main objective is to achieve more predictable and reliable levels of safety and operability against natural hazards. On the other hand, reliability-based optimization (RBO) methods directly account for the variability of the design parameters into the formulation of the optimization problem. The objective of this work is to incorporate PBD methodologies under seismic loading into the framework of RBO in conjunction with innovative tools for treating computational intensive problems of real-world structural systems. Two types of random variables are considered: Those which influence the level of seismic demand and those that affect the structural capacity. Reliability analysis is required for the assessment of the probabilistic constraints within the RBO formulation. The Monte Carlo Simulation (MCS) method is considered as the most reliable method for estimating the probabilities of exceedance or other statistical quantities albeit with excessive, in many cases, computational cost. First or Second Order Reliability Methods (FORM, SORM) constitute alternative approaches which require an explicit limit-state function. This type of limit-state function is not available for complex problems. In this study, in order to find the most efficient methodology for performing reliability analysis in conjunction with performance-based optimum design under seismic loading, a Neural Network approximation of the limit-state function is proposed and is combined with either MCS or with FORM approaches for handling the uncertainties. These two methodologies are applied in RBO problems with sizing and topology design variables resulting in two orders of magnitude reduction of the computational effort.     

An efficient heuristic for reliability design optimization problems

This paper develops an efficient heuristic to solve two typical combinatorial optimization problems frequently met when designing highly reliable systems. The first one is the redundancy allocation problem (RAP) of series-parallel binary-state systems. The design goal of the RAP is to select the optimal combination of elements and redundancy levels to maximize system reliability subject to the system budget and to the system weight. The second problem is the expansion-scheduling problem (ESP) of multi-state series-parallel systems. In this problem, the study period is divided into several stages. At each stage, the demand is represented as a piecewise cumulative load curve. During the system lifetime, the demand can increase and the total productivity may become insufficient to assume the demand. To increase the total system productivity, elements are added to the existing system. The objective in the ESP is to minimize the sum of costs of the investments over the study period while satisfying availability constraints at each stage. The heuristic approach developed to solve the RAP and the ESP is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. Numerical results for the test problems from previous research are reported and compared. The results show the advantages of the proposed approach for solving both problems.     

Two stochastic optimization algorithms for convex optimization with fixed point constraints

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of fixed point sets of nonexpansive mappings in a real Hilbert space. This setting of fixed point constraints enables consideration of the case in which the projection onto each of the constraint sets cannot be computed efficiently. Both algorithms use a convex function and a nonexpansive mapping determined by a certain probabilistic process at each iteration. One algorithm blends a stochastic gradient method with the Halpern fixed point algorithm. The other is based on a stochastic proximal point algorithm and the Halpern fixed point algorithm; it can be applied to nonsmooth convex optimization. Convergence analysis showed that, under certain assumptions, any weak sequential cluster point of the sequence generated by either algorithm almost surely belongs to the solution set of the problem. Convergence rate analysis illustrated their efficiency, and the numerical results of convex optimization over fixed point sets demonstrated their effectiveness.     

随机ADD算法的不确定网络优化研究

传统的网络优化问题通过对偶梯度下降算法来解决,虽然该算法能够以分布式方式来实现,但其收敛速度较慢.加速对偶下降算法(ADD)通过近似牛顿步长的分布式计算,提高了对偶梯度下降算法的收敛速率.但由于通信网络的不确定性,在约束不确定时,该算法的收敛性难以保证.基于此,提出了一种随机形式的ADD算法来解决该网络优化问题.理论上证明了随机ADD算法当不确定性的均方误差有界时,能以较高概率收敛于最优值的一个误差邻域;当给出更严格的不确定性的约束条件时,算法则可以较高概率收敛于最优值.实验结果表明,随机ADD算法的收敛速率比随机梯度下降算法快两个数量级.     

不确定可靠性优化问题的多目标粒子群优化算法

针对元件可靠性为区间值的系统可靠性优化问题, 提出一种区间多目标粒子群优化方法. 首先, 建立问题的区间多目标优化模型; 然后, 利用粒子群算法优化该模型, 定义一种不精确Pareto 支配关系, 并给出编码、约束处理、外部存储器更新、领导粒子选择等关键问题的解决方法; 最后, 将该方法应用于可靠性优化问题实例, 验证了方法的有效性.

     

求解带约束优化问题的混合式多策略萤火虫算法

目前多目标优化算法主要针对如何处理多个目标之间的冲突,对于如何处理约束考虑较少,鉴于此,提出一种求解带约束优化问题的混合式多策略萤火虫算法(HMSFA-PC).首先,提出一种改进的动态罚函数策略对约束优化问题进行预处理,将其转换为非约束优化问题;其次,对萤火虫算法本身进行改进,采用Lévy flights搜索机制有效地增大搜索范围;接着,引入随机扩张因子改进算法吸引模型,使种群突破束缚,有效避免早熟收敛,提出自适应维度重组机制,根据不同迭代时期选择差异性较大的个体进行信息交互、相互学习.为检验算法处理无约束优化问题的性能,将其在基准测试函数上与部分典型算法进行比较;为检验算法处理约束优化问题的性能,将其在实际约束测试问题中与一些顶尖约束求解算法进行比较.结果表明,HMSFA-PC在处理无约束优化问题时具有收敛速度快、收敛精度高等优势,并且在动态罚函数的协作下求解实际约束优化问题时仍具有良好的优化性能.     

Direct cut-off method for combinatorial optimization problems with additional constraints

A direct cut-off method to solve combinatorial optimization problems on polyarrangements with additional constraints is proposed and justified. The method allows obtaining a feasible solution at each stage without constructing the linear hull of the set of polyarrangements.     

An improved algorithm for optimization problems with functional inequality constraints

This paper presents an algorithm for optimization problems with distributed constraints. The algorithm is of the combined phase I-phase II feasible directions type, similar to one proposed by Polak and Mayne. It was developed as an improved version of the Polak-Mayne algorithm; by performing certain approximations in a different way it was possible to eliminate an expensive test required by Polak and Mayne.     

Improved cuckoo search for reliability optimization problems

An efficient approach to solve engineering optimization problems is the cuckoo search algorithm. It is a recently developed meta-heuristic optimization algorithm. Normally, the parameters of the cuckoo search are kept constant. This may result in decreasing the efficiency of the algorithm. To cope with this issue, the cuckoo search parameters should be tuned properly. In this paper, an improved cuckoo search algorithm, enhancing the accuracy and convergence rate of the cuckoo search algorithm, is presented. Then, the performance of the proposed algorithm is tested on some complex engineering optimization problems. They are four well-known reliability optimization problems, a large-scale reliability optimization problem as well as a complex system, which is a 15-unit system reliability optimization problem. Finally, the results are compared with those given by several well-known methods. Simulation results demonstrate the effectiveness of the proposed algorithm.     

Structural optimization by displaying the reliability constraints

This paper presents an approach for structural optimization design by means of displaying the reliability constraints. To begin with, a variety of non-normal random loads to which the structure is subjected are transformed into normal types of loads by means of normal tail transformation. Then the reliability constraints, namely displacement and stress, are transformed into constraints of conventional forms according to the characteristics of invariance in a linear elastic structures to the normal loads. At the end, the problem of reliabliltiy optimization is solved by the mixed method and satisfactory results have been obtained.     

Discrete optimization with logical constraints for design of complex products

Consideration was given to the optimization problem arising at designing complex products. It was assumed that the products are formed of the components with allowance for certain conditions and criteria. To solve the problem, an approach relying on discrete optimization with logical constraints was developed. An algorithm to determine the precise solution on the basis of enumeration of L-classes was developed, and a computer-aided experiment carried out. The algorithm was incorporated in the software of the computer-aided clothing design system.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

Functionally redundant constraints for Boolean quadratic-type optimization problems

A method of construction of functionally redundant quadratic constraints is proposed for Boolean quadratic-type optimization problems. The method is based on an extension of a set of Boolean variables and formation of functionally redundant constraints that relate the initial and added variables. Examples of improvement of Lagrangian dual quadratic estimates obtained by using the constructed redundant constraints are given. This work was carried out thanks to partial financial support under grant UM2-2547-KV-03 (CRDF Cooperative Grants Program.). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 168–172, November–December 2005.     

An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.     

A simple computational procedure for optimization problems with functional inequality constraints

In this note, a simple computational procedure is given for solving a class of optimization problems, where an objective function is to be minimized subject to conventional inequality constraints as well as to inequality constraints of the functional type.     

随机优化问题基于假设检验的遗传算法

为了有效解决具有不确定性和多极小性的随机优化问题 ,提出了一类基于假设检验的遗传算法 .该方法通过多次评价来进行解性能的合理估计 ,利用遗传操作来进行解空间的有效搜索 ,采用假设检验来增加种群的多样性和算法的探索能力 ,从而避免遗传算法的早熟收敛 .基于典型的随机函数优化和组合优化问题 ,仿真研究了假设检验、性能估计次数、噪声幅度对算法性能的影响 ,验证了所提方法的有效性和鲁棒性     

An intelligent moving object optimization algorithm for design problems with mixed variables, mixed constraints and multiple objectives

This paper presents an optimization algorithm for engineering design problems having a mix of continuous, discrete and integer variables; a mix of linear, non-linear, differentiable, non-differential, equality, inequality and even discontinuous design constraints; and conflicting multiple design objectives. The intelligent movement of objects (vertices and compounds) is simulated in the algorithm based on a Nelder–Mead simplex with added features to handle variable types, bound and design constraints, local optima, search initiation from an infeasible region and numerical instability, which are the common requirements for large-scale, complex optimization problems in various engineering and business disciplines. The algorithm is called an INTElligent Moving Object algorithm and tested for a wide range of benchmark problems. Validation results for several examples, which are manageable within the scope of this paper, are presented herein. Satisfactory results have been obtained for all the test problems, hence, highlighting the benefits of the proposed method.     

求解一类随机优化问题的社会认知算法

提出了解随机优化问题的社会认知算法.该算法易于理解及程序易实现,克服了随机优化问题难以高效实现全局优化的缺点,为随机优化问题的求解提供了一种新的途径,并为社会认知算法的应用拓展了新的空间.