On the quality evaluation of scientific entities in Poland supported by consistency-driven pairwise comparisons method

Comparison, rating, and ranking of alternative solutions, in case of multicriteria evaluations, have been an eternal focus of operations research and optimization theory. There exist numerous approaches at practical solving the multicriteria ranking problem. The recent focus of interest in this domain was the event of parametric evaluation of research entities in Poland. The principal methodology was based on pairwise comparisons. For each single comparison, four criteria have been used. One of the controversial points of the assumed approach was that the weights of these criteria were arbitrary. The main focus of this study is to put forward a theoretically justified way of extracting weights from the opinions of domain experts. Theoretical bases for the whole procedure are based on a survey and its experimental results. Discussion and comparison of the two resulting sets of weights and the computed inconsistency indicator are discussed.     

A COMPARISON OF THREE METHODS FOR GENERATING THE PARETO OPTIMAL SET

This paper describes and compares three approaches to solving design optimization problems with multiple conflicting objectives. The three techniques are described in detail and then applied lo an example which demonstrates how information is accumulated which leads to a logical and efficient multicriteria optimal design. The techniques employed (weighting, noninferior set estimation and constraint methods) ate compared to each other by considering their computational efficiencies and their abilities to produce an approximation of the Pareto optimal set.     

An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation‐based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd.     

A bilevel game theoretic approach to optimum design of flywheels

Multiobjective optimization problems arise frequently in mechanical design. One approach to solving these types of problems is to use a game theoretic formulation. This article illustrates the application of a bilevel, leader–follower model for solving an optimum design problem. In particular, the optimization problem is modelled as a Stackelberg game. The partitioning of variables between the leader and follower problem is discussed and a variable partitioning metric is introduced to compare various variable partitions. A computational procedure based on variable updating using sensitivity information is developed for exchanging information between the follower and leader problems. The proposed approach is illustrated through the design of a flywheel. The two objective functions used for the design problem include maximizing the kinetic energy stored in the flywheel while simultaneously minimizing the manufacturing cost.     

Reliability-based optimal structural design by the decoupling approach

A decoupling approach for solving optimal structural design problems involving reliability terms in the objective function, the constraint set or both is discussed and extended. The approach employs a reformulation of each problem, in which reliability terms are replaced by deterministic functions. The reformulated problems can be solved by existing semi-infinite optimization algorithms and computational reliability methods. It is shown that the reformulated problems produce solutions that are identical to those of the original problems when the limit-state functions defining the reliability problem are affine. For nonaffine limit-state functions, approximate solutions are obtained by solving series of reformulated problems. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, thus allowing flexibility in the choice of the optimization algorithm and the reliability computation method.     

一种基于正交试验设计的土中爆炸数值模型确认方法

提出了一种基于正交试验设计的土中爆炸数值模型确认方法。结合相应物理实验数据,该方法将数值模型确认问题转化为确定影响数值计算结果的各因素及其水平最佳搭配的优化问题。采用正交试验设计作为优化手段,达到了用较少的试验次数获得各因素及其水平最佳搭配的目的。通过极差分析,研究了在不同确认准则条件下,各因素及其水平对土中爆炸数值模拟结果的影响。计算结果表明:分别以最小计算耗时和最高计算精度为确认准则时,网格尺寸是影响数值结果的主要因素;以两者综合评估为确认准则时,计算方法是影响数值结果的主要因素。该文提出的这种方法为复杂数值模型确认问题的研究提供了新的思路。     

An application of the analytic network process in multiple criteria material selection

Using the Analytic Network Process (ANP), this article aims at presenting a new concept for multicriteria material selection by means of allowing feedback and interactions within and between sets of design criteria and alternatives. The approach and its advantages are discussed using a multicriteria material selection case study on non-metallic gears under multifunctional design requirements (thermal performance, mechanical performance, and weight). In particular, it is shown how the selection of material alternatives under different criteria can be viewed as a network problem, as opposed to a conventional hierarchical decision-making process. The effect of different weighting factors of criteria clusters on the final solution is also discussed.     

Evolutionary thickness design with stiffness maximization and stress minimization criteria

A shape or topology design with the stiffness maximized and the maximum stress minimized is usually of practical significance in structural optimization. This paper proposes a thickness based evolutionary procedure for such multicriteria design problems. To make the multicriteria optimization suit to more realistic structural situations, multiple maximum stress locations and multiple load cases are taken into account in this paper. To balance the stiffness and stress criteria, a weighting average scheme is adopted to identify the overall effects on the two components of design objective due to varying an element's thickness. Adopting the proposed optimization procedure, a design with maximized static stiffness and minimized peak stress is achieved by gradually shifting material from the under‐utilized regions onto the over‐utilized ones. The examples show the capabilities of the proposed method for solving multicriteria size and topology designs for both single and multiple load cases. Copyright © 2001 John Wiley & Sons, Ltd.     

Reliability-based design optimization with progressive surrogate models

Reliability-based design optimization (RBDO) has traditionally been solved as a nested (bilevel) optimization problem, which is a computationally expensive approach. Unilevel and decoupled approaches for solving the RBDO problem have also been suggested in the past to improve the computational efficiency. However, these approaches also require a large number of response evaluations during optimization. To alleviate the computational burden, surrogate models have been used for reliability evaluation. These approaches involve construction of surrogate models for the reliability computation at each point visited by the optimizer in the design variable space. In this article, a novel approach to solving the RBDO problem is proposed based on a progressive sensitivity surrogate model. The sensitivity surrogate models are built in the design variable space outside the optimization loop using the kriging method or the moving least squares (MLS) method based on sample points generated from low-discrepancy sampling (LDS) to estimate the most probable point of failure (MPP). During the iterative deterministic optimization, the MPP is estimated from the surrogate model for each design point visited by the optimizer. The surrogate sensitivity model is also progressively updated for each new iteration of deterministic optimization by adding new points and their responses. Four example problems are presented showing the relative merits of the kriging and MLS approaches and the overall accuracy and improved efficiency of the proposed approach.     

Scattering analysis of conducting axisymmetic particles using the extended boundary condition method with discrete source

Abstract

In this paper the extended boundary condition method with discrete sources (DS) is introduced for the electromagnetic scattering problem of a conducting axisymmetric particle. The approximate solution is constructed as a linear combination of “Mie-potentials” with different origins. In order to take advantage of the rotational symmetry the DS are distributed on an auxiliary curve in the plane of the generatrix. The complete system of vector functions have an explicit exp (jm?-dependence which lead to a decoupling of the scattering problem over each azimuthal mode. It is shown that with the method discussed herein, the computational efficiency can be improved in comparison to that which use DS distributed on auxiliary surfaces.     

Multi-objective optimization of fuzzy structural systems

It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.     

A multiple surrogate assisted evolutionary algorithm for optimization involving iterative solvers

In many real-world optimization problems, the underlying objective and constraint function(s) are evaluated using computationally expensive iterative simulations such as the solvers for computational electro-magnetics, computational fluid dynamics, the finite element method, etc. The default practice is to run such simulations until convergence using termination criteria, such as maximum number of iterations, residual error thresholds or limits on computational time, to estimate the performance of a given design. This information is used to build computationally cheap approximations/surrogates which are subsequently used during the course of optimization in lieu of the actual simulations. However, it is possible to exploit information on pre-converged solutions if one has the control to abort simulations at various stages of convergence. This would mean access to various performance estimates in lower fidelities. Surrogate assisted optimization methods have rarely been used to deal with such classes of problem, where estimates at various levels of fidelity are available. In this article, a multiple surrogate assisted optimization approach is presented, where solutions are evaluated at various levels of fidelity during the course of the search. For any solution under consideration, the choice to evaluate it at an appropriate fidelity level is derived from neighbourhood information, i.e. rank correlations between performance at different fidelity levels and the highest fidelity level of the neighbouring solutions. Moreover, multiple types of surrogates are used to gain a competitive edge. The performance of the approach is illustrated using a simple 1D unconstrained analytical test function. Thereafter, the performance is further assessed using three 10D and three 20D test problems, and finally a practical design problem involving drag minimization of an unmanned underwater vehicle. The numerical experiments clearly demonstrate the benefits of the proposed approach for such classes of problem.     

A multiple criteria decision making approach for the assembly line balancing problem

In practice, measuring total profit for a given assembly line balancing (ALB) problem is an involved process that is sometimes impossible because of much uncertainty and unavailability of data. In this paper, ALB is formulated as a multiple criteria problem where several easily quantifiable criteria (objectives) and constraints are defined. Objective functions include number of stations, cycle time, and operations cost, all to be minimized. After a discussion of applications and an overview of multiple criteria decision making (MCDM) approaches for ALB, the MCDM-ALB problem is formulated. Basic definitions and properties of MCDM for ALB are outlined and then an interactive MCDM approach is developed for solving the MCDM-ALB problem. To solve the problem, the decision maker (DM) interactively responds to paired comparisons of multicriteria alternatives. Through a limited number of interactions with the DM, the most preferred alternative is obtained. Many unexplored alternatives are eliminated by using a one-dimensional multiple criteria search. To present the DM's preference, we use the most flexible and general class of utility functions; namely, either quasi-concave or quasi-convex utility functions. An example is solved and computational experiments are reported. It is demonstrated that the bicriteria ALB, cycle time versus number of stations, can be easily solved by using the developed procedure. For the case that there are different criteria, an improved goal programming is developed to solve the MCDM-ALB problem. The motivation for development of the method, based on a case study of a lamp-making plant of the General Electric Company, is discussed.     

Robust design optimization of nonlinear energy sink under random system parameters

Generally, in designing nonlinear energy sink (NES), only uncertainties in the ground motion parameters are considered and the unconditional expected mean of the performance metric is minimized. However, such an approach has two major limitations. First, ignoring the uncertainties in the system parameters can result in an inefficient design of the NES. Second, only minimizing the unconditional mean of the performance metric may result in large variance of the response because of the uncertainties in the system parameters. To address these issues, we focus on robust design optimization (RDO) of NES under uncertain system and hazard parameters. The RDO is solved as a bi-objective optimization problem where the mean and the standard deviation of the performance metric are simultaneously minimized. This bi-objective optimization problem has been converted into a single objective problem by using the weighted sum method. However, solving an RDO problem can be computationally expensive. We thus used a novel machine learning technique, referred to as the hybrid polynomial correlated function expansion (H-PCFE), for solving the RDO problem in an efficient manner. Moreover, we adopt an adaptive framework where H-PCFE models trained at previous iterations are reused and hence, the computational cost is less. We illustrate that H-PCFE is computationally efficient and accurate as compared to other similar methods available in the literature. A numerical study showcasing the importance of incorporating the uncertain system parameters into the optimization procedure is shown. Using the same example, we also illustrate the importance of solving an RDO problem for NES design. Overall, considering the uncertainties in the parameters have resulted in a more efficient design. Determining NES parameters by solving an RDO problem results in a less sensitive design.     

An enhanced genetic algorithm for structural topology optimization

Genetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problem‐specific knowledge. The original discrete black‐and‐white (0–1) problem is directly solved by using a bit‐array representation method. To address the related pronounced connectivity issue effectively, the four‐neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well‐posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge‐free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM‐based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near‐optimum solutions and viable topologies with checkerboard free, mesh independent and hinge‐free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem‐specific knowledge can be a powerful global search tool for structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.     

Multicriteria analysis based on constructing payoff matrices and applying methods of decision making in?fuzzy environment

There exist two classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion or several criteria, but their unique solutions are unachievable, due to decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of models (??X,M?? and ??X,R?? models) can be constructed. Analysis of ??X,M?? and ??X,R?? models (based on applying the Bellman-Zadeh approach to decision making in a fuzzy environment and using fuzzy preference modeling techniques, respectively) serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. The paper results are of a universal character and are illustrated by an example.     

An efficient framework for the reliability-based design optimization of large-scale uncertain and stochastic linear systems

This paper is focused on the development of an efficient reliability-based design optimization algorithm for solving problems posed on uncertain linear dynamic systems characterized by large design variable vectors and driven by non-stationary stochastic excitation. The interest in such problems lies in the desire to define a new generation of tools that can efficiently solve practical problems, such as the design of high-rise buildings in seismic zones, characterized by numerous free parameters in a rigorously probabilistic setting. To this end a novel decoupling approach is developed based on defining and solving a limited sequence of deterministic optimization sub-problems. In particular, each sub-problem is formulated from information pertaining to a single simulation carried out exclusively in the current design point. This characteristic drastically limits the number of simulations necessary to find a solution to the original problem while making the proposed approach practically insensitive to the size of the design variable vector. To demonstrate the efficiency and strong convergence properties of the proposed approach, the structural system of a high-rise building defined by over three hundred free parameters is optimized under non-stationary stochastic earthquake excitation.     

An efficient approach for reliability-based topology optimization

This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15–30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.     

求解二进制二次规划问题的一种连续化方法

本文提出了一种求解二进制二次规划问题的连续化方法。首先利用NCP函数方法,将二进制变量转化为等价的非光滑方程,再用凝聚函数法对其进行光滑化处理,从而把原来的组合优化问题转化成了一般的可微非线性规划问题。通过对一些标准考题进行计算,表明了该连续化方法的可行性、高效性以及稳定性。     

A multicriteria approach to timeout collaboration protocol

This paper presents a multicriteria approach to exploring the properties of timeout collaboration protocol with different timeout thresholds in general testing environments. This is formulated as a discrete multiple criteria optimisation problem by choosing five representative timeout thresholds as alternatives with five common performance measures of production systems. The PROMETHEE method is adopted to deal with this multicriteria problem. The divide-and-label algorithm is developed to rank all the alternatives with the overall intensity of their performance, by using multiple valued outranking graphs from the PROMETHEE with multiple replications. It is shown that two extreme timeout thresholds, T ₀ = 0 and ∞, are efficient over multiple criteria in almost all cases. The divide-and-label algorithm is a very efficient approach to overcome the limitations of the PROMETHEE algorithm and Belz and Mertens's procedure with multiple criteria and replications.