Evolutionary squeaky wheel optimization: a new framework for analysis

Squeaky wheel optimization (SWO) is a relatively new metaheuristic that has been shown to be effective for many real-world problems. At each iteration SWO does a complete construction of a solution starting from the empty assignment. Although the construction uses information from previous iterations, the complete rebuilding does mean that SWO is generally effective at diversification but can suffer from a relatively weak intensification. Evolutionary SWO (ESWO) is a recent extension to SWO that is designed to improve the intensification by keeping the good components of solutions and only using SWO to reconstruct other poorer components of the solution. In such algorithms a standard challenge is to understand how the various parameters affect the search process. In order to support the future study of such issues, we propose a formal framework for the analysis of ESWO. The framework is based on Markov chains, and the main novelty arises because ESWO moves through the space of partial assignments. This makes it significantly different from the analyses used in local search (such as simulated annealing) which only move through complete assignments. Generally, the exact details of ESWO will depend on various heuristics; so we focus our approach on a case of ESWO that we call ESWO-II and that has probabilistic as opposed to heuristic selection and construction operators. For ESWO-II, we study a simple problem instance and explicitly compute the stationary distribution probability over the states of the search space. We find interesting properties of the distribution. In particular, we find that the probabilities of states generally, but not always, increase with their fitness. This nonmonotonocity is quite different from the monotonicity expected in algorithms such as simulated annealing.     

Evolutionary robustness analysis for multi-objective optimization: benchmark problems

This paper presents a new approach to robustness analysis in multi-objective optimization problems aimed at obtaining the most robust Pareto front solutions and distributing the solutions along the most robust regions of the optimal Pareto set. A new set of test problems accounting for the different types of robustness cases is presented in this study. Non-dominated solutions are classified according to their degree of robustness and are distributed along the Pareto front according to specific algorithm parameter values. Verification of the proposed method is carried out using the developed test problems and artificial and real world benchmark test problems present in the literature.     

An optimization algorithm for shape analysis of regular polygons

Machine vision has the potential to impact both quality and productivity significantly in computer integrated manufacturing due to its versatility, flexibility, and relative speed. Unfortunately, algorithm development has not kept pace with the advances in vision-hardware technology, particularly in the areas of analysis and decision making. The specific subject of this investigation is the development of a machine-vision algorithm for the dimensional checking, pose estimation, and overall shape verification of regular polygonal objects (e.g., surface-mounted electronic components and fastener heads). Algorithmically, the image boundary data is partitioned inton segments, and then a non-ordinary least squares technique is used to find the best fitting polygon. The algorithm is well-suited for online implementation in an automated environment due to its flexibility and demonstrated speed.     

Evolutionary shape optimization of thermoelastic bodies exchanging heat by convection and radiation

Shape optimization of heat conducting, elastic bodies subjected to thermal and standard loads is considered. Interaction of stress and temperature fields is modelled using the formulation of steady state thermoelasticity. The presence of heat radiation with mutual irradiation of the boundaries and the presence of shadow zones is taken into account. Evolutionary algorithm is used to evaluate the optimal shape. The boundary element method is applied to discretize the thermoelasticity, conduction and radiation problems.     

A multiresolution descriptor for deformable 3D shape retrieval

In this paper, we present a spectral graph wavelet framework for the analysis and design of efficient shape signatures for nonrigid 3D shape retrieval. Although this work focuses primarily on shape retrieval, our approach is, however, fairly general and can be used to address other 3D shape analysis problems. In a bid to capture the global and local geometry of 3D shapes, we propose a multiresolution signature via a cubic spline wavelet generating kernel. The parameters of the proposed signature can be easily determined as a trade-off between effectiveness and compactness. Experimental results on two standard 3D shape benchmarks demonstrate the much better performance of the proposed shape retrieval approach in comparison with three state-of-the-art methods. Additionally, our approach yields a higher retrieval accuracy when used in conjunction with the intrinsic spatial partition matching.     

An efficient decoupled sensitivity analysis method for multiscale concurrent topology optimization problems

The conventional coupled sensitivity analysis method for concurrent topology optimization problems is computationally expensive for microscale design variables. This study thus proposes an efficient decoupled sensitivity analysis method for concurrent topology optimization based on the chain differentiation rule. Two numerical studies are performed to demonstrate the effectiveness of the decoupled sensitivity analysis method for concurrent topology optimization problems with single or multiple porous materials. It can be concluded from the results that the decoupled method is computationally much more efficient than the coupled method, while they are mathematically equivalent. The outstanding merits of the decoupled method are two-fold: (1) computational efficiency of sensitivity analysis with respect to the microscale design variables; and (2) applicability to concurrent topology optimization problems with single or multiple porous materials as well as with composite microstructure and multi-phase materials.     

Structural modelling and sensitivity analysis of shape optimization

It is presented in this paper that the structural modelling of shape optimization is composed of, in general cases, four distinct processes on geometry, design, analysis and perturbation models. The relationships between these models are discussed. An integrated modelling approach based on geometric shape parameterization and automatic mesh generation is proposed. In cooperation with this modelling approach, the semi-analytic sensitivity analysis has been effectively employed. These techniques join shape optimization with FEM and CAD packages and apply it versatilely to optimum designs of general structures. The implementation and applications of the integrated modelling approach and semi-analytic sensitivity analysis to shape optimization of structures with coupling of stress and temperature fields are illustrated.Presented at NATO ASI Optimization of Large Structural Systems, held in Berchtesgaden, Germany, Sept. 23 — Oct. 4, 1991     

Sensitivity analysis in shape optimization of continuum structures

This paper describes an efficient method for sensitivity analysis in shape optimum design. One feature is the use of limited number of master nodes to characterize the surfaces of a set of isoparametric finite elements, and the adoption of their coordinates as design variables of the shape optimization. Another is the derivation of analytical formulations of the gradients of both the stiffness terms and the load vectors with respect to the design variables. A finite element analysis code is adapted to the purposes of the method and numerical examples are performed and comparisons made with sensitivity analysis based on forward finite differences.     

Eulerian shape design sensitivity analysis and optimization with a fixed grid

Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach.     

Evolutionary optimization of a geometrically refined truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly, traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation—genetic algorithms and differential evolution—to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this paper, specifically, a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization tool set.     

Mesh refinement for shape optimization

The numerical solution of shape optimization problems is considered. The algorithm of successive optimization based on finite element techniques and design sensitivity analysis is applied. Mesh refinement is used to improve the quality of finite element analysis and the computed numerical solution. The norm of the variation of the Lagrange augmented functional with respect to boundary variation (residuals in necessary optimality conditions) is taken as an a posteriori error estimator for optimality conditions and the Zienkiewicz—Zhu error estimator is used to improve the quality of structural analysis. The examples presented show meaningful effects obtained by means of mesh refinement with a new error estimator.