A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

A level set method for structural topology optimization

The paper presents a compact Matlab implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk.

/pdf/a-99-line-topology-optimization-code-written-in-matlab-ww0712da5i.pdf

A 99 line topology optimization code written in Matlab

Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

Topology optimization approaches: A comparative review

Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review.

Shape Optimisation of Interior Cutouts in Composite Panels

Level-set topology optimization for maximizing fracture resistance of brittle materials using phase-field fracture model

An intuitive approach for the determination of voltage distribution in the application to shape control of smart structures using piezoelectric actuators is presented here. The algorithm called the Buildup Voltage Distribution (BVD) is based on an iterative approach inspired by a combination of existing iterative techniques. The mathematical model of the smart structure is based on a High Order Displacement (HOD) field coupled with a Layerwise Linear electric potential. The current shape control work will make use of the Finite Element (FE) formulation based on the above mentioned mathematical model. The development of the BVD algorithm makes no linearity assumption between displacement and voltage and hence can be applied to non-linear mathematical models. The algorithm will then be compared with two well-known algorithms. In addition, a patch insensitivity index is defined to identify the most and least effective locations for piezoelectric actuators.

A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures

Optimum design of frames with multiple constraints using an evolutionary method

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

/pdf/a-performance-index-for-topology-and-shape-optimization-of-2y7n7vnl1p.pdf

Grant P. Steven

Papers

Shape Optimisation of Interior Cutouts in Composite Panels

Level-set topology optimization for maximizing fracture resistance of brittle materials using phase-field fracture model

A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures

Optimum design of frames with multiple constraints using an evolutionary method

A performance index for topology and shape optimization of plate bending problems with displacement constraints