Genetic algorithms (GAs) can precisely handle the discrete structural topology optimization of single-piece elastic structures called compliant mechanisms. The initial population of these elastic structures is mostly generated by assigning the material at random. This causes disconnected or unfeasible designs and further rule-based repairing can result in representation degeneracy. However, the problem-specific initial population can affect the performance of GAs like other operators. In this paper, a domain-specific initial population strategy is developed that generates geometrically feasible structures for path generating compliant mechanisms (PGCMs). It is coupled with the elitist non-dominated sorting genetic algorithm (NSGA-II) which has been customized for structural topology optimization. The performance of initial population strategy over random initialization using customized NSGA-II is checked on single and bi-objective optimization problems. Based on the results, it is observed that the custom initialization outperforms the random initialization by dominating all the solutions and exploring larger area of posed objectives. The elastic structures obtained by solving two examples of PGCMs using domain specific initial population strategy are also presented.

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Domain-specific initial population strategy for compliant mechanisms using customized genetic algorithm

Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures. Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks. In this article, we discuss topology optimization as a black-box optimization problem. We review the main BBTO methods, discuss their challenges and present approaches to relax them. Dealing with those challenges effectively can lead to wider applicability of topology optimization, as well as the ability to tackle industrial, highly constrained, nonlinear, many-objective, and multimodal problems. Consequently, future research in this area may open the door for innovating new applications in science and engineering that may go beyond solving classical optimization problems of mechanical structures. Furthermore, algorithms designed for BBTO can be added to existing software toolboxes and packages of topology optimization.

Evolutionary Black-Box Topology Optimization: Challenges and Promises

Although structural topology optimization, as a discrete optimization problem, has been successfully solved several times in the literature using evolutionary algorithms (EAs), the two key difficulties lie in generating geometrically feasible structures and handling a high computation time. These two challenges are addressed in this paper by adopting triangular representation for two-dimensional continuum structures, related crossover and mutation operators, and by performing computations in parallel on the graphics processing unit (GPU). Two case studies are solved on the GPU that show 5× of speedup over CPU implementation. The parametric study on the population size of EA shows that the approximate Pareto-optimal solutions can be evolved using a small population with the proposed EA operators.

Evolutionary and GPU computing for topology optimization of structures

Compliant mechanism is a single piece elastic structure which can deform to perform the assigned task. In this work, compliant mechanisms are evolved using a constraint based bi-objective optimization formulation which requires one user defined parameter (η). This user defined parameter limits a gap between a desired path and an actual path traced by the compliant mechanism. The non-linear and discrete optimization problems are solved using the hybrid Genetic Algorithm (GA) wherein domain specific initialization, two-dimensional crossover operator and repairing techniques are adopted. A bit-wise local search method is used with elitist non-dominated sorting genetic algorithm to further refine the compliant mechanisms. Parallel computations are performed on the master-slave architecture to reduce the computation time. A parametric study is carried out for η value which suggests a range to evolve topologically different compliant mechanisms. The applied and boundary conditions to the compliant mechanisms are considered the variables that are evolved by the hybrid GA. The post-analysis of results unveils that the complaint mechanisms are always supported at unique location that can evolve the non-dominated solutions.

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Generation of Compliant Mechanisms using Hybrid Genetic Algorithm

In this paper, an improved initial random population strategy using a binary (0–1) representation of continuum structures is developed for evolving the topologies of path generating complaint mechanism. It helps the evolutionary optimization procedure to start with the structures which are free from impracticalities such as ‘checker-board’ pattern and disconnected ‘floating’ material. For generating an improved initial population, intermediate points are created randomly and the support, loading and output regions of a structure are connected through these intermediate points by straight lines. Thereafter, a material is assigned to those grids only where these straight lines pass. In the present study, single and two-objective optimization problems are solved using a local search based evolutionary optimization (NSGA-II) procedure. The single objective optimization problem is formulated by minimizing the weight of structure and a two-objective optimization problem deals with the simultaneous minimization of weight and input energy supplied to the structure. In both cases, an optimization problem is subjected to constraints limiting the allowed deviation at each precision point of a prescribed path so that the task of generating a user-defined path is accomplished and limiting the maximum stress to be within the allowable strength of material. Non-dominated solutions obtained after NSGA-II run are further improved by a local search procedure. Motivation behind the two-objective study is to find the trade-off optimal solutions so that diverse non-dominated topologies of complaint mechanism can be evolved in one run of optimization procedure. The obtained results of two-objective optimization study is compared with an usual study in which material in each grid is assigned at random for creating an initial population of continuum structures. Due to the use of improved initial population, the obtained non-dominated solutions outperform that of the usual study. Different shapes and nature of connectivity of the members of support, loading and output regions of the non-dominated solutions are evolved which will allow the designers to understand the topological changes which made the trade-off and will be helpful in choosing a particular solution for practice.Copyright © 2008 by ASME

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An Improved Initial Population Strategy for Compliant Mechanism Designs Using Evolutionary Optimization

While designing the Compliant Mechanisms (CM), an equal attention is required on both the problem formulation and the optimization algorithm used. Authors of this paper have successfully proposed the formulation of CM tracing user-defined paths based on the precision points. In this paper, authors modify the NSGA-II algorithm by incorporating (i) a helper objective and (ii) a domain specific crossover which assist in generating a diverse set of non-dominated solutions. First, the single-objective optimization problem of minimizing the weight of structure is solved and named the topology as a reference design. Thereafter, a bi-objective optimization problem is dealt to evolve 'trade-off' solutions for a primary objective of minimizing the weight and a secondary objective of maximizing the diversity with respect to the reference design. Both the optimization problems are solved using a local search based NSGA-II procedure. This study has further compared its results with another GA implementation having a different crossover operator.

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N. N. Kishore

Papers

A domain-specific crossover and a helper objective for generating minimum weight compliant mechanisms