An Optimization Approach/Technique for Solving Graph Based Design Problems

2008 ◽  
Author(s):  
Jay Patel ◽  
Matthew I. Campbell
Keyword(s):  
Optimization Technique ◽  
Optimization Method ◽  
Graph Grammar ◽  
Topological Optimization ◽  
Optimization Approach ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Resistive Networks ◽  
Better Than

This paper discusses a new topological optimization technique to solve graph based engineering design problems by decoupling parameters and topology changes. Using this approach optimal solutions are synthesized in the form of graph topologies for engineering problems. Currently we have successfully applied it to routing problems, resistive networks, neural networks, and sheet metal. This final problem has proven the most challenging but the results are not only novel and manufacturable but also satisfy multiple objective functions such as material cost and manufacturability. This paper presents Topological and Parametric Tune and Prune (TP2) as the first topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with the problems that been tested, (TP2) had proven better than genetic algorithm in terms of the quality of solutions and time taken to acquire them.

An Approach to Automate and Optimize Concept Generation of Sheet Metal Parts by Topological and Parametric Decoupling

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Jay Patel ◽  
Matthew I. Campbell
Keyword(s):  
Sheet Metal ◽  
Optimization Technique ◽  
Optimization Method ◽  
Graph Grammar ◽  
Topological Optimization ◽  
Concept Generation ◽  
Metal Parts ◽  
Sheet Metal Parts ◽  
Rectangular Patch ◽  
Engineering Design Problems

This paper describes an approach to automate the design for sheet metal parts that satisfy multiple objective functions such as material cost and manufacturability. Unlike commercial software tools such as PRO/SHEETMETAL, which aids the user in finalizing and determining the sequence of manufacturing operations for a specified component, our approach starts with spatial constraints in order to create the component geometries and helps the designer design. While there is an infinite set of parts that can feasibly be generated with sheet metal, it is difficult to define this space systematically. To solve this problem, we have created 108 design rules that have been developed for five basic sheet metal operations: slitting, notching, shearing, bending, and punching. A recipe of the operations for a final optimal design is then presented to the manufacturing engineers thus saving them time and cost. The technique revealed in this paper represents candidate solutions as a graph of nodes and arcs where each node is a rectangular patch of sheet metal, and modifications are progressively made to the sheet to maintain the parts manufacturability. This paper also discusses a new topological optimization technique to solve graph-based engineering design problems by decoupling parameters and topology changes. This paper presents topological and parametric tune and prune ((TP)2) as a topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with abovementioned sheet metal problem, (TP)2 had proven better than genetic algorithm in terms of the quality of solutions and time taken to acquire them.

A Unified Approach to Solving Graph Based Design Problems

2007 ◽  
Author(s):  
Matthew I. Campbell ◽  
Sandeep Nair ◽  
Jay Patel
Keyword(s):  
Engineering Design ◽  
Graph Transformation ◽  
Electric Circuit ◽  
Optimization Method ◽  
Graph Grammar ◽  
Science Literature ◽  
Design Problems ◽  
Novel Approach ◽  
Engineering Design Problems ◽  
Graph Transformation Systems

This paper proposes a new perspective of using graph transformation systems as a way of organizing and solving engineering design problems. Using this novel technique the synthesis of optimal solutions in the form of graph topologies for design problems is made possible. Though the concept of graph grammars has existed for several decades in computer science literature, researchers in the field of design have now begun to realize the merit of using them to harness both the knowledge and heuristics of a particular problem domain. This paper examines the fundamental challenges in applying graph transformations in a design context. The paper also presents the first topology optimization method that has been developed specifically for domains representable by a graph grammar schema. This novel approach could also be used in several problems such as network problems (especially in determining the placement of hubs), electric circuit design, neural networks, sheet metal, and product architecture. The abstraction afforded by graphs also enables us to tackle multi-disciplinary problems found throughout engineering design. A few engineering examples are shown in this paper in order to illustrate the power of the approach in automating the design process.

scholarly journals An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems

2022 ◽  
Vol 19 (1) ◽  
pp. 473-512
Author(s):  
Rong Zheng ◽  
◽  
Heming Jia ◽  
Laith Abualigah ◽  
Qingxin Liu ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Heuristic Method ◽  
Population Diversity ◽  
Test Functions ◽  
Design Problems ◽  
Local Optima ◽  
Switching Mechanism ◽  
Engineering Design Problems

<abstract> <p>Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (<italic>RMOP</italic>) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.</p> </abstract>

scholarly journals Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1914
Author(s):  
Kaizhi Chen ◽  
Jiahao Zhuang ◽  
Shangping Zhong ◽  
Song Zheng
Keyword(s):  
Computational Geometry ◽  
Packing Problem ◽  
Optimization Method ◽  
Raw Material ◽  
Packing Problems ◽  
Permutation Model ◽  
Feasible Solutions ◽  
Packing Method ◽  
Better Than

Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

2018 ◽  
Vol 18 (4) ◽  
Author(s):  
Tingli Xie ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Leshi Shu ◽  
Yahui Zhang ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Engineering Design ◽  
Kriging Model ◽  
Support Vector ◽  
Svm Classifier ◽  
Optimization Approach ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Application of Topological Optimization on Aluminum Alloy Automobile Wheel Designing

2012 ◽  
Vol 562-564 ◽  
pp. 705-708
Author(s):  
Zhi Jun Zhang ◽  
Hong Lei Jia ◽  
Ji Yu Sun ◽  
Ming Ming Wang
Keyword(s):  
Topology Optimization ◽  
Lightweight Design ◽  
Optimization Method ◽  
Variable Density ◽  
Topological Optimization ◽  
Optimal Topology ◽  
Element Analysis ◽  
Material Interpolation ◽  
Strength And Stiffness

Topology optimization method based on variable density and the minimum compliance objective function was used on designing the wheel spokes. SIMP material interpolation model was established to compensate these deficiencies of variable density method. Considering manufacturing process and stress distribution, five bolt wheels was chose to topology optimization. The percentage of material removal of the optimal topology 40% was reasonable. Finite element analysis was used to test the strength and stiffness of the structure of the wheel, the result meets the requirements after wheel topology optimization, and reduces the quality of wheels to 7.76kg, achieve the goals of lightweight design.

scholarly journals New multiobjective optimization algorithm using NBI-SASP approaches for mechanical structural problems

2022 ◽  
Vol 13 ◽  
pp. 4
Author(s):  
Samira El Moumen ◽  
Siham Ouhimmou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Structural Problems ◽  
Engineering Design Problems ◽  
Set Of Points

Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.

scholarly journals Greenfly Aphid Swarm Optimization Algorithm

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Hanan A.R. Akkar ◽  
Sameem Abbas Salman
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Design Problems ◽  
Swarm Optimization ◽  
Engineering Design Problems ◽  
Grasshopper Optimization Algorithm ◽  
Grasshopper Optimization ◽  
Swarm Intelligence Optimization ◽  
Practical Impact

A new metaheuristic swarm intelligence optimization technique, called general greenfly aphid swarm optimization algorithm, which is proposed by enhancing the performance of swarm optimization through cockroach swarm optimization algorithm. The performance of 23 benchmark functions is tested and compared with widely used algorithms, including particle swarm optimization algorithm, cockroach swarm optimization and grasshopper optimization algorithm. Numerical experiments show that the greenfly aphid swarm optimization algorithm outperforms its counterparts. Besides, to demonstrate the practical impact of the proposed algorithm, two classic engineering design problems, namely, pressure vessel design problem and himmelblau’s optimization problem, are also considered and the proposed greenfly aphid swarm optimization algorithm is shown to be competitive in those applications.

scholarly journals An improved African vultures optimization algorithm based on tent chaotic mapping and time-varying mechanism

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260725
Author(s):  
Jiahao Fan ◽  
Ying Li ◽  
Tan Wang
Keyword(s):  
Optimization Algorithm ◽  
Optimization Algorithms ◽  
Time Varying ◽  
Metaheuristic Algorithm ◽  
Design Problems ◽  
Chaotic Mapping ◽  
Metaheuristic Optimization ◽  
Engineering Design Problems ◽  
Metaheuristic Optimization Algorithms ◽  
Better Than

Metaheuristic optimization algorithms are one of the most effective methods for solving complex engineering problems. However, the performance of a metaheuristic algorithm is related to its exploration ability and exploitation ability. Therefore, to further improve the African vultures optimization algorithm (AVOA), a new metaheuristic algorithm, an improved African vultures optimization algorithm based on tent chaotic mapping and time-varying mechanism (TAVOA), is proposed. First, a tent chaotic map is introduced for population initialization. Second, the individual’s historical optimal position is recorded and applied to individual location updating. Third, a time-varying mechanism is designed to balance the exploration ability and exploitation ability. To verify the effectiveness and efficiency of TAVOA, TAVOA is tested on 23 basic benchmark functions, 28 CEC 2013 benchmark functions and 3 common real-world engineering design problems, and compared with AVOA and 5 other state-of-the-art metaheuristic optimization algorithms. According to the results of the Wilcoxon rank-sum test with 5%, among the 23 basic benchmark functions, the performance of TAVOA has significantly better than that of AVOA on 13 functions. Among the 28 CEC 2013 benchmark functions, the performance of TAVOA on 9 functions is significantly better than AVOA, and on 17 functions is similar to AVOA. Besides, compared with the six metaheuristic optimization algorithms, TAVOA also shows good performance in real-world engineering design problems.

Sign in / Sign up

Export Citation Format

Share Document