Book ChapterDOI

# Coupler-Curve synthesis of a planar four-bar mechanism using NSGA-II

16 Dec 2012-pp 460-469
TL;DR: The proposed enhancements of the basic scheme of NSGA-II deliver promising improvements in terms of accuracy, and rate of convergence of the solutions, and are illustrated via applications to two well-studied problems in the domain of coupler-curve synthesis.

Abstract: This paper applies a genetic algorithm-based optimisation procedure, namely, NSGA-II, to the problem of synthesis of a four-bar mechanism. The internal parameters of ${\texttt{\rm NSGA-II}}$ are tuned using a Design of Experiments (DoE) procedure to enhance the quality of the final results. Constraints are handled through a penalty formulation. Further, a scaling function is introduced, which transforms the penalty terms in a manner that leads to faster convergence of the solutions. The theoretical developments are illustrated via applications to two well-studied problems in the domain of coupler-curve synthesis. A comparison of the results vis-a-vis existing ones shows that the proposed enhancements of the basic scheme of ${\texttt{\rm NSGA-II}}$ deliver promising improvements in terms of accuracy, and rate of convergence of the solutions.

Topics: Rate of convergence (51%)
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01 Jan 2013-

##### References
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Journal ArticleDOI
TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.

Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.

30,928 citations

Journal ArticleDOI
Kalyanmoy Deb1Institutions (1)
TL;DR: GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter to guide the search towards the constrained optimum.

Abstract: Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter. Careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region. Once sufficient feasible solutions are found, a niching method (along with a controlled mutation operator) is used to maintain diversity among feasible solutions. This allows a real-parameter GA's crossover operator to continuously find better feasible solutions, gradually leading the search near the true optimum solution. GAs with this constraint handling approach have been tested on nine problems commonly used in the literature, including an engineering design problem. In all cases, the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier.

3,096 citations

Journal ArticleDOI
Elon Rimon1, Daniel E. Koditschek1Institutions (1)
01 Oct 1992-
TL;DR: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented.

Abstract: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided. >

1,774 citations

Journal ArticleDOI
J.A. Cabrera1, A. Simon1, Maria Prado1Institutions (1)
TL;DR: The main advantages of the solution methods of optimal synthesis of planar mechanisms are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space.

Abstract: This paper deals with solution methods of optimal synthesis of planar mechanisms. A searching procedure is defined which applies genetic algorithms based on evolutionary techniques and the type of goal function. Problems of synthesis of four-bar planar mechanisms are used to test the method, showing that solutions are accurate and valid for all cases. The possibility of extending the method to other mechanism type is outlined. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space.

263 citations

10

Journal ArticleDOI
TL;DR: This work presents a combined genetic algorithm–fuzzy logic method to solve the problem of path generation in mechanism synthesis and proved to be more efficient in finding the optimal mechanism.

Abstract: This work presents a combined genetic algorithm–fuzzy logic method to solve the problem of path generation in mechanism synthesis. The proposed method is made of a classical genetic algorithm coupled with a fuzzy logic controller (GA–FL). This controller monitors the variation of the design variables during the first run of the genetic algorithm and modifies the initial bounding intervals to restart a second round of the genetic algorithm. Compared to previous works on the same problem, our method proved to be more efficient in finding the optimal mechanism.

139 citations

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