The methods for discrete-integer-continuous variable nonlinear optimization are reviewed. They are classified into the following six categories: branch and bound, simulated annealing, sequential linearization, penalty functions, Lagrangian relaxation, and other methods. Basic ideas of each method are described and details of some of the algorithms are given. They are transcribed into a step-by-step format for easy implementation into a computer. Under “other methods”, rounding-off, heuristic, cutting-plane, pure discrete, and genetic algorithms are described. For nonlinear problems, none of the methods are guaranteed to produce the global minimizer; however, “good practical” solutions can be obtained.

Methods for optimization of nonlinear problems with discrete variables : a review

A method for the optimum design of manipulator workspace is provided based on a recently established criterion. Analytical and computer-aided procedures are presented for the determination of the geometrical proportions of a manipulator for optimum workspace. An effective algorithm is developed by combining a heuristic optimization technique and a computer program for kinematic analysis of manipulators. Two problems are investigated. The first is concerned with the optimum design of a manipulator that has three revolute joints and a spherical joint at the wrist, called the RRRS manipulator; the second is concerned with the problem of design improvement for five commercial robots for larger workspace volume. The potential applicability of the procedure is demonstrated.

Heuristic combinatorial optimization in the design of manipulator workspace

This paper is Part II of a three part series on the design, analysis and construction of a flexible press with a double knuckle linkage drive. In Part I, this drive was shown to have the desirable characteristics of large force (mechanical advantage) over the ram stroke and controllability (constant ram velocity in the working stroke). In this paper, this linkage design is further optimized by kinematic simulation using programs CATIA and KINLYN, and an enumeration search procedure. This optimization results in increased echanical advantage in the working part of the stroke and reduced cycle times. Mechanical advanatage and ram velocity curves for the optimal design are compared with several design variants. This design with constant force and velocity in the working storke is espcially suited to applications in precision forming especially cold extrusion and sheet metal-forming processes.

Optimization of a double knuckle linkage drive with contrast mechanical advantage for mechanical presses

Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing the graph of a structure is transformed into one representing a mechanism. A procedure is presented that enables the exhaustive generation of these graphs for deployable structures of any given number of nodes and links. From these graphs, it is then possible to obtain enumerable novel deployable truss structures as well as those that have been reposed in the literature

Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 1: Graph Generation

A modified adaptive random-search algorithm for the design of helical gears has been developed. The proposed methodology allows for the implementation of nonlinear design functions and constraints without the need for linearization. In addition, the technique has the capability of starting from either feasible regions or infeasible regions of the design domain. Application examples demonstrate the feasibility of the proposed technique as a practical method for design optimization. The viability is further illustrated in a performance test against the conjugategradient search method.

T. W. Lee

Papers

Heuristic Combinatorial Optimization in the Kinematic Design of Mechanisms—Part 1: Theory

Heuristic Combinatorial Optimization in the Kinematic Design of Mechanisms—Part 2: Applications