Design of arc welding processes: a causal perspective

Monotonicity in goal and geometric programming.

In dealing with numerical problems for which classical methods of solution are unfeasible, many people have tried various procedures of searching for an answer on a computer. Our efforts in this direction have produced procedures which seem to have had (for us and for others who have used them) more success than has been achieved elsewhere, so that we have been encouraged to publish this report of our studies. We use the phrase \"direct search\" to describe sequential examination of trial solutions involving comparison of each trial solution with the \"best\" obtained up to that time together with a strategy for determining (as a function of earlier results) what the next trial solution will be. The phrase implies our preference, based on experience, for straightforward search strategies which employ no techniques of classical analysis except where there is a demonstrable advantage in doing so. We have found it worthwhile to study direct search methods for the following reasons: (a) They have provided solutions to some problems, of importance to us, which had been unsuccessfully attacked by classical methods. (Examples are given below.) (b) They promise to provide faster solutions for some problems that are solvable by classical methods. (For example, a method for solving systems of linear equations, proposed in Section 5, seems to take an amount of time that is proportional only to the first power of the number of equations.) (c) They are well adapted to use on electronic computers, since they tend to use repeated identical arithmetic operations with a simple logic. Classical methods, developed for human use, often stress minimization of arithmetic by increased sophistication of logic, a goal which may not be desirable when a computer is to be used. (d) They provide an approximate solution, improving all the while, at all stages of the calculation. This feature can be important when a tentative solution is needed before the calculations are completed. (e) They require (or permit) different kinds of assumptions about the functions involved in various problems, and thus suggest new classifications of functions which may repay study. Direct search is described roughly in Section 2, and explained heuristically in Section 3. Section 4 describes a kind of strategy. Sections 5 and 6 describe

`` Direct Search'' Solution of Numerical and Statistical Problems

Goal programming for decision analysis

Mathematical Theory of Heat Distribution during Welding and Cutting

Greater understanding of the physics of welding is leading to improved application and control of welding processes. Further gains in welding productivity could follow. Electric arc welding, high energy density welding and future developments are described

https://iopscience.iop.org/article/10.1088/0305-4624/15/2/I05/pdf

Design of arc welding processes: a causal perspective

Citations

Monotonicity in goal and geometric programming.

References

`` Direct Search'' Solution of Numerical and Statistical Problems

Goal programming for decision analysis

Mathematical Theory of Heat Distribution during Welding and Cutting

The Physics of Welding

On an Axiomatic Approach to Manufacturing and Manufacturing Systems

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