Douglass J. Wilde

Global Non-Iterative Design Optimization Using Monotonicity Analysis

The numerical techniques used in conventional optimization may not work for engineering design problems, which often present peculiar difficulties. Monotonicity analysis can identify a global optimum without any special computations and also prevent acceptance of false solutions generated by the numerical techniques. In the present paper, these advantages are demonstrated in a problem taken from the literature, for which diverse numerical solutions have been obtained. Monotonicity analysis identifies and proves the global optimum. Its application may require some algebraic rearrangement of the problem statement.

The simulation and optimization of a single effect multi-stage flash desalination plant

Abstract A physical and economic model is built for a 150 million gallon per day single effect multi-stage flash desalination plant. The development of the model is reviewed from previous papers. The limitations of the model are discussed. The model is optimized using a combination of the discrete maximum principle and direct search procedures. This technique permits detailed optimization of design variables at each stage so that in the optimum plant over 100 variables are optimized. Previously, in this type of plant, typical optimization studies considered about five variables. The results of the optimization are given and a sensitivity analysis on the constraints is performed.

Regional Monotonicity in Optimum Design

Regional monotonicity is introduced to identify dominant constraints and simplify non-monotonic expressions in optimum design problems. The technique is applied to obtain a simple solution for the design of an explosive-actuated cylinder, a problem formulated and solved by various methods in the literature. The concept of regional monotonicity provides an extension to the method of monotonicity analysis. Computational work is reduced to a simple plotting over a narrow interval. The design rules developed assist in quick parametric analysis.

THE MONOTON1GITY TABLE IN OPTIMAL ENGINEERING DESIGN

A method, known as monotonicity analysis, for rigorously simplifying engineering design optimization problems, is presented and demonstrated on two examples. The technique involves organizing qualitative information on the monotonicities of objective and constraints in a “monotonicity table” to eliminate combinations of active and inactive constraints which cannot be optimal. In the examples, a hydraulic cylinder and a chemical reactor, only two cases remain to be evaluated, one having no degrees of freedom and the other having but one. No detailed modelling or knowledge of coefficients or exponents is needed, and iterative numerical nonlinear programming is avoided entirely.

THE EXPLICIT APPROXIMATION METHOD FOR DESIGN OPTIMIZATION PROBLEMS WITH IMPLICIT CONSTRAINTS

The Explicit Approximation Method for design optimization problems with implicit constraints is presented. This is a zero-order sequential approximation method. Only function values of the implicit constraint are needed, and no gradient calculation is required. The basic idea is to use engineering knowledge instead of purely numerical gradient information to form an explicit approximation to the implicit constraint. Design examples are presented to show how good explicit approximations to the implicit constraints can be formed, and a good and feasible, if not theoretically optimum, design can be found very efficiently by the Explicit Approximation Method using only zero-order information.

Signomial Dual Kuhn-Tucker Intervals

Signomial programs are a special type of nonlinear programming problems which are especially useful in engineering design. This paper applies interval arithmetic, a generalization of ordinary arithmetic, to a dual equilibrium problem in signomial programming. Two constructive applications are considered. Application I involves uniqueness of local solutions; Application II involves existence and error bounds.

Interval Arithmetic in Unidimensional Signomial Programming

This paper applies an interval arithmetic version of Newtons method to unidimensional problems in signomial programming. Unidimensional dual problems occur in engineering design problems formulated as a signomial program with a single degree of difficulty. Unidimensional primal problems are of interest, since many multidimensional search procedures involve unidimensional searches. The interval arithmetic method is guaranteed to generate all the local optima.

Psychological Teamology, Emotional Engineering, and the Myers–Briggs Type Indicator (MBTI)

This chapter summarizes the author’s Teamology: The Construction and Organization of Effective Teams, and also describes later advances that simplify and clarify the theory. First, it develops the personality theory of psychiatrist C.G. Jung, which theorizes that people solve problems by eight mental processes called “function-attitudes” or “cognitive modes”. Then it discusses how to determine these preferred modes for each person in a group to be formed into teams. Next, ways are suggested of using this modal information to construct teams covering as many of the eight modes as possible. Finally, a novel graphical way is displayed that organizes each team to focus on every mode while reducing duplication of effort.

Graphical Interpretation of the Teamology Transformation

The “teamology” approach to psychologically constructing and organizing design teams is based on an original transformation of personality questionnaire responses on to the four cognitive mode pairs of C. G. Jung’s underlying personality theory. This article shows how to interpret the transformation as the combination of a pair of square graphs, one for the two information collection (perception) mode pair scores; the other, for the two decision-making (judgment) mode pair scores. Questionnaire data are plotted in each square’s rectangular coordinates. The mode scores in each square are the projections of the questionnaire points on to the two diagonals. To illustrate, example graphs are used to guide the organization of a student trio to identify and strengthen a potential weakness. This can be done whether or not the team was constructed according to teamological principles.Copyright

ECONOMIC DESIGN OF A PIPELINE WITH DISCHARGE RESERVOIR

As an example of using optimization theory to obtain simple but rigorous design procedures, the minimum cost design of a fluid pipeline with discharge reservoir is analyzed. The problem has one continuous and four discrete variables, all nonlinear. Monotonicity analysis determines two discrete variables. Partial optimization combined with posynomial geometric programming gives interesting design rules for identifying an optimal design. To obtain discrete values, the new concept of “relative derivative” is used. An exhaustive search on the one continuous variable is often not needed to find the global minimum, since, in several cases, it can be determined in advance that either the only stationary point is the global minimum or that the global minimum occurs at a boundary of the feasible region. This study led to a 50 million saving.