This paper presents an overview of our most recent results concerning the Particle Swarm Optimization (PSO) method. Techniques for the alleviation of local minima, and for detecting multiple minimizers are described. Moreover, results on the ability of the PSO in tackling Multiobjective, Minimax, Integer Programming and e1 errors-in-variables problems, as well as problems in noisy and continuously changing environments, are reported. Finally, a Composite PSO, in which the heuristic parameters of PSO are controlled by a Differential Evolution algorithm during the optimization, is described, and results for many well-known and widely used test functions are given.

Recent approaches to global optimization problems through Particle Swarm Optimization

The objective of this paper is to review the state-of-the-art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are presented.

Reservoir Management and Operations Models: A State‐of‐the‐Art Review

NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.

NLPQL: A fortran subroutine solving constrained nonlinear programming problems

Atomic radii are not precisely defined but are nevertheless widely used parameters in modeling and understanding molecular structure and interactions. The van der Waals radii determined by Bondi from molecular crystals and data for gases are the most widely used values, but Bondi recommended radius values for only 28 of the 44 main-group elements in the periodic table. In the present Article, we present atomic radii for the other 16; these new radii were determined in a way designed to be compatible with Bondi's scale. The method chosen is a set of two-parameter correlations of Bondi's radii with repulsive-wall distances calculated by relativistic coupled-cluster electronic structure calculations. The newly determined radii (in A) are Be, 1.53; B, 1.92; Al, 1.84; Ca, 2.31; Ge, 2.11; Rb, 3.03; Sr, 2.49; Sb, 2.06; Cs, 3.43; Ba, 2.68; Bi, 2.07; Po, 1.97; At, 2.02; Rn, 2.20; Fr, 3.48; and Ra, 2.83.

Consistent van der Waals Radii for the Whole Main Group

Confirmatory factor analytic tests of measurement invariance (MI) based on the chi-square statistic are known to be highly sensitive to sample size. For this reason, G. W. Cheung and R. B. Rensvold (2002) recommended using alternative fit indices (AFIs) in MI investigations. In this article, the authors investigated the performance of AFIs with simulated data known to not be invariant. The results indicate that AFIs are much less sensitive to sample size and are more sensitive to a lack of invariance than chi-square-based tests of MI. The authors suggest reporting differences in comparative fit index (CFI) and R. P. McDonald's (1989) noncentrality index (NCI) to evaluate whether MI exists. Although a general value of change in CFI (.002) seemed to perform well in the analyses, condition specific change in McDonald's NCI values exhibited better performance than a single change in McDonald's NCI value. Tables of these values are provided as are recommendations for best practices in MI testing.

Power and sensitivity of alternative fit indices in tests of measurement invariance.

: The purpose of this paper is to describe a Generalized Reduced Gradient (GRG) algorithm for nonlinear programming, its implementation as a FORTRAN program for solving small to medium size problems, and some computational results. Our focus is more on the software implementation of the algorithm than on its mathematical properties. This is in line with the premise that robust, efficient, easy to use NLP software must be written and made accessible if nonlinear programming is to progress, both in theory and in practice.

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

In designing the spreadsheet optimizer that is bundled with Microsoft Excel, we and Microsoft made certain choices in designing its user interface, model processing, and solution algorithms for linear, nonlinear, and integer programs. We describe some of the common pitfalls users encounter and remedies available in the latest version of Microsoft Excel. The Solver has many applications and great impact in industry and education.

Design and Use of the Microsoft Excel Solver

http://link.springer.com/content/pdf/10.1007/978-94-009-9935-0_15.pdf

Generalized Reduced Gradient Software for Linearly and Nonlinearly Constrained Problems

It is shown that many engineering design problems can be formulated in terms of inequality constraints on the system response function(s) and on the design parameters. Any set of design variables for which these constraints are satisfied constitutes an acceptable design. There may be many acceptable designs or none at all. In either case it is possible to define a best or optimal design in a meaningful minimax sense. Such an optimal design is the solution of a related nonlinear programming problem involving the minimization of an easily determined objective function, subject to inequality constraints. Some suggested minimization techniques for solving such problems are briefly described. Two reasonably complex examples, using these methods, are presented: the first details the design of an under-water sonar system and the second describes the design of a wideband crystal filter.

Optimization in engineering design

This paper presents a penalty function approach to the solution of inequality constrained optimal control problems. The method begins with a point interior to the constraint set and approaches the optimum from within, by solving a sequence of problems with only terminal conditions as constraints. Thus, all intermediate solutions satisfy the inequality constraints. Conditions are given which guarantee that the un "constrained" problems have solutions interior to the constraint set and that in the limit these solutions converge to the constrained optimum. For linear systems with convex objective and concave inequalities, the unconstrained problems have the property that any local minimum is global. Further, under these conditions, upper and lower bounds in the optimum are easily available. Three test problems are solved and the results presented.

A. D. Waren

Papers

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

Design and Use of the Microsoft Excel Solver

Generalized Reduced Gradient Software for Linearly and Nonlinearly Constrained Problems

Optimization in engineering design

An interior penalty method for inequality constrained optimal control problems