Global Optimization Stochastic methods for essentially unconstrained multimodal nonlinear optimization problems.
Simulation Nets Extended Petri Net tools for concurrent modelling and model execution.
Software Quality Quality evolution models, software quality metrics, information system quality.
Local optimization can be compared to climbing a hill to the top. There are many strategies (algorithms) that can be used for local optimization. One obvious is steepest ascent which means that given a starting position one is moving in the direction where the the steepest ascent can be made. By using this strategy it is hoped to be able to reach the top (the maximum) along the shortest possible path.
For a man this might not be the optimal strategy because there may be other paths that might take less time to climb. The same is true in science. There are many local optimization algorithms that can be used and which is best will depend on the hill to be climbed. Even if some algorithms may fail to find the top, local optimization problems are in principle solvable.
Global optimization is finding the highest top in some geographical region. In order to make the geographical allegory truly correspond to the mathematical problem we have to assume that the weather is misty which means that beeing on one top, other tops cannot be seen. We further assume that we are carrying an instrument which makes it possible to determine the height of our current position.
It is rather obvious that global optimization is a much more difficult task than local optimization. An obvious strategy would be to make several climbs using different starting positions. The starting positions could be determined for instance by random parachuting in the region of interest. It is also easy imaging that several climbs might result in finding the same top and that even after rather ambitious parachuting and climbing we cannot in general be sure that we have seen the highest top.
In science this means that global optimization problems are in principle unsolvable, i.e., after applying some algorithm one can in general not be sure that the global maximum has been determined. .
Topographical global optimization (TGO) aims at avoiding several climbs to the same top. This is done by first determining a set of starting positions, classifying some of the starting positions as promising and then make a climb only from the promising positions. A position is classified as promising if a prespecified number k of its nearest neighboors all are below this position.
TGO has been presented at main global optimization conferences (Princeton) and in the Journal of Global Optimization. The technique has also been used in global optimization algorithms developed by other researchers. It is also part of a commercial software package used by hundreds of scientists and engineers to analyze and design thin film coatings (Software Spectra, Inc.). TGO is a result of reasearch in global optimization since 1973. Other results are a large number of publications (see http://www.abo.fi/~atorn/Globopt.html) including the first monograph on unconstrained global optimization, A. Törn & A. Zilinskas: "Global Optimization", published by Springer Verlag, 1989 and reprinted by World Publishing Corporation, Beijing, 1990.
Traditionally simulation designs were described by using simulation language dependent tools, and in the absence of such, tools developed for ordinary programming. However, simulation involves parallel processes, and the tools used were not suitable for describing such processes. The use of these tools often resulted in programs that did not work correctly.
In 1981 Törn proposed an extended Petri Net tool, Simulation Graphs, to be used for modeling simulation designs (Simulation 37:6). This was recognized by Reizig as one of the earliest applications of Petri Nets. Three software tools, SimNet, XSimNet, and DSimNex, for design of software for simulating discrete event systems have been developed. They are on different platforms and allow different extensions to be used. The tool DSimNex allows that simulations are run in parallel on UNIX workstations. The latest developments in this project is now on simulating project networks (Fredrick von Schoultz) and on aiding in the design of hardware (Åke Gustavson). For further information, see http://www.abo.fi/fak/mnf/infbeh/software/simnet/.
In software engineering software quality has become a topic of major concern. As software is becoming critically important for an organization to be competitive in its business, the requirement that the software is highly supportive for the organization in achieving its goals means that the software should have high utility and user quality. It has also been recognized that software maintenance is becoming the main activity in software work. With the growing collection of software in organizations this cost is becoming substantial. The amount of maintenance needed and the effort needed to perform a certain maintenance task is critically dependent on the technical quality of software resulting from the software development process.An international research group, the IS Quality Group (SOLE - SOftware Library Evolution), consisting of more than 20 researchers in Europe and the USA have been working on Software Quality - Information System Quality during the years 1988-1995. The results include 3 Ph.D. Thesis, 3 Licentiate Thesis, some 20 Masters Thesis, a large number of publications (see http://www.abo.fi/~atorn/sole.html). The main results of SOLE will be published as a special issue, A. Törn & I. Eriksson: "Information System Quality" in the journal Information and Software Technology in 1997.