General Problem Solver

Lest there be any confusion that schema theory is consistent with all theories of problem solving, let me hasten to add that not all approaches to problem solving are so consistent. For instance, Newell and Simon s justifiably famous General Problem Solver (GPS) is quite different (and will be discussed at length in part V). 

This research itself can be divided into two main areas, the development of approximation algorithms for particular problems, e.g. Traveling salesman problem, and into the area of metaheuristics, which is more concerned with the development of general problem solvers. 

In 1958 Alan Newell, Cliff Shaw, and Herbert Simon published their General Problem Solver . Using only basic logical functions the program was intended to solve complex problems. It was applied to artificial (toy) decision problems like Towers of Hanoi or Missionaries and Cannibals and gave reasonable results. However, large and complex decision problems could not be solved. 

Expert system technology was one of the first branches of artificial intelligence [1,2], It is by now well tried and mature. Nevertheless, expert systems are tools to support human thinking, not magic problem-solvers. While the name expert system is based on the notion that the systems behave like experts, it is generally considered that they should be used by experts or at least the well-informed. 

In multiphase reactor simulations, the momentum, heat and species mass balances may thus contain several terms that can be placed in this framework. However, in these problem solvers, the generalized proportionality coefficient K is usually derived from the steady drag force, and the convective heat and mass transfer fluxes, respectively. 

The general analytical process is shown in Figure 1.1. The analytical chemist should be involved in every step. The analyst is really a problem solver, a critical part of the team deciding what, why, and how. The unit operations of analytical chemistry that are common to most types of analyses are considered in more detail below. 

We added Problem-Solving Strategy boxes to focus students attention on the very important process of problem solving. One of the main goals of general chemistry is to help students become creative problem solvers. 

The last step, generalize, is important but is usually neglected. In this step you try to learn as much as possible from the problem. What have you learned about the physical situation Did including a particular phenomenon have an inportant effect, or could you have ignored it Generalizing allows you to learn and become a better problem solver. 

If you approach problem solving using this general method you will be able to learn to solve more and more difficult problems on your own. As you gain confidence you will become an independent, creative problem solver and be able to use this skill wherever you go in real life . 

In order to obtain complete tools and avoid side effects, all rules have to be considered at once without any order. There are so called formal solvers that accomplish these requirements. However, the methods that these solvers implement are computationally expensive. This means that they are not feasible for industrial size problems, in general. As a consequence, the methods as well as their implementation in solvers have to be adapted to the respective input in order to obtain efficient solvers for dealing with the variability in industry. Although general purpose solvers can be applied to many industrial problems with some success, it is in our opinion not enough to be able to solve say 80 % of the problems and leave the rest with the so-called local heroes . 

Linear Solvers Although general purpose solvers exist, major improvements in efficiency can be gained by exploiting structural features of the linear equations that are particular to reservoir simulation. The key parts of any linear solver are (i) a method of pre-conditioning, essentially an approximation to the system of equations that can be solved directly, but without storage or speed problems (ii) an iteration scheme. 

The partial differential equations describing the catalyst particle are discretized with central finite difference formulae with respect to the spatial coordinate [50]. Typically, around 10-20 discretization points are enough for the particle. The ordinary differential equations (ODEs) created are solved with respect to time together with the ODEs of the bulk phase. Since the system is stiff, the computer code of Hindmarsh [51] is used as the ODE solver. In general, the simulations progressed without numerical problems. The final values of the rate constants, along with their temperature dependencies, can be obtained with nonlinear regression analysis. The differential equations were solved in situ with the backward... 

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