To avoid this problem, we display of the variety of all feasible values of criteria (so called Feasible Set in Criterion Space, the FSCS), which describes the variety of feasible goals. This is the main idea of the Feasible Goals Method (FGM). Due to this, the above problem vanishes. The concept of the FGM was introduced by A.Lotov in 70s.
So, the concept of the FGM is quite simple: if somebody wants to make a decision, he/she needs first to explore possible results of all feasible decisions. Traditional simulation is related to a difficult problem of the choice of a reasonable decision for simulation. We suggest to start with the opposite mode: first to explore all possible results. This will help to surmount the above difficulty of simulation. In the FGM, a user has first to explore all potential results of all feasible decisions and to identify the most preferable result. Then, computer will provide the user with a decision, which brings to the identified result.
In the framework of the FGM, the objective information on decision situation is displayed in a clear graphical form of various decision maps. The decision maps is a well known, but rarely used multiple criteria technique developed for the case of three choice criteria: several efficiency frontiers of two criteria depending on the value of the third criterion are depicted. An efficiency frontier displays an objective (criterion) tradeoff among the two criteria. Changing one efficiency frontier for another, user can see how the increment (or decrement) of the value of the third criterion influences the efficiency frontier. By this, a decision map helps to understand the criterion tradeoff among three criteria. The curves on a decision map look like the height curves of a usual topographical map, and so one can understand them quite easily. Decision maps are provided by the Interactive Decision Maps technique in the FGM.
The FGM turned to be an efficient support for development of environmental, economic, business, etc. strategies as well as decision support tool in Geographical Information Systems. In negotiations on environmental and economic problems, the FGM helps to implement the ideas of Principled Negotiations developed at Harvard University.
The FGM technique has been used for screening possible decisions in several problems, including:
These and other applications of the FGM technique are collected in two books and papers.
The software that implements the FGM was coded for PC in MS DOS and MS Windows environment as well as on work stations in Unix environment using C language. Now the client-server scheme in Java environment is under development. Several recent demo software systems can be downloaded.
The FGM turned to be a simple tool for decision and negotiation support tool with a minimal information exchange. For this reason, we develop and apply the FGM-based tools on computer networks, including INTERNET. One can try an old (1996) FGM-based prototype of future Internet resources that will exercise the civil right for independent information on possible public strategies. A new FGM-based prototypes in Java are now under development.
Now about the algorithms of the FGM. One has to distinguish among linear and non-linear models. In the case of linear models, the algorithms are based mostly on approximation of multi-dimensional convex bodies by polytopes. Algorithms for approximation in non-linear case are based on stochastic covering of bodies by systems of simple figures (say, balls).
The theory is published in recent books and in multiple papers. A short review of the mathematics (including algorithms) related to the method is provided in the paper
Comment to the paper by D.J.White A characterization of the feasible set of objective function vectors in linear multiple objective problems
See absrtract of the paper.