The seminar is devoted to decision support in the case of complicated multi-objective (multi-criteria) decision problems. Approximating the Pareto frontier and subsequent informing the decision makers about it is now a recognized method of decision support especially in environmental and other public problems in the framework of which multiple decision makers have to be informed about the objective tradeoffs.

The method used in our studies (the Interactive Decision Maps (IDM) technique) applies visualization of the tradeoff among the objectives in form of decision maps, i.e. collections of bi-objective slices of the Pareto frontier. The IDM technique is based on approximating the Edgeworth-Pareto hull of the feasible objective set. Then, bi-objective slices of the Pareto frontier can be displayed on request of a user. The IDM technique can be applied in the case of more than four objectives (in the so called many-objective decision problems).

A complicated multi-objective problem is considered as an example. It is the problem of constructing control rules for a cascade of reservoirs with criteria reflecting the reliability with which the requirements imposed on the cascade are met. The problem is described by 24 objectives, by several hundreds of decision variables and by non-linear relations between them and objectives. New efficient methods were developed for approximating the Edgeworth–Pareto hull. They combine classical gradient-based methods for scalar optimization and genetic algorithms for Pareto frontier approximation. It was experimentally shown that these methods are significantly superior to the original genetic algorithm in terms of order of convergence and approximation accuracy.