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The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we are able to achieve the film configuration near to the Steiner minimal tree. This film evolution may be an interesting tool for solving the Euclidean Steiner problem, but several dead-point situations may occur for a certain location of fixed points. A continuous evolution of the film is impossible by increasing the pressure in these situations. The investigation of dead-point situations gives the ways of overcoming the difficulties of dead-point situations and continuing the film evolution by temporarily decreasing pressure.

The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The problem is NP hard.

In the previous paper (Pupeikis, 1998), the problem of recursive estimation of the state of linear dynamic systems, described by an autoregressive model (AR), in the presence of time-varying outliers in observations to be processed has been considered. An approach to the robust recursive state estimation has been obtained and proved by estimating the real chemical process (Box and Jenkins, 1970). The aim of the given paper is the development of the abovementioned approach for the robust recursive state estimation of an autoregressive-moving average (ARMA) process in a case of additive noises with patchy outliers. The results of numerical simulation and the state estimation of the AR model (Figs. 1–4) and the real chemical process, described by the ARMA model, which is chosen from the same book of Box and Jenkins (Figs. 5–8) are given.

In the previous papers (Masreliez and Martin, 1977; Novovičova, 1987; Schick and Mitter, 1994) the problem of recursive estimation of linear dynamic systems parameters and of the state of such systems in the presence of outliers in observations have been considered. In this connection various ordinary recursive techniques are worked out, when systems output is corrupted by an additive noise with a time homogeneous contamination of outliers. The aim of the given paper is the development of an approach for robust recursive state estimation of linear dynamic systems in a case of additive noises with time-varying outliers. The recursive technique based on the abovementioned theoretical results is obtained and proved by state estimation of the real chemical process (Box and Jenkins, 1970). The results of numerical simulation by computer (Fig. 1–3) are given.

The following topics are important teaching operation research: games theory, decision theory, utility theory, queuing theory, scheduling theory, discrete optimization.

The following topics are important teaching operation research:

The aim of investigation was to seek new ways for the analysis of extremal problems. A method of visual analysis of a set of objective function values is proposed. It allows us to find a direction where the variation of function is maximal. The method ensures a high quality of analysis when the number of used values of the objective function is small, and a possibility of identifying a specific character of the objective function. The results of analysis are used in search of a new coordinate system of the extremal problem and in a graphical representation of the observed data. The analysis will lead us to a better optimization strategy.

We consider a possibility of automating the analysis of a computer program realizing the objective function of an extremal problem, and of distributing the calculation of the function value into parallel processes on the basis of results of the analysis. The first problem is to recognize the constituent parts of the function. The next one is to determine their computing times. The third problem is to distribute the calculation of these parts among independent processes. A special language similar to PASCAL has been used to describe the objective function. A new scheduling algorithm, seeking to minimize the maximal finishing time of processing units, was proposed and investigated. Experiments are performed using a computer network.

We consider a stochastic algorithm of optimization in the presented paper. We deal here with the average results of a “mixture” of the deterministics heuristics algorithm and uniform random search. We define the optimal “mixture”.

We compare two alternative ways to use the Bayesian approach in heuristic optimization. The “no-learning” way means that we optimize the randomization parameters for each problem separately. The “learning” way means that we optimize the randomization parameters for some “learning” set of problems. We use those parameters later on for a family of related problems.