Below are abstracts of three articles of the founder of Technology that were deposited in "ГНТБ Украины (GNTB of Ukraine)". All of them are directly related to some of the software tools to optimize DTIPs of various purpose, which are presented on the website.
For reprints of these articles, please contact the Department of deposit of the depository center of "ГНТБ Украины". Phone number — (044) 529-34-91.
Об ускорении нахождения
оптимальных стратегий управления дискретными процессами
(Burlakov M.V. On acceleration of finding optimal strategies of discrete processes control)
The process of synthesis numerically of optimal tabular strategy of controlling a discrete process (i.e. a process with clearly separated from each other states) with additive quality criterion consists of several stages. Of these, the most time consuming is usually a stage of forming an array of parameters of step transitions (МПШП). The main contribution to the time of its execution brings repeatedly realized the procedure of finding a phase state number by the phase state vector (during calculating parameters of step transitions we operate by the vectors of phase states of a discrete process, and during numerical optimization of this process — by their numbers).
Traditionally, such calculations are performed as follows. At the stage of forming an array of phase states (МФС) of a being optimized process is created a one-dimensional array of calculated states numbers (МРНС), each element of which is calculated according to some formula. In the process of forming МПШП is performed the following procedure: for every found final state is calculated its current number. After this consistently is viewed МРНС, where is found a cell with the same content. The number of this cell is the number of the final state. The above formula includes operations of multiplication, a number of which directly depends on the dimension s vector of phase states of the being optimized process . And because the procedure for determining the final state number by the vector of this state is executed repeatedly, it requires a lot of computing time of processor.
To avoid calculation of the state number by its vector is proposed to use a multi-dimensional array of the states numbers (МНС), whose dimension coincides with the dimension of the phase state vector of the being optimized process. МНС is formed simultaneously with the МФС as follows: for the current state , which number is denoted by j, is performed the next operation of assignment:, where , — normalized components of the current state vector ; — an element of the array МНС with the address in square brackets.
After creating these two arrays comes the stage of forming МПШП. At that, for each final state of the discrete process, to which is possible a transition from its current state , is found a final state number according to the following formula: .
As showed the practice of application by the author of this accelerated procedure of passing from the phase states of the being optimized process to its states numbers, in some cases the time reduction in synthesis of optimal control strategies reach tens of times. This has allowed, in particular, to increase the permissible number of phase states of the being optimized process from 300 thousands, as before, to 1 million. At that, the time of task solving at the limiting numbers of phase states was no more than a few minutes on a personal computer of average performance.
О возможности решения аналитическим путем
некоторых задач оптимизации инвестиций,
решаемых численно программой ЛИС/СИС ОИ 2.0
On possibility of solving analytically some tasks
of investment optimization solved numerically by LIS/NIS IO 2.0)
Theprogram "Local/Network instrumental system of investments optimization, version 2.0 (LIS/NIS IO 2.0)", created by the author of this article and put into operation in March 2013, is designed to solve tasks of effective investment of monetary funds in the acquisition of sources of income (SI) of various physical nature from their given set with a view to their subsequent sale (maximization of absolute income) or their exploitation (maximization of relative income, i.e. income per time uni), as well as with possible taking into account of the factors of payback and risk of investment. The program includes a statistics function that allows to evaluate the effectiveness of the investment with considering the risk factor.
LIS/NIS !O 2.0 allows to solve numerically tasks of seven types on finding the optimal investment strategies, when is reached the maximum of average absolute or relative income from acquisition of SI from their specified set. Their solution is based on the information technology of automation of control of discrete technological and information processes (IT AC DTIP), all necessary information about which is presented on the website http://dtip-burlakov.com. There soon will be placed the network version of the program in question (NIS !O 2.0).
It is of practical interest to find out whether it is possible at least some of these numerous optimization tasks, that can be solved numerically in LIS/NIS !O 2.0, to solve analytically, i.e., using formulas? Detailed analysis of all these tasks led to the following conclusion of the author: analytically can be solved those tasks which satisfy the following four restrictive conditions:
1)the investment payback factor is absent;
2)either the cost of the most expensive SI sample is much smaller of the specified amount of investment, or all samples of SI of different types have the same cost;
· for a group of tasks of maximizingthe absolute income from the sale of SI:
3) there is either a zero-sum of involved credit funds or a zero interest rate;
4) the expected average proceeds from sale of a group of m > 1 SI samples of i-th type and its value, which are denoted by ami and bmi respectively, are proportional to the values of these parameters for one such sample (a1i и b1i), namely: and .
The general algorithm of analytical solving the tasks on optimizing investments, which meet the above conditions is as follows. For each of N types of SI, specified in the task, is found according to a certain formula the priority index pri, i = 1, …, N. Then, the array of these indexes is sorted in the direction of their reduction. Then is formed a set of numbers of chosen to acquire the SI samples in sorted order of their types placement, which represents itself the optimal investment strategy.
Об информации о продаваемых на бирже ценных
для нахождения по ней оптимальных стратегий их купли-продажи
On Information about securities being sold
on a stock exchange
for finding optimal strategies for their purchase and sale
Those numerous persons who by the nature of their activities are engaged in purchase and sale of securities (SC) on stock exchanges, are well aware how it is a risky business. After all, the trend in stock prices of SC is often difficult to forecast because it depends on a mass of random factors and unpredictable events. Currently, it is widely believed that in the trade of SC is enough to have a quality forecast of changing SC prices and thus no optimization is necessary. In the opinion of the author, this view is mistaken for the reason that the quality forecast will allow to solve a much more serious and important optimization tasks than just determining the best moment for the purchase or sale of securities.
We give here a general statement of the task of optimizing purchase and sale of securities. Let there be N types of SC, which in unlimited quantities are being sold on the stock exchange at market prices, at that, a number of them of various types may already be acquired by the trader. At some point in time the trader decided to invest some money (it may be zero) in purchase of new SC. This amount may consist of two parts: 1 — the trader's own funds and 2 — his credit funds funds raised under a specified loan rate. The trader knows the current market prices (at the moment of solving this task) for all types of SC being solved, as well as dividends (specific revenues) from owning them. At that, he must decide on the time interval, during which he would like to sell all or almost all of his securities (old and newly acquired ones). The aim is to find such optimal set of SC and optimal prices of their future sale at which the trader will receive the maximum average income. Besides, It may be imposed an additional condition to return the amount of money spent by the trader.
To solve this optimization tasks is required a certain information about the behavior of SC stock prices for a sufficiently long period of time, which is a probabilistic characteristic. To explain its essence, we introduce the following notation for SC of i-th type, i = 1, …, N: Ai — a current cost of a SC sample; Bi >= Ai — a possible value of a price of future sale of the sample, selected as a result of optimization; Fi (Ai, Bi; t) — a distribution function of a random time t up to the appearance on the stock exchange of a request for purchase of SC at the price Bi for their sample, provided that the current price of the sample is equal to Ai. This function is the above-mentioned probabilistic characteristic of securities (there are three possibilities of its representation). It must be found as a result of an operation of forecasting and then be entered into a program that solves the optimization task of purchase and sale of securities.
Such a program already exists. It was recently developed by the author of this article and is called: "Local/Network instrumental system of investments optimization, version 2.0 (LIS/NIS IO 2.0)". In the near future its network variant (NIS IO 2.0) will be placed on the author's website http://dtip-burlakov.com for free use it in test mode.