minimax

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minimax

[′min·ə‚maks]
(mathematics)
The minimum of a set of maxima.
In the theory of games, the smallest of a set of maximum possible losses, each representing the most unfavorable outcome of a particular strategy.

Minimax

 

in mathematics, the value of the expression

of a real function f(x,y) of two variables. The concept of maximin equal to maxy minxf(x, y) is related to the concept of minimax. In the theory of zero-sum games, the fundamental optimality principle is the minimax principle, which consists in the attempt of a player to minimize his loss, assuming that his opponent’s strategy takes the most unfavorable form.

minimax

(games)
An algorithm for choosing the next move in a two player game. A player moves so as to maximise the minimum value of his opponent's possible following moves. If it is my turn to move, I give a value to each legal move I might make. If the result of a move is an immediate win for me I give it positive infinity and, if it is an immediate win for you, negative infinity. The value to me of any other move is the minimum of the values resulting from each of your possible replies.

The above algorithm will give every move a value of positive or negative infinity since the value of every move will be the value of some final winning or losing move. This can be extended if we can supply a heuristic evaluation function which gives values to non-final game states without considering all possible following complete sequences. We can then limit the minimax algorithm to look only a certain number of moves ahead. This number is called the "look-ahead" or "ply".

See also alpha/beta pruning.

References in periodicals archive ?
The MinMax optimization formula is defined as follows:
Thus two allocations costs are computed, one is the MinMax cost, which represents the length of the longest subtour in the allocation, and the other is the total overall cost of all subtours.
In our experiment, we use two scaling methods, MinMax scaling and standard scaling, and use two distance metrics, Euclidean distance and Manhattan distance (details are in Section 3).
The mean R/S ratio was found as 0.63[+ or -]0.48 (minmax: 0.2-2) before treatment and 0.53[+ or -]0.41 (minmax: 0.2-2) after treatment.
Preisig, "Optimal Minmax Estimation and the Development of Minmax Estimation Error Bounds," IEEE International Conference on Acoustics, Speech, and Signal Processing, San Francisco, USA, 1992, pp.
A minmax thermometer is essential; anything over 30C is damaging to plants, although cacti and succulents can withstand intense heat.
Niendorf and Voss [10] take advantage of the fact that all eigenvalues of a definite matrix polynomial can be characterized as minmax values of the appropriate Rayleigh functional and that the extreme eigenvalues in each of the intervals (-[infinity], [xi]), ([xi], [mu]) and ([mu], +[infinity]) are the limits of monotonically and quadratically convergent sequences.
For person i (i = 1, 2), processing a job per unit time will bring [b.sub.i](i = 1, 2) unit profit; the processing cost is defined as the minimum value of the maximum lateness of jobs, that is, min [L.sup.i.sub.max] = minmax {[C.sub.j] - d | j [member of] [X.sub.i]}, and then the profit function of person i is defined by [u.sub.i] = [b.sub.i] [[summation].sub.j[member of]] [X.sub.i] [P.sub.j,r] - min [L.sup.i.sub.max].
El problema P-Centro es tambien conocido como MinMax, busca reducir al minimo las distancias maximas entre cualquier demanda y su centro de distribucion mas cercano Este tipo de modelos son utilizados para determinar la ubicacion de una instalacion sobre cualquier lugar de una red establecida, a los cuales se les denomina, problemas de centro absoluto [37].
The comparative analysis of presented models clearly shows that the greater accuracy of estimation is achieved by models formed based on the data prepared by the minmax normalisation procedure.
Abstract: First several new classes of higher order (ph, , o, p, p, th, m)-invexities are introduced, and then a set of higher-order parametric necessary optimality conditions and several sets of higher order sufficient optimality conditions for a discrete minmax fractional programming problem applying various higher order (ph, , o, p, p, th, m)-invexity constraints are established.