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 ?
Keywords: Discrete minmax fractional programming, (ph, , o, p, p, th, m)-invex functions, necessary optimality conditions, sufficient optimality conditions.
n] in ([xi], [mu]) which satisfy a minmax characterization with respect to p, and the safeguarded iterations aiming at [[lambda].
Interpolating in these points will yield good polynomial approximants for the geometry, compared to the minmax polynomial approximant.
Minmax Power announced expansion of their M78A and M78SA switching regulators that are pin-compatible and size-compatible with older and less-efficient LM78xx devices.
Competition-based neural network for the multiple traveling salesmen problem with minmax objective".
Mixed Strategies in Strictly Competitive Games: A Further Test of the Minmax Hypothesis.
Moreover, most of the previous works usually design LLA by using single-objective optimization techniques, such as GA [16], particle swarm optimization (PSO) algorithm [17], differential evolution (DE) algorithm [18,19], or minmax optimization (MO) algorithm [20], where all the objectives were combined into a single fitness function by adding different weighting factors to different objectives and the selection of the weighting factors depends highly on the rule of thumb.
En la literatura se encuentran varias formas de seleccionar el umbral, tales como umbrales fijos y la regla minmax, pero estos son solo adecuados para eliminar ruido blanco.
Minmax refers to a part of mixed strategy in zero-sum game used by players in decision making.
The weighted sum C for each individual membership can be defined by using minmax aggregation [28] operators as given below:
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