Patent GB-900580-A (GB)
Title: Improvements relating to analogue computing devices for linear programming
Inventor: VOLES ROGER
IPC: G06G7/122
Filed: 1957-10-23
Abstract: 900,580. Electric analogue computers. ELECTRIC & MUSICAL INDUSTRIES Ltd. Oct. 16, 1958 [Oct. 23, 1957], No. 33013/57. Class 37. An analogue computing device for maximizing a linear function (F) of a set of attributes (A) subject to a set of constraints, the number (n) of which is greater than the number (m) of the attributes, for example, for finding the maximum profit of a manufacturing process involving a number of constituents, comprises a number of magnetizable cores A 1 <SP>1</SP>, A 2 <SP>1</SP> . . . A<SP>1</SP>m, one for   each attribute A 1 , A 2  . . . An, the n constraints being expressed as a set of n inequalities of linear functions of m attributes A. (a 11 A 1 +a 12 A 2 + . . . a 1m A m  b 1 ) (a 21 A 1 +a 22 A 2 + . . . a 2m Am b 2 ) (a n1 A 1 +a n2 A 2 + . . . a nm A m  b n ) (where a 11 , a 12 , &c. and b 1 , b 2 , &c. are constants) the fluxes in the separate cores corresponding to the desired solution, that is, the values of A 1 , A 2,  &c. when F is a maximum. F=C 1 A 1 + C 2 A 2 + . . . C m Am where C 1 C 2  . . . C m  are constants. The cores A 1 <SP>1</SP>, A 2 <SP>1</SP> . . . A<SP>1</SP>m of the transformers, which may be toroidal, carry n sets of windings, one for each inequality condition each winding having m windings in series with it. Each winding of the first set on each core A 1 <SP>1</SP> &c. is proportional to one of the terms a 11 , a 12 , &c. of the second set to a 21 , a 22 , &c. One end of each set of windings is connected to a tapping on an autotransformer 20 the amplitudes of the voltages from the tappings corresponding to b 1 , b 11 , &c. The other end of each set of windings a 11 , a 12 , &c. is connected to a phase-sensitive impedance such as PSI 1 , PSI 2 , &c., which represents the constraint that a 11 A 1 +a 12 A 2  . . . a 1m a m  does not exceed b 1  &c. stated in the set of inequalities set out above and which switches from a very high to a very low impedance as soon as the phase of the total E.M.F.'s induced in windings a 11 , a 12  becomes the same as that of the potential of b 1 . A phase-sensitive impedance is described in detail in the Specification and consists in essence of two or four diode gates each gate being connected in series with a further diode (Fig. 1, not shown). The linear function F is represented by a further set of windings c 1 c 2  . . . c m  on A 1 <SP>1</SP>, A 2 1 . . . A m <SP>1</SP>. Further phase sensitive impedances PSI 1 <SP>1</SP>, PSI 2 <SP>1</SP>, &c. are connected to a winding on each core and impose the constraint on each attribute that it must be either positive or zero by switching from a high to a low impedance state and thereby affecting the flux in the respective core when the flux in that core changes from a phase denoting a positive attribute to one denoting a negative attribute. Further windings S 1 S 2  &c. on the cores are connected to output terminals at which the A solutions to the problem can be read off by voltage sampling. The operation of the device is as follows. The computer is set up for a given problem and the tap on auto-transformer 23 is set at the bottom of the winding and then moved upwards so that the amplitude of current in windings C increases progressively, the windings a 11  &c., however, imposing no constraint on the flux in the cores until the phase sensitive impedances PSI 1  &c. switch to the very low impedance state when the algebraic sun of the E.M.F.'s in a 11 , a 11  . . .aim exceeds potential b 1  and provides back E.M.F. which opposes the potential due to b 1  &c. imposing a constraint on the fluxes in cores A 1 <SP>1</SP>, A 2 <SP>1</SP> . . . A m <SP>1</SP>. The displacement of the tap is continued until the voltage indicated on V 1  drops to a low value, when the number of impedances PSI in the low impedance state is sufficient to determine the fluxes in the cores and the current in the C windings tends to exceed the value compatible with these fluxes, the reading of V 1  just before the drop representing the maximum value of F.