Improved Greedy Algorithm Based Matrix Satellite Cable Connection Optimal Design

. An improved greedy algorithm based matrix satellite cable optimal design method is presented in this paper aim to overcome the difficulties including designing complexity, designing cycle and iterative designing process. An optimal algorithm model is built to help designer not only to accomplish design correctly and efficiently, but also to obtain better designing outcomes. Firstly, matrix cable designing model is pre-translated by turning electrical interface to equivalent digital model. Then the digital model is turned into computer language. At last, optimal design rules and method are extracted according to improved greedy algorithm. Real project data are used to prove the feasibility and validity of the proposed method.


Introduction
Matrix circuit including matrix telemetry and command is a core technology of on-board integrated electronic technology [1] to reduce the amount of electronic components and cables.This technology is widely used in all kinds of satellites to observably lose the weight of satellite platform.The devices with matrix telemetry and command can be connected with integrated electronic subsystem by matrix cable to send commands and receive telemetries.Matrix cable design has great possibility to be improved by reducing the usage of cables because matrix circuit usually has a large number of brunches which may cause the redundancy of design.
Consequently, an improved greedy algorithm based matrix satellite cable optimal design method in presented in this paper aim to overcome the difficulties listed above.Computer based design can acquire correct and preferred outcome, meanwhile, improve the work efficiency.

Matrix cable contact design principle
Matrix command contact circuit comprises command drive device and command load device.Command drive device can control m×n pieces of load device by control m row cables and n column cables [2] .It takes 2(m+n) cables to control m×n pieces of load device if backup is included.Matrix telemetry contact circuit is using the same principle.Matrix cable contact design principle is to build a point-to-point mapping relation between drive devices and load devices.By building a physical cable connection, drive devices can control load devices to executive commands and receive telemetries.Formula expression of design model is { Rx, Cy,k}.
Rx represents for row cable, Cy represents for column cable, k represents for the number of matrix model on one device.

Improved greedy algorithm based matrix cable connection optimal design method
Optimal design is achieved by algorithm based programming on the basis of digital model and formula expression input.
A greedy algorithm does not consider the overall result, but aim to find a partial optimum.In most cases, a greedy strategy follows an optimal principle and takes partial optimum step by step.The greedy algorithm structure is as follows.
Beginning with an original solution for a problem, While ( making one step forward to final goal) { Use available strategies to find a solution } Get a final solution by combining all the solutions VLSI routing problem [3] and 2D packing problem [4] chooses different row cable and column cable will get different matrix connections.Travelling salesmen problem [5] has capacity restriction and mutual restriction.Unlike VLSI or TSP problem, this case is a 2D vehicle routing problem [6] with confliction and capacity restriction.To solve this problem, this article raised an improved greedy algorithm with complexity of O (M*n).M represents the maximum of row or column, N represents the amount of matrix.

Optimal Design rules summary
Step 1 List all Matrix signals.{T} is the set of telemetries; {C} is the set of commands.{TM} is the set of matrix telemetries; {CM} is the set of matrix commands.
Step 2 Separate all devices into different secions.Put devices into correspoding section lists by recognize their coordinates.
Definition 1 TMax is the matrix telemetry with maximum of row or column in {TM}.

Definition 2 CMax is the matrix command with maximum of row or column in {CM}.
Definition 3 TSum is the matrix telemetry with maximum sum of row and column in a specific set of telemetries.

Definition 4
CSum is the matrix command with maximum sum of row and column in a specific set of commands.
Step 3 Find TMax and CMax.If there are more than one TMax or CMax, we get {TMax} or{ CMax }.Then we find TSum or CSum.If there are more than one TSum or CSum, the priority is random.
Rule 1 Using row cable is prior to column cable if the total increment and partial increment are fixed.
Definition 5 If one device has been appointed to be DAim, algorithm cannot move on to other device until all the matrix signals are allocated.

Definition 6
The set of all matrix telemetries of DAim except TMax is TNext.The set of all matrix commands of DAim except CMax is CNext.
Step 4 When TMax or CMax is chosen, the device TMax or CMax becomes DAim.TNext of CNext must be assembled with TMax or CMax to get the minimum sum of rows and columns in order to use cables as less as possible.

Definition 7
The set of devices on the same branch of DAim except DAim is {DNext}.
Definition 8 TAim or CAim is the matrix signal which is going to be allocated then.

Rule 2
The second junction point is the flag of where a branch starts.

Rule 3
If there are more than one position with minimum cost increment, length increment is the solution to find the best choice.
Step 6 When {DNext} is finished, repeat step 1 to 5 for the rest.

Rule 4
Choose matrixes which have the same structure as TAim or CAim to assemble if priority cannot be recognized so that unnecessary blank can be avoided as far as possible.This rule is also made to reduce the usage of cable and shorten cable length.
Step 7 After all matrix signals were allocated, do a final check to see if any adjustment can be done to get a better result.

Improved greedy algorithm based matrix cable connection optimal design
Definition 9 SR×C is the capacity of matrix cable allocation.

Definition 10
is the cost increment when choosing position.

Definition 11
is the length increment.
Definition 12 P is insertion point.P is on the first line and first row of TAim or CAim.

If SR×C=
, 16 row lines and 24 column lines can be shown in a sketch map as follows.
In figure 1   The programming logic is showed in figure 4. Comparing with original design result, the optimal design result reduces total cable weight by 8% which is 0.416 kg.

Conclusion
An improved greedy algorithm based matrix cable connection optimal design method is proposed in this article and the method is tested by real data project to prove its reasonableness and effectiveness.The result shows that optimal design result reduced weight by 8% comparing with original design result.Some complicated situation may occur in real projects such as branch terminals and layout adjustments.Later we will make further improvement of this optimal design method.

1
Design model pre-processingCircuit model is tuned into structural digital model to achieve optimal design.Assuming that a command load device has 9 matrix commands controlled by 3 row cables and 3 column cables, it can be shown asMRC=.Similarly, drive device can be shown as NRC= .From the knowledge mentioned above, row 1 and column 1 take control of M11.According to the principle, circuit connection can be translate into mapping relation between drive device model and load device model.If NRC= ,the relation can be shown as .1.2Formula expression of design modelMATEC Web of Conferences 139, 00039 (2017) DOI: 10.1051/matecconf/201713900039 ICMITE 2017

Figure 1
Figure 1 Cable layout sketch map CN1 and CMax belong to the same device, they share same column lines.CN1 brings a new row line.So =1, =QA=8.Then CN2 and CMax belong to the same device, CN2 share the same column lines with CMax , meanwhile, share the same row line with CN1.So =0 ， =0 。 Total length of DAim is 64+8=72.In {DNext},

Figure 2 Interface 4
Figure 2 branch judgment flag

Figure 3
Figure 3 structure sketch

Figure 4 Figure 5
Figure 4 Programming logic