Introduction to Natural Computation. Lecture 15. Fruitflies for Frequency Assignment. Alberto Moraglio

Transcription

1 Introduction to Natural Computation Lecture 15 Fruitflies for Frequency Assignment Alberto Moraglio 1/39

2 Fruit flies 2/39

3 Overview of the Lecture The problem of frequency assignment in mobile phone networks. Fruit flies and the self-organisation of cells. The flyphone algorithm. Some results. 3/39

4 Real World Problems 4/39

5 Cell Phone Channel Planning A cell phone network consists of: A number of fixed base stations. A much larger number of mobile handsets, which each connect to a base station via a radio channel. 5/39

6 Cell Phone Channel Planning A cell phone network consists of: A number of fixed base stations. A much larger number of mobile handsets, which each connect to a base station via a radio channel. There is a limited number of radio channels, much lower than the number of handsets. The implication of this is that channels must be reused by different base stations. 6/39

7 Cell Phone Channel Planning A cell phone network consists of: A number of fixed base stations. A much larger number of mobile handsets, which each connect to a base station via a radio channel. There is a limited number of radio channels, much lower than the number of handsets. The implication of this is that channels must be reused by different base stations. Potential problems with channel reuse Two or more handsets communicating on the same channel will result in interference. Handsets using adjacent channels may also receive some lesser interference. 7/39

8 Cell Phone Channel Planning A cell phone network consists of: A number of fixed base stations. A much larger number of mobile handsets, which each connect to a base station via a radio channel. There is a limited number of radio channels, much lower than the number of handsets. The implication of this is that channels must be reused by different base stations. Potential problems with channel reuse Two or more handsets communicating on the same channel will result in interference. Handsets using adjacent channels may also receive some lesser interference. Objective for the network operator To allocate channels to base stations such that demand for channels across the network is met, while keeping interference below acceptable levels. 8/39

9 Cell Phone Channel Planning A cell phone network consists of: A number of fixed base stations. A much larger number of mobile handsets, which each connect to a base station via a radio channel. There is a limited number of radio channels, much lower than the number of handsets. The implication of this is that channels must be reused by different base stations. Potential problems with channel reuse Two or more handsets communicating on the same channel will result in interference. Handsets using adjacent channels may also receive some lesser interference. Objective for the network operator To allocate channels to base stations such that demand for channels across the network is met, while keeping interference below acceptable levels. Additional issues Handsets are not distributed uniformly among base stations. Demand will be different at different times, perhaps unpredictably so. 9/39

10 Problem: Frequency Assignment 10/39

11 Problem: Frequency Assignment Not just an engineering problem, also a hard mathematical problem: In a network with j base stations and k available channels, the number of different ways of allocating l channels to each base station is: ( k! ) j ((k l)!)(l!) j = 3,k = 5,l = j = 5,k = 10,l = j = 10,k = 10,l = j = 58,k = 29,l = Clearly, an exhaustive search to find the optimal configuration is just not feasible! 11/39

12 Problem: Frequency Assignment Not just an engineering problem, also a hard mathematical problem: In a network with j base stations and k available channels, the number of different ways of allocating l channels to each base station is: ( k! ) j ((k l)!)(l!) j = 3,k = 5,l = j = 5,k = 10,l = j = 10,k = 10,l = j = 58,k = 29,l = Clearly, an exhaustive search to find the optimal configuration is just not feasible! Typically, operators use a fixed channel allocation plan. The plans might not change for months, and the assignments not for several days. 12/39

13 Dynamic Planning There are two families of approaches to solving a dynamic optimisation problem like this: Offline, in which an entire plan is formulated in advance, perhaps according to known fluctuations in demand. The plan is then fixed and simply followed. Subsequently, a different plan is tried, followed by another etc. etc., until an optimal plan is found. Online, in which there is no fixed plan in advance, but channels are allocated and reallocated in response to changes as they occur. 13/39

14 Dynamic Planning There are two families of approaches to solving a dynamic optimisation problem like this: Offline, in which an entire plan is formulated in advance, perhaps according to known fluctuations in demand. The plan is then fixed and simply followed. Subsequently, a different plan is tried, followed by another etc. etc., until an optimal plan is found. Online, in which there is no fixed plan in advance, but channels are allocated and reallocated in response to changes as they occur. While offline plans may be able to exploit more knowledge about known patterns of behaviour, online approaches are potentially better able to deal with the unexpected. 14/39

15 Fruit flies 15/39

16 Fruit flies Observe that the bristles on the fruitfly s back are evenly spaced. Each bristle arises from a single cell and is separated by several other cells. 16/39

17 Fruit flies Observe that the bristles on the fruitfly s back are evenly spaced. Each bristle arises from a single cell and is separated by several other cells. This is not achieved by a central controller with a plan. But by a combinations of interactions among the cells themselves. The cells multiply and position themselves with exquisite precision. 17/39

18 Self-Organisation in Cell Development All cells are initially equivalent. Some cells then randomly acquire bristle potential. As they do so, they also produce a ligand, a molecule which binds to receptors on neighbouring cells. The ligand inhibits their neighbours, so that they do not grow and produce as much. Those which produce the most are therefore not inhibited as much and actually grow bristles. 18/39

19 Self-Organisation in Cell Development All cells are initially equivalent. Some cells then randomly acquire bristle potential. As they do so, they also produce a ligand, a molecule which binds to receptors on neighbouring cells. The ligand inhibits their neighbours, so that they do not grow and produce as much. Those which produce the most are therefore not inhibited as much and actually grow bristles. This is therefore a self-organising process, with no central control. A key advantage is that it is a robust process, where small amounts of damage to the organism cannot result in large losses of functionality. 19/39

20 Basic Idea The mechanism used to ensure that two adjacent fruit fly cells do not both make bristles can be adapted to ensure that two nearby cell phone cells do not use the same channel. 20/39

21 Basic Idea The mechanism used to ensure that two adjacent fruit fly cells do not both make bristles can be adapted to ensure that two nearby cell phone cells do not use the same channel. Translating concepts: Fruit fly cell base station. Inhibitory ligand feedback mechanism between adjacent base stations (cells). All base stations begin with the potential to use all frequencies, but then inhibit their neighbours. This avoids two adjacent base stations using the same frequency and reduces interference. 21/39

22 Basic Idea The mechanism used to ensure that two adjacent fruit fly cells do not both make bristles can be adapted to ensure that two nearby cell phone cells do not use the same channel. Translating concepts: Fruit fly cell base station. Inhibitory ligand feedback mechanism between adjacent base stations (cells). All base stations begin with the potential to use all frequencies, but then inhibit their neighbours. This avoids two adjacent base stations using the same frequency and reduces interference. Offline vs online 22/39

23 Basic Idea The mechanism used to ensure that two adjacent fruit fly cells do not both make bristles can be adapted to ensure that two nearby cell phone cells do not use the same channel. Translating concepts: Fruit fly cell base station. Inhibitory ligand feedback mechanism between adjacent base stations (cells). All base stations begin with the potential to use all frequencies, but then inhibit their neighbours. This avoids two adjacent base stations using the same frequency and reduces interference. Offline vs online In an offline approach, the fruit fly would have grown an entire configuration of bristles, then another, etc. and compared them. In this online approach, an initial uniform configuration is used, which then self-organises to a better solution. 23/39

24 The Flyphone Algorithm 24/39

25 The Flyphone Algorithm Initialisation Construct a co-channel interference table, C. This is a j j matrix which gives a value to the strength of interference between two base stations. Obtain the maximum number of simultaneous calls (demand) which is to be met by each base station. Set the initial usage of each channel in each cell (uniform). 25/39

26 The Flyphone Algorithm Initialisation Construct a co-channel interference table, C. This is a j j matrix which gives a value to the strength of interference between two base stations. Obtain the maximum number of simultaneous calls (demand) which is to be met by each base station. Set the initial usage of each channel in each cell (uniform). Iteration Calculate the new usage of each channel in each cell based on: The current usage and The inhibition perceived by that base station on the channel in question. 26/39

27 The Flyphone Algorithm Initialisation Construct a co-channel interference table, C. This is a j j matrix which gives a value to the strength of interference between two base stations. Obtain the maximum number of simultaneous calls (demand) which is to be met by each base station. Set the initial usage of each channel in each cell (uniform). Iteration Calculate the new usage of each channel in each cell based on: The current usage and The inhibition perceived by that base station on the channel in question. Solution Extraction At any time, a filter can be used to produce a valid solution from the usage values. Allocate channels to base stations in decending order of their usage in that cell, until their demand is met. 27/39

28 Usage What is usage? Usage is an artificial concept. Initially, each base station is assumed to be partially using all of the available channels. Based on the inhibitions, over time some base stations use some channels more and others less. Usage does not then represent exactly a solution, but is used by the solution extractor to produce one. 28/39

29 Usage What is usage? Usage is an artificial concept. Initially, each base station is assumed to be partially using all of the available channels. Based on the inhibitions, over time some base stations use some channels more and others less. Usage does not then represent exactly a solution, but is used by the solution extractor to produce one. Updating usage At each time step, the new usage for each base station is calculated from the old value: U jkt = U jk(t 1) (1 +I jk ) where U jkt is the usage of channel k in cell j at time t, and I jk is the inhibition calculated for channel k in cell j. Updates are performed synchronously. 29/39

30 Calculating Inhibition The inhibition for channel k on base station j, I jk is the sum of all the usages of channel k by all other base stations, each multiplied by the interference coefficient (from the interference table) for base station k and the other base station: I jk = U jkt C j,j j J The co-channel interference for the same base station (i.e. when j = j ) is assumed to be 0, so that a base station does not inhibit itself. 30/39

31 Example Scenario 31/39

32 Varying Demand The key shows the number of channels required by each of 58 base stations. 32/39

33 Dynamic Demand Simulated dynamic demand. Initially demand is uniform 6 across the network and interference is successfully eliminated. At iteration 100 rush hour is simulated. At iteration 600 a road accident is simulated and traffic queues form in surrounding cells at iterations 800 and /39

34 Some Observations Anytime solutions We don t have to wait for the algorithm to complete in order to obtain a solution. A solution can be extracted at any time. Over time, the quality of the solutions extracted will improve. This is a common feature of many nature-inspired techniques. 34/39

35 Some Observations Anytime solutions We don t have to wait for the algorithm to complete in order to obtain a solution. A solution can be extracted at any time. Over time, the quality of the solutions extracted will improve. This is a common feature of many nature-inspired techniques. Ability to adapt The solutions found were not found to be any better than using previous approaches (such as simulated annealing). However, the flyphone approach had a greater ability to move quickly and smoothly from one solution to another, as demand changes. There is a tradeoff here, between optimality and adaptivity. 35/39

36 Summary Used a self-organisation mechanism from fruit fly bristle cells, To solve an industrially relevant and mathematically hard problem. 36/39

37 Summary Used a self-organisation mechanism from fruit fly bristle cells, To solve an industrially relevant and mathematically hard problem. The algorithm achieves progressively better solutions over time, Using a process of mutual inhibition between neighbouring cells. There is no global information in the system, and no central controller. 37/39

38 Summary Used a self-organisation mechanism from fruit fly bristle cells, To solve an industrially relevant and mathematically hard problem. The algorithm achieves progressively better solutions over time, Using a process of mutual inhibition between neighbouring cells. There is no global information in the system, and no central controller. This approach is therefore both robust to damage and well suited to this dynamic problem. 38/39

39 Further Reading Tateson R. Self-Organising Pattern Formation: Fruit Flies and Cell Phones. In: Eiben AE, Bäck T, Schoenauer M, Schwefel HP, editors. Parallel Problem Solving From Nature - PPSN V. Kunz Amsterdam, The Netherlands: Springer; p /39