Artificiel Bee Colony (ABC) Algorithme Isfahan University of Technology Fall 2010 1 Elham...

Artificiel Bee Colony (ABC) Algorithme

Isfahan University of Technology Fall 2010

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Elham SeifossadatFaegheh Javadi

A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING

Job shop scheduling problems are considered to bea member of a large class of intractable numerical problemsknown as NP-hard.

Job shop scheduling is concerned with finding a sequentialallocation of competing resources that optimizes a particularobjective function.


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A finite set J of n jobs to be processed on a finite set M of m machines.

Each job Ji must be processed on every machine and consists of a chain of mi operations Oi1, Oi2,…,Oim which have to be scheduled in a pre-determined given order.

Oij is the jth operation of job Ji which has to be processed on a machine Mx for a processing time period of τij without interruption and preemption.


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Each machine can process only one job and each job can be processed by only one machine at a time.

The longest duration in which all operations of all jobs are completed is referred to as the makespan Cmax.


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A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULINGAi be the set of ordered pairs of operations

constrained by the precedence relations for each job Ji.

For each machine Mx, the set Ex describes the set of all pairs of operations to be performed on the machine.

For each operation Oij, let its earliest possible process start time be Tij.


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The challenge is to adapt the self-organization behavior of the colony for solving job shop scheduling problems.

There are two major characteristics of the bee colony in searching for food sources: waggle dance and forage (or nectar exploration).


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waggle dance• A forager fi on return to the hive from nectar

exploration will attempt with probability p to perform waggle dance on the dance floor with duration D = di A,

• it will also attempt with probability ri to observe and follow a randomly selected dance.


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Profitability rating for a forager:



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The bee colony’s average profitability rating:



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The dance duration:



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Adjusting Probability of Following a Waggle Dance:


Forage (Nectar Exploration)


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• A population of L foragers is defined in the colony.

• When a forager is at a specific node, it can only move to next node that is defined in a list of presently allowed nodes, imposed by precedence constraints of operations.



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A forager chooses the next node from the list according to the state transition rule:



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The rating ρij of the edge (directed) between node I and node j is given by:



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The performance of the honey bee colony scheduling approach is studied by evaluating them on the following 82 job shop problem instances.

The sizes of these problems range from 6 to 50 jobs and 5 to 20 machines.


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Bee Colony Optimization (BCO)


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There are two alternating phases (forward pass and backward pass) constituting single step in the BCO algorithm.

The hive is an non-natural object, with no precise location and does not influence the algorithm execution.


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Bee Colony Optimization (BCO)In each forward pass, every artificial bee

visits NC solution components, creates partial solution, and after that returns to the hive.


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Bee Colony Optimization (BCO)In the backward pass, all artificial bees share

information about the quality of their partial solutions. Having all solutions evaluated, each bee decides with a certain probability whether it will stay loyal to its solution or not.


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Bee Colony Optimization (BCO)When all solutions are completed the best

one is determined, it is used to update global best solution and an iteration of the BCO is accomplished.

At this point all B solutions are deleted, and the new iteration could start. The BCO runs iteration by iteration until a stopping condition is met.


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Bee Colony Optimization (BCO)B - The number of bees in the hive;

NC - The number of constructive moves during one forward pass.


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Bee Colony Optimization (BCO)(1) Initialization: an empty solution is assigned to each bee;(2) For each bee: // (the forward pass)

(a) Set k = 1; // (count constructive moves in the forward pass)(b) Evaluate all possible constructive moves;(c) Choose one move using the roulette wheel;(d) k = k + 1; If k ≤ NC Goto step (b).

(3) All bees are back to the hive; // (backward pass starts)(4) Evaluate (partial) objective function value for each bee;(5) Each bee decides randomly whether to continue its own exploration and become a recruiter,

or to become a follower;(6) For each follower, choose a new solution from recruiters by the roulette wheel;(7) If solutions are not completed Goto step 2;(8) Evaluate all solution and find the best one;(9) If the stopping criteria is not met Goto step 2;(10) Output the best solution found.

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Loyalty decision


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Recruiting process

Scheduling Independent Tasks by BCO

Let T = {1, 2, . . . , n} be a given set of independent tasks, and P = {1, 2, . . .,m} a set of identical machines.

The processing time of task i (i = 1, 2, . . . , n) is denoted by li.


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Probability pi that specific bee chooses task i was equal:



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Probability pj that specific bee chooses processor j was calculated as:

References A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP

SCHEDULING- Chong, Low, Sivakumar, and Gay-Proceedings of the 2006 Winter Simulation Conference.

Bee Colony Optimization: The Applications Survey - DUˇSAN TEODOROVIĆ TATJANA DAVIDOVIĆ and MILICA ˇSELMIĆ- ACM Transactions on Computational Logic,2011.


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Thanks for your attention!

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