PPT – Ant Colony Optimization Power. Point presentation free to view. Title: Ant Colony Optimization 1. Ant Colony Optimization. Prepared by Ahmad Elshamli, Daniel Asmar, Fadi Elmasri 2. Presentation Outline. Section I (Introduction) Historical Background Ant System Modified algorithms Section II (Applications) TSP QAP Section III (Applications Conclusions) NRP VRP Conclusions, limitations and Danny.
Fadi. Ahmad 3. Section 1. Introduction (Swarm intelligence) Natural behavior of ants First Algorithm Ant System Improvements to Ant System Applications 4. Swarm intelligence. Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination Achieving a collective performance which could not normally be achieved by an individual acting alone Constituting a natural model particularly suited to distributed problem solvinghttp//www. Y/notes/SI2. 0Lecture.
The Ant Colony Optimization (ACO) Metaheuristic: a Swarm Intelligence Framework for Complex Optimization Tasks. 'The Ant System: Optimization by a colony of. . abstractsnet.com/pdfs/abstract_2443.pdf THANKS Ant colony optimization HISTORY. Ant colony optimization HISTORY INTRODUCTION introduction.
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Evolutionary process of Ant Colony Optimization algorithm adapts genetic operations. Since Ant colony algorithm may produce. 5.pdf Appendex [6] Figures. Title: Ant Colony Optimization 1 Ant Colony Optimization Prepared by Ahmad Elshamli, Daniel Asmar, Fadi Elmasri 2 Presentation Outline. Section I (Introduction). Ant colony optimization is a part of the larger field of swarm intelligence in which scientists study the behavior patterns of bees, termites. Ant colony optimization is particularly suited to this task. “Ant System: Optimization by a colony of cooperating agents,” IEEE Transactions on Systems. Ant colony optimization: Introduction and recent trends. ant colony optimization in more general. An example of a Gaussian kernel PDF consisting of five. Engineering Optimization and Metaheuristics. Optimization Algorithm and Metaheuristics. Ant colony optimization (Dorigo 1992). Introduction to Ant Colony Optimization (ACO) Ant Behaviour Stigmergy Pheromones Basic Algorithm Example. Blum C., Ant colony optimization: Introduction and recent.
Inherent features. Inherent parallelism Stochastic nature Adaptivity Use of positive feedback Autocatalytic in nature 1. Natural behavior of an ant Foraging modes. Wander mode Search mode Return mode Attracted mode Trace mode Carry mode 1. Natural behavior of ant. Ant Algorithms (P.
Koumoutsakos based on notes L. Gamberdella (www.
Work to date 1. 4Work to date 1. How to implement in a program. Ants Simple computer agents Move ant Pick next component in the const.
Pheromone Memory MK or Tabu. K Next move Use probability to move ant 1. A simple TSP example. ABCDEd. AB 1. 00d. BC 6. 0d. DE 1. 50 1. Iteration 1. ABCDE 1. How to build next sub- solution?
ABCDE 1. 9Iteration 2. ABCDE 2. 0Iteration 3.
ABCDE 2. 1Iteration 4. ABCDE 2. 2Iteration 5. ABCDE 2. 3Path and Pheromone Evaluation. L1 3. 00. L2 4. 50. L3 2. 60. L4 2. 80.
L5 4. 20 2. 4End of First Run. Save Best Tour (Sequence and length) All ants die.
New ants are born 2. Ant System (Ant Cycle) Dorigo 1 1. NC 0 tij(t)c for ? Place the m ants on the n nodes Initialize.
Update tabuk(s)Tabu list management Choose the city j to move to. Use probability. Move k- th ant to town j. Insert town j in tabuk(s)Compute the length Lk of every ant Update the shortest tour found For every edge (i,j) Compute For k. Yes. Yes. NClt. NCmax not stagn. Set t t n NCNC1 ? No. End 2. 6Stopping Criteria.
Stagnation Max Iterations 2. General ACOA stochastic construction procedure Probabilistically build a solution Iteratively adding solution components to partial solutions - Heuristic information - Pheromone trail Reinforcement Learning reminiscence Modify the problem representation at each iteration 2. General ACOAnts work concurrently and independently Collective interaction via indirect communication leads to good solutions 2. Variations of Ant System. Ant Cycle (O(NC. n. Ant Density (Quantity Q) Ant Quantity (Quantity Q/dij) Taken from Dorigo 1 3. Basic Analysis. Taken from Dorigo 1 3.
Basic Analysis. Taken from Dorigo 1 3. Optimal number of ants for ASTaken from Dorigo 1 3. Versatility. Application to ATSP is straightforward No modification of the basic algorithm 3. Some inherent advantages. Positive Feedback accounts for rapid discovery of good solutions Distributed computation avoids premature convergence The greedy heuristic helps find acceptable solution in the early solution in the early stages of the search process. The collective interaction of a population of agents. Disadvantages in Ant Systems.
Slower convergence than other Heuristics Performed poorly for TSP problems larger than 7. No centralized processor to guide the AS towards good solutions 3.
Improvements to ASDaemon actions are used to apply centralized actions Local optimization procedure Bias the search process from global information 3. Improvements to AS 3. Improvements to ASACS Strong elitist strategy Pseudo- random proportional rule With Probability q.
With Probability (1- q. Improvements to ASUpdate pheromone trail while building the solution Ants eat pheromone on the trail Local search added before pheromone update 4.
Improvements to ASHigh exploration at the beginning Only best ant can add pheromone Sometimes uses local search to improve its performance 4. Dynamic Optimization Problems. ABC (circuit switched networks) Ant. Net (routing in packet- switched networks) 4.
Applications. Traveling Salesman Problem Quadratic Assignment Problem Network Model Problem Vehicle routing 4. Section IITraveling Salesman Problem Quadrature Assignment Problem. Mr. Fadi Elmasri 4. Travelling Salesman Problem (TSP)TSP PROBLEM Given N cities, and a distance function d between cities, find a tour that 1. Goes through every city once and only once 2. Minimizes the total distance.
Classical combinatorial optimization problem to test. ACO for the Traveling Salesman Problem. The TSP is a very important problem in the context of Ant Colony Optimization because it is the problem to which the original AS was first applied, and it has later often been used as a benchmark to test a new idea and algorithmic variants.
The TSP was chosen for many reasons It is a problem to which the ant colony metaphor It is one of the most studied NP- hard problems in the combinatorial optimization it is very easily to explain. So that the algorithm behavior is not obscured by too many technicalities. Search Space Discrete Graph To each edge is associated a static value returned by an heuristic function ? Each edge of the graph is augmented with a pheromone trail ? Pheromone is dynamic and it is learned at run- ime 4. Ant Systems (AS) Ant Systems for TSP Graph (N,E) where N cities/nodes, E edges the tour cost from city i to city j (edge weight) Ant move from one city i to the next j with some transition probability. Ant Systems Algorithm for TSPInitialize.
Place each ant in a randomly chosen city. For Each Ant. Choose Next. City(For Each Ant)more cities to visityes.
No. Return to the initial cities. Update pheromone level using the tour cost for each ant No. Stopping criteria yes.
Print Best tour 4. Rules for Transition Probability. Whether or not a city has been visited Use of a memory(tabu list) set of all cities that are to be visited visibility. Heuristic desirability of choosing city j when in city i. Pheromone trail This is a global type of information.
Transition probability for ant k to go from city i to city j while building its route. Pheromone trail and heuristic function are they useful? Comparison between ACS standard, ACS with no heuristic (i. B0), and ACS in which ants neither sense nor deposit pheromone. Problem Oliver. 30.
Averaged over 3. 0 trials, 1. Trail pheromone in AS After the completion of a tour, each ant lays some pheromone for each edge that it has used. Trail pheromone decay 5.
Ant Colony Optimization (ACO) Dorigo Gambardella introduced four modifications in AS 1. Local/global pheromone trail updates, 3. ACS Ant Colony System for TSP 5. ACO State Transition Rule Next city is chosen between the not visited cities according to a probabilistic rule Exploitation the best edge is chosen. Exploration each of the edges in proportion to its value 5. ACS State Transition Rule Formulae 5. ACS State Transition Rule example with probability exploitation (Edge AB 1.
AB with probability 1. AC with probability 5/2. AD with probability 6/2. ACS Local Trail Updating similar to evaporation 5. ACS Global Trail Updating At the end of each iteration the best ant is allowed to reinforce its tour by depositing additional pheromone inversely proportional to the length of the tour 5. Effect of the Local Rule Local rule learnt desirability of edges changes dynamically Local update rule makes the edge pheromone level diminish.
Visited edges are less less attractive as they are visited by the various ants. Favors exploration of not yet visited edges. This helps in shuffling the cities so that cities visited early in one ants tours are being visited later in another ants tour. ACO vs AS Pheromone trail update.
Deposit pheromone after completing a tour in ASHere in ACO only the ant that generated the best tour from the beginning of the trial is allowed to globally update the concentrations of pheromone on the branches (ants search at the vicinity of the best tour so far) In AS pheromone trail update applied to all edges. Here in ACO the global pheromone trail update is applied only to the best tour since trial began. ACO Candidate List Use of a candidate list. A list of preferred cities to visit instead of examining all cities, unvisited cities are examined first. Cities are ordered by increasing distance list is scanned sequentially.
Choice of next city from those in the candidate list. Other cities only if all the cities in the list have been visited. Performance Algorithm found best solutions on small problems (7.
On larger problems converged to good solutions but not the best On static problems like TSP hard to beat specialist algorithms Ants are dynamic optimizers should we even expect good performance on static problems Coupling ant with local optimizers gave world class results. Quadratic Assignment Problem(QAP)Problem is Assign n activities to n locations (campus and mall layout). D , , distance from location i to location j F , ,flow from activity h to activity k Assignment is permutatio Minimize Its NP hard 6.
QAP Example. ALocations. Facilities. B? Cbiggest flow A - BHow to assign facilities to locations ? ACBCABHigher cost. Lower cost 6. 5SIMPLIFIED CRAFT (QAP)Simplification Assume all departments have equal size Notation distance between locations i and j travel frequency between departments k and h 1 if department k is assigned to location i 0 otherwise. Example. 12. Location. Department (Facility)3.
Distance. Frequency 6. Ant System (AS- QAP)Constructive method step 1 choose a facility j step 2 assign it to a location i.