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FORS 8450 • Advanced Forest Planning Lecture 19 Ant Colony Optimization Ant Colony Optimization Background The ant colony optimization (ACO) search process was initially described by Dorigo (1992), and has been used to address problems in many different fields, including forestry. ACO algorithms are based on the mechanics of ants searching for food from a nest area. It was initially suggested for route management problems. Each solution corresponds to an ant's route through the solution space. The objective function value of each solution is computed, and the route taken is noted. Ants that take the same portion of a route influence the acceptability and desirability of the portion of the route. In this manner, the search process evolves. Ant Colony Optimization Characteristics of the algorithm (first take) 1) This is a stochastic, population-based, swarm-type heuristic. 2) Ants wander randomly initially, looking for food. • Solutions are generated using Monte Carlo simulation. • Therefore an ant is a solution. 3) Upon finding the food, ants return to their colony while laying down pheromones. 4) If other ants find a part of the path, they are likely to use it rather than wandering randomly. 5) The path is reinforced if food is found again by another ant. 6) Over time, the path's trail of pheromones evaporates, reducing its attractive strength. The more time it takes for an ant to travel down a trail, the more pheromones evaporate. • Shorter paths are traveled more frequently, and pheromones are stronger there as well. Ant Colony Optimization Characteristics of the algorithm (second take) 1) An ant (called a blitz) travels around randomly. 2) If the ant discovers food, it returns to the colony, and leaves behind a trail of pheromones for others to follow. 3) Nearby ants will follow the trail, if it is attractive. • Shorter paths are increasingly more attractive as more pheromones are laid down • Longer paths will become less attractive, as the pheromone trail evaporates • Interestingly, all ants should eventually have the same route Ant Colony Optimization Characteristics of the algorithm An ant is a solution. Solutions (ants) are at different places in the solution space. How they change is based on the probability of changing to a different schedule. An ant completes its tour after selection a choice for each stand. Utilities (objective function values) of each tour are calculated. Pheromone levels are updated after all of the ants have completed all of their tours. Ant Colony Optimization Characteristics of the algorithm The probability of moving from Point A to Point B depends on the attractiveness of the move and the trail level. A Attractiveness - an a priori desirability (typically based on the inverse distance) of the move. ? Trail level - an a posteriori, computed attractiveness. This is computed after an ant completes a solution, increasing or decreasing the desirabilities of components of a solution. Prob A B Amount of pheromone Amounts A B Desirabili of pheromones B ty of state transition Desirabili ties C A B Ant Colony Optimization Characteristics of the algorithm Amounts of pheromones are updated after a solution has been generated. A (1-p) prior pheromone + pheromone ? Where: p = a coefficient related to the evaporation rate. if AB path is used, pheromone levels increase pheromone = Q / Lk Where: Q = a constant Lk = solution length (quality) Else pheromone levels decrease, since in this case pheromone = 0 B C Ant Colony Optimization Advantages: • It is intuitive to biologically-minded people, mimicking nature. • The system is built on positive feedback (pheromone attraction) and negative attractiveness (pheromone evaporation). • Pheromone evaporation helps avoid convergence to a local optima. Disadvantages: • For routing problems it may make more sense, but for harvest scheduling problems, it requires a conceptual leap of faith. • Fine-tuning the sensitive parameters may require significant effort. Ant Colony Optimization Necessary parameters 1) The initial population of ants (an ant cycle). 2) The total number of tours. 3) The evaporation rate. 4) The amount of pheromone applied to a section of a cycle or solution. 5) The constant Q. Generate initial ants Ant Colony Optimization For all ants, develop an ant tour Basic Process Assess the quality of the ant tours Change probabilities of pieces of each potential tour Has the best solution Yes been improved? Update pheromone levels No No Have we reached the stopping criteria? Yes Stop and report the best solution found during search Save best solution