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flores y follajes caprinos - Fia

flores y follajes caprinos - Fia


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Relaxations in distributed constraint optimisation 37optimal solution is one which minimises F. The solution process, however, is restricted:each agent is responsible for the assignment of its own variables, and thus agents mustcommunicate with each other, describing assignments and costs, in order to find a globallyoptimal solution.Adopt (Modi et al. 2005) is a complete DisCOP algorithm where agents execute asynchronously.Initially, the agents are prioritised into a depth-first search (DFS) tree, such thatneighbouring agents appear on the same branch in the tree. Each agent a i maintains a lower(LB i ) and upper (UB i ) bound on the cost of its subtree, which means that the lower andupper bounds of the root agent are bounds for the problem as a whole. Let H i be the setof higher priority neighbours of a i ,andletL i be the set of its children. During search, allagents act independently and asynchronously from each other. Each agent a i executes in aloop, repeatedly performing a number of tasks:1. VALUE messages, containing variable assignments, are received from higher priorityagents and added to the current context CC i , which is a record of higher priority neighbours’current assignments: CC i ∈ ∏ j:a j ∈H iD j .2. COST messages, containing lower and upper bounds, are received from children andstored if they are valid for the current context—for each subtree, rooted by an agenta j ∈ L i , a i maintains a lower bound, lb(l i , a j ), and an upper bound ub(l i , a j ) for eachof its assignments l i . Each cost is valid for a specific context CX(l i , a j ) ∈ ∏ k:a k ∈H jD k .Any previously stored cost with a context incompatible with the current context is resetto have lower/upper bounds of 0/∞.3. A THRESHOLD message is received from the immediate parent of a i —the threshold t iis the best known lower bound for the subtree rooted by a i . 24. The local assignments with minimal lower and upper bound costs are calculated. LetC ij be the constraint between x i and x j . The partial cost, δ(l), for an assignment of l ito x i is the sum of the agent’s local cost f i (l i ), plus the costs of constraints between a iand higher priority neighbours: δ(l i ) = f i (l i ) + ∑ j:a j ∈H iC ij (l i , CC i↓x j). The lowerbound, LB(l i ), for an assignment of l i to x i is the sum of δ(l i ) and the currently knownlower bounds for all subtrees: LB(l i ) = δ(l i ) + ∑ j:a j ∈L ilb(l i , a j ). The upper bound,UB(l i ),isthesumofδ(l i ) and the currently known upper bounds for all subtrees:UB(l i ) = δ(l i ) + ∑ j:a j ∈L iub(l i , a j ). The minimum lower bound over all assignmentpossibilities, LB i , is the lower bound for the agent a i : LB i = min li ∈D iLB(l i ). Similarly,UB i is the upper bound for the agent a i : UB i = min li ∈D iUB(l i ).5. The agent’s current assignment, d i , is updated and sent to all neighbours in L i :ift i ==UB i then d i ← l i that minimises UB(l i ),elseifLB(d i ) > t i then d i ← l i thatminimises LB(l i ).6. LB i and UB i are passed as costs to the parent of a i , along with the context to whichthey apply, CC i .As the search progresses, the bounds are tightened in each agent until the lower and upperbounds are equal. If an agent detects this condition, and its parent has terminated, then anoptimal solution is found and it may terminate.2 The threshold in Adopt is used to reduce thrashing. During search agents discover lower bounds for differentcontexts. When an agent returns to a previously explored context, the search is guided by the fact that theagent knows it cannot find an assignment with a cost better than the threshold. For a detailed explanation ofthresholds and Adopt , please refer to (Modi et al. 2005).123

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