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CSE 460 Hybrid Optimization In this section we will look at hybrid search methods That combine stochastic search with systematic search Problem Classes.

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Presentation on theme: "CSE 460 Hybrid Optimization In this section we will look at hybrid search methods That combine stochastic search with systematic search Problem Classes."— Presentation transcript:

1 CSE 460 Hybrid Optimization In this section we will look at hybrid search methods That combine stochastic search with systematic search Problem Classes for Hybrid Search Constructive Meta-Heuristics Constraint Propagation Integrating Constraint Propagation into Constructive Meta-Heuristics

2 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

3 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

4 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

5 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

6 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

7 Ant Colony Optimization Constructive Meta-Heuristics Edge Selection Pheromone Deposit

8 Job Scheduling Release timeDeadline Processing timeSet-up time Job time window Job 4Job 1Job 2Job 3Job 5 Job sequence schedule time

9 ACO for Scheduling Edge Length: set-up time / tardiness... Visibility (Heuristics):shortest setup time / earliest completion time shortest processing time / minimum slack time … Job 4 Job 1 Job 2 Job 3

10 Adaptiveness vs. Optimality Optimal route is only found at the expense of adaptiveness ECT: fair+ elitistECT: elitist only ECT: fair+ elitist + 2opt (distribution can be achieved with other parameter changes) Elitist reward simulates non-linear distorted reward function

11 Constraint Types  Feasibility Hard Deadlines Hard Release Times Job Priorities  Dependencies Setup-times sequence dependent Interdependent task couplings  hard: fixed delay  soft: delay is cost component

12 Constraint Types  Hard Deadlines  Hard Release Times  Job Priorities

13 Search Method Types  Systematic (Enumeration) Constraint Programming Integer Programming / MIP Beam Search  Heuristic ACO GA / EC GRASP EDA Tabu SA

14 Search Method Types Tree Search Constructive Stochastic Search  Systematic (Enumeration) Constraint Programming Integer Programming / MIP Beam Search  Heuristic ACO GA / EC GRASP EDA Tabu (deterministic) SA (not constructive)

15 Degrees of Tightness tight loose T1T1 T2T2 Stochastic Search (Meta Heuristics) Systematic Search (Enumeration) intermediate T3T3 Hybrid Methods !

16 Degrees of Tightness tight loose T1T1 T2T2 intermediate T3T3 Hybrid Methods ! Stochastic Search (Meta Heuristics) Systematic Search (Enumeration)

17 Constraint Programming  Systematic search  Domains: FD, N, R, …  Explicit High-Level Modelling  Search Space Reduction by Domain Reduction (in FD) CP(FD) = Tree Search + Tree Pruning

18 Constraint Programming  Systematic search  Domains: FD, N, R, …  Explicit High-Level Modelling  Search Space Reduction by Domain Reduction (in FD) CP(FD) = Tree Search + Tree Pruning

19 Constraint Programming  Systematic search  Domains: FD, N, R, …  Explicit High-Level Modelling  Search Space Reduction by Domain Reduction (in FD) CP(FD) = Tree Search + Tree Pruning

20 Constraint Programming  Systematic search  Domains: FD, N, R, …  Explicit High-Level Modelling  Search Space Reduction by Domain Reduction (in FD) CP(FD) = Tree Search + Tree Pruning

21 Constraint Programming  Systematic search  Domains: FD, N, R, …  Explicit High-Level Modelling  Search Space Reduction by Domain Reduction (in FD) CP(FD) = Tree Search + Tree Pruning

22 CP(FD)=Tree Search + Pruning  Very efficient for tight problems  Degenerates into full enumeration  Heuristic ordering programmed manually, Value ordering Variable ordering no automatic learning of order objective typically as constraint  Balance propagation cost with search cost

23 Constraint Handling in MH

24 require 1.Explicit Model 2.Customized Algorithms

25 CP - ACO Hybrid learning via reinforcement ACO + CP feasible construction / search space pruning

26 Constraint Programming procedure label(list xs) if xs=nil then return true else let x=first(xs) in if not bind(x) then return false else begin if (label(rest(xs)) return true else begin unbind(x) return label(xs) end end. Algorithm CP-basic setup domains for x 1, …, x n post initial constraints label([x 1, …, x n ]) end.

27 Coupling of Problem Models

28 CP with ACO Algorithm CP-with-ACO for each ant do begin setup domains for x 1, …, x n post initial constraints if label-probabilistically([x 1, …, x n ]) then update pheromone for global best solution end end. Labeling probabilistic value ordering based on pheromone amount performs “local” pheromone evaporation

29 Algorithm CP-ACS for JSP initialize solver; post initial constraints; initialize pheromone   ; place each ant on a randomly chosen city; for t := 1 to t_max do reset solver state for k := 1 to #ants do T k := nil; Mark all jobs as unscheduled for ant k; While n<#jobs & feasible do begin n := n+1; i := last job scheduled do C := fd_domain(job n ) choose next job j  C with feasible := post(job n =j) if not feasible then post(job n  j) until feasible or C={} if feasible then begin T k := append(T k, j) evaporate locally; mark job j as scheduled end end; update pheromone levels & best solution memory.

30 CP-ACO Model for JSP Setup 1 Setup 2 … Domain restrictions ACO Model based on Job-IDs Job ID 1 Start 1 End 1 Release 1 Duration 1 Due 1 Job ID 2 Start 2 End 2 Release 2 Duration 2 Due 2

31 CP-ACO Model for JSP Setup 1 Setup 2 … Coupling to Data ACO Model based on Job-IDs Job ID 1 Start 1 End 1 Release 1 Duration 1 Due 1 Job ID 2 Start 2 End 2 Release 2 Duration 2 Due 2

32 CP-ACO Model for JSP Setup 1 Setup 2 … Internal Coupling ACO Model based on Job-IDs Job ID 1 Start 1 End 1 Release 1 Duration 1 Due 1 Job ID 2 Start 2 End 2 Release 2 Duration 2 Due 2

33 CP-ACO Model for JSP Setup 1 Setup 2 … Chaining ACO Model based on Job-IDs Job ID 1 Start 1 End 1 Release 1 Duration 1 Due 1 Job ID 2 Start 2 End 2 Release 2 Duration 2 Due 2

34 CP-ACO Model for JSP Setup1Setup 2 … Chaining ACO Model based on Job-IDs Job ID 1 Start 1 End 1 Release 1 Duration 1 Due 1 Job ID 2 Start 2 End 2 Release 2 Duration 2 Due 2

35 Pure CP Model for JSP Black-Box Constraints Specialized scheduling solver Job #1 Start 1 End 1 Release 1 Duration 1 Due 1 Job #2 Start 2 End 2 Release 2 Duration 2 Due Job #n Start n End n Release n Duration n Due n based on Job Times (Start/End)

36 Coupling of Constraint Models Cross-Propagation

37 Evaluation

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41 Conclusions Best for intermediate tightness requires fewer labeling steps than CP better results than pure ACO Runtime tradeoff not entirely clear propagation can be costly backtracking should be exploited


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