Artificial Intelligence Methods (G52AIM)

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1 Artificial Intelligence Methods (G52AIM) Dr Rong Qu Constructive Heuristic Methods

2 Constructive Heuristics method Start from an empty solution Repeatedly, extend the current solution until a complete solution is constructed Use heuristics to try to extend in such a way that the final solution is a good one Some of the slides in this part are based on Dr Parkes previous teaching materials. See Constructive Heuristic Methods at

3 Constructive Heuristics method It is essential to know the difference between: Constructive methods Extend empty solution until get complete solution Local search Take complete solution and try to improve it via local moves

4 Constructive Heuristics for TSP Start: Pick a start city but an empty path Repeatedly: Extend the path by adding an edge to an unvisited city selected using a heuristic choice Until no more unvisited cities, then close the path to give a tour

5 Constructive Heuristics for TSP Heuristics Nearest Neighbour (NN) Heuristic Pick the next city which is the nearest unvisited city Any other good heuristics? Online demo NN from A A-D-B-C-A = =12 A-C-D-B-A = = 10 Optimal? D 1 A 2 1 B C

6 Constructive Heuristics for GC Graph colouring Given a graph G(V, E), assign colours to vertices Constraint Adjacent vertices cannot be coloured the same Objective Minimize: the number of colours to the graph A B A B D C F D C F E E

7 Constructive Heuristics for GC Heuristics Largest degree Pick the vertices with the largest degree Most Constraining Saturation degree Pick vertices with the fewest remaining colours Most Constrained Any other good heuristics?

8 Constructive Heuristics Putting this into the context of depth first search in G51IAI* At each choice suppose that branches are ordered left-to-right by the heuristic, with the preferred option on left Standard one-shot construction is just to take one branch of the search tree * You should be familiar with the blind search methods in G51IAI

9 Constructive Heuristics Putting this into the context of depth first search in G51IAI* To avoid mistakes in picking the wrong branches, heuristics can help to pick branches which lead to relatively good solutions * You should be familiar with the blind search methods in G51IAI

10 Heuristics Variable selection Which variable to work on In GC: which vertex to colour Value selection Which value to assign In GC: assign which colour to the chosen vertex

11 Heuristics Variable selection Most constrained In GC: largest degree Value selection Least constraining: imposes fewest constraints on remainder of problem In GC: which colour leaves the most colours to the remaining vertices

12 Constructive Heuristics Generally give better answers than random methods Very quick, but usually far from optimal Widely used with other methods Often used as initialization for meta-heuristics Pick the best solution from several runs

13 Constructive Heuristics - hybridize As initialization for local search Pick the best solution from several runs Hybridized with other meta-heuristics With local search: GRASP, etc With Genetic algorithms: Memetic algorithms

14 Constructive Heuristics - hybridize GRASP Greedy Randomized Adaptive Search Procedure Hybrid of Constructive methods Randomized & adaptive Local search Pick your favourite

15 Constructive Heuristics - hybridize GRASP Loop Create a solution, s, using randomized constructor g utilizing RCL Improve s using a local search End loop

16 Constructive Heuristics - hybridize GRASP Main idea of Restricted candidate list (RCL) At each iteration, within randomized constructor g 1. Use heuristic to select a limited number of good solution components; the RCL 2. Randomly select a choice from the RCL 3. Use this in order to extend the current partial assignment B D 1 A C

17 Constructive Heuristics - hybridize GRASP Main idea of Restricted candidate list (RCL) Size of RCL r If r is too big, then g becomes random If r is 1, then g becomes pure greedy heuristic Typical size of RCL is 3~5, but maybe problem dependent

18 Learning Objectives Know the general idea of constructive heuristics Know GRASP so you could apply them in your coursework if you had to

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