Overview. Heuristic Search. Deskripsi. Simulated Annealing IF-UTAMA 1

Transkripsi

1 Jurusan Teknik Informatika Universitas Widyatama Overview Heuristic Search Pertemuan : 4 Dosen Pembina : Sriyani Violina Danang Junaedi Deskripsi Heuristic Search Simulated nnealing Simplified Memory ounded * i-directional * Modified i-directional * Dynamic Weighthing * IF-UTM 1 IF-UTM 2 Deskripsi Pertemuan ini mempelajari bagaimana memecahkan suatu masalah dengan teknik searching. Metode searching yang dibahas pada pertemuan ini adalah heuristic search atau informed search yang terdiri dari: Simulated nnealing Simplified Memory ounded * i-directional * Modified i-directional * Dynamic Weighthing * Simulated nnealing alternative to a random-restart hill-climbing when stuck on a local maximum is to do a reverse walk to escape the local maximum. This is the idea of simulated annealing. The term simulated annealing derives from the roughly analogous physical process of heating and then slowly cooling a substance to obtain a strong crystalline structure. The simulated annealing process lowers the temperature by slow stages until the system ``freezes" and no further changes occur. IF-UTM 3 IF-UTM 4 IF-UTM 1

2 Search using Simulated nnealing Simulated nnealing = hill-climbing with non-deterministic search asic ideas: like hill-climbing identify the quality of the local improvements instead of picking the best move, pick one randomly say the change in objective function is δ if δ is positive, then move to that state otherwise: move to this state with probability proportional to δ thus: worse moves (very large negative δ) are executed less often however, there is always a chance of escaping from local maxima over time, make it less likely to accept locally bad moves (Can also make the size of the move random as well, i.e., allow large steps in state space) IF-UTM 5 Physical Interpretation of Simulated nnealing Physical nalogy: imagine letting a ball roll downhill on the function surface this is like hill-climbing (for minimization) now imagine shaking the surface, while the ball rolls, gradually reducing the amount of shaking this is like simulated annealing nnealing = physical process of cooling a liquid or metal until particles achieve a certain frozen crystal state simulated annealing: free variables are like particles seek low energy (high quality) configuration get this by slowly reducing temperature T, which particles move around randomly IF-UTM 6 Simulated nnealing Probability of transition to higher energy state is given by function: P = e E/kt Where E is the positive change in the energy level T is the temperature K is oltzmann constant. Differences The algorithm for simulated annealing is slightly different from the simple-hill climbing procedure. The three differences are: The annealing schedule must be maintained Moves to worse states may be accepted It is good idea to maintain, in addition to the current state, the best state found so far. IF-UTM 7 IF-UTM 8 IF-UTM 2

3 lgorithm: Simulate nnealing Simulate nnealing: Implementation 1. Evaluate the initial state. If it is also a goal state, then return it and quit. Otherwise, continue with the initial state as the current state. 2. Initialize EST-SO-FR to the current state. 3. Initialize T according to the annealing schedule 4. Loop until a solution is found or until there are no new operators left to be applied in the current state. a. Select an operator that has not yet been applied to the current state and apply it to produce a new state. b. Evaluate the new state. Compute: E = ( value of current ) ( value of new state) If the new state is a goal state, then return it and quit. If it is a goal state but is better than the current state, then make it the current state. lso set EST-SO-FR to this new state. If it is not better than the current state, then make it the current state with probability p as defined above. This step is usually implemented by invoking a random number generator to produce a number in the range [0, 1]. If the number is less than p, then the move is accepted. Otherwise, do nothing. c. Revise T as necessary according to the annealing schedule 5. Return EST-SO-FR as the answer It is necessary to select an annealing schedule which has three components: Initial value to be used for temperature Criteria that will be used to decide when the temperature will be reduced mount by which the temperature will be reduced. IF-UTM 9 IF-UTM 10 Memory ounded Search To address complex search problems, we often put constraints on memory requirements. We will examine two algorithms: (a) ID* search and (b) SM* search. Iterative Deepening * Search (ID*) uses a DFS for every iteration where an f-cost limit is used instead of a depth limit. Each iteration expands all the nodes that lie inside a contour for the current f-cost. The time complexity depends on the different values that the heuristic can take on. ID* is complete, optimal, and memory-bounded. To improve ID*, we often increase the f-cost limit by a fixed amount ε on each iteration. Such an approach is called ε-admissible. IF-UTM 11 SIMPLIFIED MEMORY-OUNDED * (SM*) ID* cannot remember its previous steps since it uses too little memory (between iterations only the f-cost limit is kept). If the state space is graph, ID* often repeats itself. Uses all available memory for the search drops nodes from the queue when it runs out of space those with the highest f-costs If there is a tie (equal f-values) we first delete the oldest nodes first. complete if there is enough memory for the shortest solution path often better than * and ID* but some problems are still too tough trade-off between time and space requirements It is complete and optimal if the available memory allows SM* to store the shallowest solution path. When enough memory is available for the whole search tree, the search is optimally efficient. 12 IF-UTM 12 IF-UTM 3

4 SM* Code IF-UTM 13 Simple Memory-bounded * (SM*) 10+5= C 20+5=25 E 30+5=35 f = g+h F Search space D 20+0= = =12 (Example with 3-node memory) = goal =13 H 16+2= J K I 24+0= = =29 Progress of SM*. Each node is labeled with its current f- cost. Values in parentheses show the value of the best forgotten descendant. 24( ) 12 () 24 I C (24) H 13() 20(24) 8 20( ) Optimal & complete if enough memory Can be made to signal when the best solution found might not be optimal - E.g. if J=19 IF-UTM 14 D 20 Ex: Rute Perjalanan Solusi SM* n h(n) b(n) S C 25 D E 74 5 F H J K L 20 M 60 h(n):heuristic jarak antar suatu kota dan b(n):perkiraan biaya menuju kota asal IF-UTM IF-UTM 16 IF-UTM 4

5 lgoritma i-directional * (D*) Function D*(masalah) return solusi inputs: masalah ruang masalah,jenis solusi, start(s) dan goal() variable lokal : Ns,ng{est node dr start & goal} OPENs,OPENg{open dr start & goal} CLOSEDs, CLOSEDg{Closed dar start & goal} loop sampai goal ditemukan Ns,OPENs,CLOSEDs *(OPENs,CLOSEDs,S,) if Ns in CLOSEDs then {goal ditemukan} v simpul di CLOSEDg yang sama dengan Ns g_terbaik g(,v) {biaya sebenarnya dari ke v melalui parent lama} loop untuk semua suk=simpul di CLOSEDg yang merupakan suksesor v if g(,v) melalui suk < g_terbaik then g_terbaik g(,v) melalui suk parent_baru suk endif endloop g(v) g_terbaik parent dari v parent_baru returns solusi endif IF-UTM 17 lgoritma i-directional * (D*) contd. Ng, OPENg, CLOSEDg *(OPENg, CLOSEDg,,S) if Ng in CLOSEDg then {goal ditemukan} u simpul di CLOSEDs yang sama dengan Ng g_terbaik g(s,u) {biaya sebenarnya dari S ke u melalui parent lama} loop untuk semua suk=simpul di CLOSEDg yang merupakan suksesor u if g(s,u) melalui suk < g_terbaik then g_terbaik g(s,u) melalui suk parent_baru suk endif endloop g(s,u) g_terbaik parent dari u parent_baru returns solusi endloop end IF-UTM 18 Solusi i-directional * Modified i-directional * Yang dimodifikasi adalah fungsi heuristiknya menjadi Untuk pencarian maju f(n)=g(s,n) * (h(n) - b(n)) Untuk pencarian mundur f(n)=g(,n) * (b(n) - h(n)) Dimana S g(s,n) g(,n) h(n) b(n) = node asal atau initial state = node tujuan atau goal state = jarak/biaya sebenarnya dari S ke n = jarak/biaya sebenarnya dari ke n = heuristik jarak node n = heuristik biaya node n IF-UTM 19 IF-UTM 20 IF-UTM 5

6 Solusi Modified i-directional * Dynamic Weighting * Fungsi heuristik yang digunakan f(n)=g(s,n)+(w(n) * h(n)) Dimana S g(s,n) h(n) w(n) = node asal atau initial state = node tujuan atau goal state = jarak/biaya sebenarnya dari S ke n = heuristik jarak node n = bobot dari fungsi heuristik IF-UTM 21 IF-UTM 22 Solusi Dynamic Weighting * Referensi 1. Suyanto rtificial Intelligence.Informatika. andung Search[online]. users.cselabs.umn.edu/classes/fall- 2010/csci5511/lectures/Ilecture3.ppt.Tanggal kses : 18 Februari Informed Search [online], Tanggal kses : 18 Februari Ramin Halavati.-. Informed Search and Exploration]. 04a-Informed%20Search%20and%20Exploration.ppt.Tanggal kses: 18 Februari Dan sumber-sumber lain yang terkait IF-UTM 23 IF-UTM 24 IF-UTM 6