This document summarizes several informed search algorithms:
- Best-first search expands nodes based on an evaluation function f(n) that estimates desirability. Special cases are greedy best-first and A* search.
- Greedy best-first search uses a heuristic h(n) as the evaluation function and may get stuck in loops.
- A* search uses an evaluation of f(n)=g(n)+h(n) where g(n) is cost to reach n and h(n) estimates cost from n to goal. A* is optimal if h is admissible or consistent.
- Local search algorithms like hill-climbing search and simulated annealing search operate on a
Types of inference engines
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification
Types of inference engines
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
As Expert Systems evolved many new techniques were incorporated into various types of inference engines. Some of the most important of these were:
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification.
Truth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology ClassificationTruth Maintenance.
Hypothetical Reasoning.
Fuzzy Logic.
Ontology Classification
Lecture slides by Mustafa Jarrar at Birzeit University, Palestine.
See the course webpage at: http://jarrar-courses.blogspot.com/2012/04/aai-spring-jan-may-2012.html
and http://www.jarrar.info
and on Youtube:
http://www.youtube.com/watch?v=aNpLekq6-oA&list=PL44443F36733EF123
Solving problems by searching Informed (heuristics) Searchmatele41
Informed Search – a strategy that uses problem-specific knowledge beyond the definition of the problem itself
Best-First Search – an algorithm in which a node is selected for expansion based on an evaluation function f(n)
This presentation discusses the state space problem formulation and different search techniques to solve these. Techniques such as Breadth First, Depth First, Uniform Cost and A star algorithms are covered with examples. We also discuss where such techniques are useful and the limitations.
Lecture slides by Mustafa Jarrar at Birzeit University, Palestine.
See the course webpage at: http://jarrar-courses.blogspot.com/2012/04/aai-spring-jan-may-2012.html
and http://www.jarrar.info
and on Youtube:
http://www.youtube.com/watch?v=aNpLekq6-oA&list=PL44443F36733EF123
Solving problems by searching Informed (heuristics) Searchmatele41
Informed Search – a strategy that uses problem-specific knowledge beyond the definition of the problem itself
Best-First Search – an algorithm in which a node is selected for expansion based on an evaluation function f(n)
This presentation discusses the state space problem formulation and different search techniques to solve these. Techniques such as Breadth First, Depth First, Uniform Cost and A star algorithms are covered with examples. We also discuss where such techniques are useful and the limitations.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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4. Review: Tree search
• input{file{algorithms}{tree-search-short-
algorithm}}
•
• A search strategy is defined by picking the
order of node expansion
•
5. Best-first search
• Idea: use an evaluation function f(n) for each node
– estimate of "desirability"
–
Expand most desirable unexpanded node
• Implementation:
Order the nodes in fringe in decreasing order of
desirability
• Special cases:
– greedy best-first search
– A* search
7. Greedy best-first search
• Evaluation function f(n) = h(n) (heuristic)
• = estimate of cost from n to goal
•
• e.g., hSLD(n) = straight-line distance from n
to Bucharest
•
• Greedy best-first search expands the node
that appears to be closest to goal
•
12. Properties of greedy best-first
search
• Complete? No – can get stuck in loops,
e.g., Iasi Neamt Iasi Neamt
•
• Time? O(bm), but a good heuristic can give
dramatic improvement
•
• Space? O(bm) -- keeps all nodes in
memory
•
13. A* search
• Idea: avoid expanding paths that are
already expensive
•
• Evaluation function f(n) = g(n) + h(n)
•
• g(n) = cost so far to reach n
• h(n) = estimated cost from n to goal
• f(n) = estimated total cost of path through
n to goal
20. Admissible heuristics
• A heuristic h(n) is admissible if for every node n,
h(n) ≤ h*(n), where h*(n) is the true cost to reach
the goal state from n.
• An admissible heuristic never overestimates the
cost to reach the goal, i.e., it is optimistic
•
• Example: hSLD(n) (never overestimates the
actual road distance)
•
• Theorem: If h(n) is admissible, A* using TREE-
21. Optimality of A* (proof)
• Suppose some suboptimal goal G2 has been generated and is in the
fringe. Let n be an unexpanded node in the fringe such that n is on a
shortest path to an optimal goal G.
•
• f(G2) = g(G2) since h(G2) = 0
• g(G2) > g(G) since G2 is suboptimal
• f(G) = g(G) since h(G) = 0
• f(G2) > f(G) from above
22. Optimality of A* (proof)
• Suppose some suboptimal goal G2 has been generated and is in the
fringe. Let n be an unexpanded node in the fringe such that n is on a
shortest path to an optimal goal G.
•
• f(G2) > f(G) from above
• h(n) ≤ h^*(n) since h is admissible
• g(n) + h(n) ≤ g(n) + h*(n)
• f(n) ≤ f(G)
•
*
23. Consistent heuristics
• A heuristic is consistent if for every node n, every successor n' of n
generated by any action a,
•
h(n) ≤ c(n,a,n') + h(n')
• If h is consistent, we have
•
f(n') = g(n') + h(n')
= g(n) + c(n,a,n') + h(n')
≥ g(n) + h(n)
= f(n)
• i.e., f(n) is non-decreasing along any path.
•
• Theorem: If h(n) is consistent, A* using GRAPH-SEARCH is optimal
24. Optimality of A*
• A* expands nodes in order of increasing f value
•
• Gradually adds "f-contours" of nodes
• Contour i has all nodes with f=fi, where fi < fi+1
•
25. Properties of A$^*$
• Complete? Yes (unless there are infinitely
many nodes with f ≤ f(G) )
•
• Time? Exponential
•
• Space? Keeps all nodes in memory
•
• Optimal? Yes
•
26. Admissible heuristics
E.g., for the 8-puzzle:
• h1(n) = number of misplaced tiles
• h2(n) = total Manhattan distance
(i.e., no. of squares from desired location of each tile)
• h1(S) = ?
• h2(S) = ?
27. Admissible heuristics
E.g., for the 8-puzzle:
• h1(n) = number of misplaced tiles
• h2(n) = total Manhattan distance
(i.e., no. of squares from desired location of each tile)
• h1(S) = ? 8
• h2(S) = ? 3+1+2+2+2+3+3+2 = 18
28. Dominance
• If h2(n) ≥ h1(n) for all n (both admissible)
• then h2 dominates h1
• h2 is better for search
•
• Typical search costs (average number of nodes
expanded):
•
• d=12 IDS = 3,644,035 nodes
A*(h1) = 227 nodes
A*(h2) = 73 nodes
• d=24 IDS = too many nodes
A*(h1) = 39,135 nodes
A*(h2) = 1,641 nodes
29. Relaxed problems
• A problem with fewer restrictions on the actions
is called a relaxed problem
•
• The cost of an optimal solution to a relaxed
problem is an admissible heuristic for the
original problem
•
• If the rules of the 8-puzzle are relaxed so that a
tile can move anywhere, then h1(n) gives the
shortest solution
•
• If the rules are relaxed so that a tile can move to
any adjacent square, then h2(n) gives the
shortest solution
30. Local search algorithms
• In many optimization problems, the path to the
goal is irrelevant; the goal state itself is the
solution
•
• State space = set of "complete" configurations
• Find configuration satisfying constraints, e.g., n-
queens
• In such cases, we can use local search
algorithms
• keep a single "current" state, try to improve it
•
31. Example: n-queens
• Put n queens on an n × n board with no
two queens on the same row, column, or
diagonal
•
34. Hill-climbing search: 8-queens problem
• h = number of pairs of queens that are attacking each other, either directly
or indirectly
• h = 17 for the above state
•
36. Simulated annealing search
• Idea: escape local maxima by allowing some
"bad" moves but gradually decrease their
frequency
•
37. Properties of simulated
annealing search
• One can prove: If T decreases slowly enough,
then simulated annealing search will find a
global optimum with probability approaching 1
•
• Widely used in VLSI layout, airline scheduling,
etc
•
38. Local beam search
• Keep track of k states rather than just one
•
• Start with k randomly generated states
•
• At each iteration, all the successors of all k
states are generated
•
• If any one is a goal state, stop; else select the k
best successors from the complete list and
39. Genetic algorithms
• A successor state is generated by combining two parent
states
•
• Start with k randomly generated states (population)
•
• A state is represented as a string over a finite alphabet
(often a string of 0s and 1s)
•
• Evaluation function (fitness function). Higher values for
better states.
•
40. Genetic algorithms
• Fitness function: number of non-attacking pairs of
queens (min = 0, max = 8 × 7/2 = 28)
•
• 24/(24+23+20+11) = 31%
•
• 23/(24+23+20+11) = 29% etc