# Least Cost Search Branch And Bound Ppt To Pdf

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- The Online Portfolio of Mike Flynn
- AI - Popular Search Algorithms
- I. Introduction
- Travelling Salesman Problem using Branch and Bound

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## The Online Portfolio of Mike Flynn

Copy embed code:. Automatically changes to Flash or non-Flash embed. WordPress Embed Customize Embed. URL: Copy. Presentation Description No description available. By: jyotisaini month s ago. By: krishnarkeyadav month s ago. By: pramodvaidya month s ago. By: kannan. By: ubale month s ago. The expansion of all live-nodes is required before the node leading to an answer node. The search for an answer node can be speeded up by using a ranking function c.

The cost of node X could be i the number of nodes in the subtree that need to be generated before an answer node is generated or ii the number of levels the nearest answer node is from X. If cost measure i is used then the search would always generate the minimum number of nodes every branch and bound algorithm must generate. If cost measure ii is used, then the only nodes to become E-nodes are the nodes on the path from the root to the nearest answer node. LC-Search with bounding functions is LC branch and bound search.

The Actual cost of X is denoted with c X. Thus c X is an estimation of C X. An LC-search expands the node with minimum cost c X. But it is not necessary that LC-search always finds an answer node with minimum cost. The starting value for U may be obtained by some heuristic or may be set to 8. Each time a new answer node is found the value of U may be updated.

A small positive constant? We only deal with minimization problems, because a maximization problem is easily converted into a minimization problem by changing the sign of the objective function.

Application of Branch and Bound contd.. Searching for an optimal solution is equivalent to searching for a least cost answer node. The c. Any node representing a feasible solution will be an answer node. Answer nodes and solution nodes are indistinguishable. In LCBB live nodes are added to a min-heap and deleted from a min-heap.

Node 1 is expanded to give two children nodes 2 and 3. Solution of Knapsack problem contd.. Let us assume node 7 is expanded. Least cost is —38 and the path is 8, 7, 4, 2,1. Follow us on:. Go to Application. US Go Premium. PowerPoint Templates. Upload from Desktop Single File Upload. Post to :. URL :. Related Presentations :. Add to Channel. The presentation is successfully added In Your Favorites. Views: Category: Education. Like it Dislike it 0. Added: March 05, Posting comment Post Reply Close.

Edit Comment Close. Premium member. Presentation Transcript. Hence such a strategy is called Least cost search or LC-Search. LC search for minimum cost answer node Contd.. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation. Careers Webinars. All rights reserved. Use HTTPs.

## AI - Popular Search Algorithms

Given a set of cities and the distance between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point. For example, consider the following graph. The term Branch and Bound refer to all state-space search methods in which all the children of an E—node are generated before any other live node can become the E—node. E—node is the node, which is being expended. State—space tree can be expended in any method, i. Both start with the root node and generate other nodes.

## I. Introduction

Now customize the name of a clipboard to store your clips. Branch and Bound Travelling Salesman Problem 2. Below is an idea used to compute bounds for Traveling salesman problem.

Artificial Intelligence is the study of building agents that act rationally. Most of the time, these agents perform some kind of search algorithm in the background in order to achieve their tasks. There are far too many powerful search algorithms out there to fit in a single article. Instead, this article will discuss six of the fundamental search algorithms, divided into two categories, as shown below.

A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search : the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. If no bounds are available, the algorithm degenerates to an exhaustive search. The method was first proposed by Ailsa Land and Alison Doig whilst carrying out research at the London School of Economics sponsored by British Petroleum in for discrete programming , [1] [2] and has become the most commonly used tool for solving NP-hard optimization problems.

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### Travelling Salesman Problem using Branch and Bound

For example, consider the graph shown in figure on right side. Cost of any tour can be written as below. A general method, based on the branch and bound technique, is developed, which solves globally the nonconvex WSRMax problem with an optimality certificate. Consider lower bound for 2 as we moved from 1 to 1, we include the edge to the tour and alter the new lower bound for this node.

Searching is the universal technique of problem solving in AI. There are some single-player games such as tile games, Sudoku, crossword, etc. The search algorithms help you to search for a particular position in such games. The games such as 3X3 eight-tile, 4X4 fifteen-tile, and 5X5 twenty four tile puzzles are single-agent-path-finding challenges. They consist of a matrix of tiles with a blank tile. The player is required to arrange the tiles by sliding a tile either vertically or horizontally into a blank space with the aim of accomplishing some objective. A set of states and set of operators to change those states.

The branch-and-bound design strategy is very similar to backtracking in that a state space tree is used to solve a problem. The differences are that the branch-and-bound method 1 does not limit us to any particular way of traversing the tree, and 2 is used only for optimization problems. A branch-and-bound algorithm computes a number bound at a node to determine whether the node is promising. The number is a bound on the value of the solution that could be obtained by expanding beyond the node. If that bound is no better than the value of the best solution found so far, the node is nonpromising. Otherwise, it is promising. The backtracking algorithm for the Knapsack problem is actually a branch-and-bound algorithm.

But it is not necessary that LC-search always finds an answer node with minimum cost. For two nodes X and Y with c(X)

Let there be N workers and N jobs.

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LC (Least Cost) Search. FIFO Branch and Bound Search: For this we will use a data structure called Queue. Initially Queue is empty. Example: Assume the node.