The document describes the traveling salesman problem (TSP) and how to solve it using a branch and bound approach. The TSP aims to find the shortest route for a salesman to visit each city once and return to the starting city. It can be represented as a weighted graph. The branch and bound method involves reducing the cost matrix by subtracting minimum row/column values, building a state space tree of paths, and choosing the path with the lowest cost at each step. An example demonstrates these steps to find the optimal solution of 24 for a 5 city TSP problem.
Introduction to Dynamic Programming, Principle of OptimalityBhavin Darji
Introduction
Dynamic Programming
How Dynamic Programming reduces computation
Steps in Dynamic Programming
Dynamic Programming Properties
Principle of Optimality
Problem solving using Dynamic Programming
TSP is np- hard problem which has number of solution but it's difficult to find optimal solution . I gave here fast,easy and efficient solution on TSP using one algorithm with good explanation.Hope you understood very well.
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
it contains the detail information about Dynamic programming, Knapsack problem, Forward / backward knapsack, Optimal Binary Search Tree (OBST), Traveling sales person problem(TSP) using dynamic programming
BackTracking Algorithm: Technique and ExamplesFahim Ferdous
This slides gives a strong overview of backtracking algorithm. How it came and general approaches of the techniques. Also some well-known problem and solution of backtracking algorithm.
Introduction to Dynamic Programming, Principle of OptimalityBhavin Darji
Introduction
Dynamic Programming
How Dynamic Programming reduces computation
Steps in Dynamic Programming
Dynamic Programming Properties
Principle of Optimality
Problem solving using Dynamic Programming
TSP is np- hard problem which has number of solution but it's difficult to find optimal solution . I gave here fast,easy and efficient solution on TSP using one algorithm with good explanation.Hope you understood very well.
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
it contains the detail information about Dynamic programming, Knapsack problem, Forward / backward knapsack, Optimal Binary Search Tree (OBST), Traveling sales person problem(TSP) using dynamic programming
BackTracking Algorithm: Technique and ExamplesFahim Ferdous
This slides gives a strong overview of backtracking algorithm. How it came and general approaches of the techniques. Also some well-known problem and solution of backtracking algorithm.
Graph theory - Traveling Salesman and Chinese PostmanChristian Kehl
Traveling Salesman and Chinese Postman problems
1. Problem Description and Complexity
2. Theoretical Approach
3. Practical Approaches and Possible Solutions
4. Examples
Learn more about social selling at http://linkd.in/1byEPQ2.
Digital disruption has revolutionized the sales and marketing landscape--72% of buyers use social media to research before making a purchase, and 81% of buyers are more likely to engage with a strong professional brand. To reach buyers, sales and marketing teams must align themselves to create a compelling social media presence.
Join LinkedIn and Oracle Marketing Cloud as we draw back the curtain and explore how to bridge the divide between sales and marketing.
You'll learn:
--Why social selling is important and valuable to both sales and marketing
--Which team is responsible for owning social selling
--How to implement a social selling strategy across both teams
As businesses increasingly look to mobile as a key element of their business model rather than simply another marketing channel, we examine the response of CMOs worldwide to the challenges and opportunities that mobile represents.
http://www.tnsglobal.com/mobilelife
A plan for new sales leaders. What to do in their first 75 days in their new position? An easy step by step guide. The first 25 days is to understand the current state of the sales team, next 25 days is about developing a GTM strategy followed by the next 25 days of implementation.
Today buyers are more cautious than ever before when it comes to making decisions. This means that you’ll need a variety of closing techniques at your disposal if you’re going to smash your sales targets.
The great news is that one or a combination of these 8 best Closing Techniques can be used in any sales situation to help you turn every prospect into a buying customer.
The traveling salesman problem (TSP) is an algorithmic problem tasked with finding the shortest route between a set of points and locations that must be visited.
In MATLAB, a vector is created by assigning the elements of the vector to a variable. This can be done in several ways depending on the source of the information.
—Enter an explicit list of elements
—Load matrices from external data files
—Using built-in functions
—Using own functions in M-files
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
1. Traveling Salesman Problem
• Problem Statement
– If there are n cities and cost of traveling from any
city to any other city is given.
– Then we have to obtain the cheapest round-trip
such that each city is visited exactly ones returning
to starting city, completes the tour.
– Typically travelling salesman problem is represent
by weighted graph.
2. Cont.
• Row Minimization
– To understand solving of travelling salesman
problem using branch and bound approach we
will reduce the cost of cost matrix M, by using
following formula.
– Red_Row(M) = [ Mij – min{ Mij | 1<=j<=n} ]
where Mij < ∞
3. Cont.
• Column Minimization
– Now we will reduce the matrix by choosing
minimum for each column.
– The formula of column reduction of matrix is
– Red_col(M)=Mij – min { Mij | 1<=j<=n}
where Mij < ∞
4. Cont.
• Full Reduction
– Let M bee the cost matrix for TSP for n vertices
then M is called reduced if each row and each
column consist of entire entity ∞ entries or else
contain at least one zero.
– The full reduction can be achieved by applying
both row_reduction and column_reduction.
5. Cont.
• Dynamic Reduction
– Using dynamic reduction we can make the choice of
edge i->j with optimal cost.
– Step in dynamic reduction technique
1. Draw a space tree with optimal cost at root node.
2. Obtain the cost of matrix for path i->j by making I row and
j column entries as ∞. Also set M[i][j]=∞
3. Cost corresponding node x with path I, j is optimal cost +
reduced cost+ M[i][j]
4. Set node with minimum cost as E-node and generate its
children. Repeat step 1 to 4 for completing tour with
optimal cost.
6. Example
• Solve the TSP for the following cost matrix
∞ 11 10 9 6
8 ∞ 7 3 4
8 4 ∞ 4 8
11 10 5 ∞ 5
6 9 2 5 ∞
7. Solution
Step 1 :
• We will find the minimum value from each row and
subtract the value from corresponding row
Minvalue
reduce matrix
∞ 11 10 9 6
8 ∞ 7 3 4
8 4 ∞ 4 8
11 10 5 ∞ 5
6 9 2 5 ∞
∞ 5 4 3 0
5 ∞ 4 0 1
4 0 ∞ 0 4
6 5 0 ∞ 0
1 4 0 0 ∞
-> 6
-> 3
->4
->5
->5
---------
23
8. Cont.
• Now we will obtain minimum value from each column. If they
column contain 0 the ignore that column and a fully reduced
matrix can be obtain.
subtracting 1 from 1st column
∞ 5 4 3 0
5 ∞ 4 0 1
4 0 ∞ 0 4
6 5 0 ∞ 0
1 4 0 0 ∞
∞ 5 4 3 0
4 ∞ 4 0 1
3 0 ∞ 0 4
5 5 0 ∞ 0
0 4 0 0 ∞
9. Cont.
• Total reduced cost
= total reduced row cost + total reduced column cost
= 23 + 1
= 24
• Now we will set 24 as the optimal cost
24->this is the lower bound
10. Cont.
• Step 2 :: Now we will consider the paths [1,2], [1,3], [1,4] and [1,5] of state
space tree as given above consider path [1,2] make 1st row and 2nd column to
∞ set M[2][1]=∞
• Now we will find min value from each corresponding column.
• c
∞ ∞ ∞ ∞ ∞
∞ ∞ 4 0 1
3 ∞ ∞ 0 4
5 ∞ 0 ∞ 0
0 ∞ 0 0 ∞
∞ ∞ ∞ ∞ ∞
∞ ∞ 4 0 1
3 ∞ ∞ 0 4
5 ∞ 0 ∞ 0
0 ∞ 0 0 ∞
11. Cont.
• Hence total receded cost for node 2 is = Optimal
cost+old value of M[1][2]
= 24 + 5
= 25
• Consider path (1,3). Make 1st row, 3rd column to be
∞ set M[3][1] = ∞
12. Cont.
There is no minimum value from any row and column
Hence total cost of node 3 is
= optimum cost + M[1][3]
= 24+ 4
= 28
∞ ∞ ∞ ∞ ∞
4 ∞ ∞ 0 1
3 0 ∞ 0 4
5 5 ∞ ∞ 0
0 4 ∞ 0 ∞
14. Cont.
• consider path [1,5] make 1st row and 5th column to ∞ set
M[5][1]=∞
subtracting 3 from 1st Row
total cost of node 5 is = reduced column cost + old value M[1][5]
= 24+ 3+0
= 27
∞ ∞ ∞ ∞ ∞
4 ∞ 4 0 ∞
3 0 ∞ 0 ∞
5 5 0 ∞ ∞
∞ 4 0 0 ∞
∞ ∞ ∞ ∞ ∞
1 ∞ 4 0 ∞
0 0 ∞ 0 ∞
2 5 0 ∞ ∞
∞ 4 0 0 ∞
15. Cont.
• The partial state space tree will be
• The node 5 shows minimum cost. Hence node 5 will be an E
node. That means we select node 5 for expansion.
27
29 28 28 27
16. Cont.
• Step 3 :: Now we will consider the paths [1,5,2], [1,5,3] and [1,5,4] of state
space tree as given above consider path [1,5,2] make 1st row , 5th row and
second column as ∞ set M[5][1] and M[2][1] =∞
subtracting 3 from 1st Column.
Hence total cost of node 6 is =optimal cost node 5+column reduced cost+ M[5][2]
= 27+ 3+4
= 34
∞ ∞ ∞ ∞ ∞
∞ ∞ 4 0 1
3 ∞ ∞ 0 4
5 ∞ 0 ∞ 0
∞ ∞ ∞ ∞ ∞
∞ ∞ ∞ ∞ ∞
∞ ∞ 4 0 1
0 ∞ ∞ 0 4
2 ∞ 0 ∞ 0
∞ ∞ ∞ ∞ ∞