Avascular Necrosis (AVN) is a condition where blood flow to the bone is reduced, causing bone cells to die. This leads to pain, joint damage, and difficulty in movement, especially in the hip. Early diagnosis and proper treatment can prevent permanent bone damage and improve quality of life. Video Chapter: AVN 00:00 Introduction 00:45 What is AVN? 01:55 About Bone Tissue 02:49 AVN Causes 03:38 AVN Symptoms 04:11 AVN Diagnosis 04:56 AVN of femoral head 05:33 How AVN Develops 07:28 Conclusions #optimization #algorithm #metaheuristic #robotics #deeplearning #ArtificialIntelligence #MachineLearning #computervision #research #projects #thesis #Python #optimizationproblem #optimizationalgorithms
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Vehicle Routing Problem (VRP) ~xRay Pixy
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Vehicle Routing Problem
Learn Vehicle Routing Problems Step-By-Step using Examples.
Video Chapters: Vehicle Routing Problem (VRP)
00:00 Introduction
00:18 VRP Example
00:52 VRP Variants
02:43 VRP Objective
03:20 VRP Component
06:06 VRP Graph Representation
05:13 VRP Challenge
05:51 TSP vs VRP
07:17 VRP Real-Life Situations
07:38 VRP Solving Rules
08:57 VRP Method
09:16 Metaheuristics for VRP
10:16 VRP Application Areas
10:24 Metaheuristics to solve VRP
11:39 Conclusion
VEHICLE ROUTING PROBLEM is a fundamental combinatorial optimization and integer programming problem in the fields of transportation, logistics, and operations research. It involves determining the most efficient routes for a fleet of vehicles to traverse in order to deliver goods or services to a set of customers, subject to various constraints.
Objective: Minimize the Total Route Cost. While satisfying all Co
Capacity Constraint
Time Window Constraints
VRP Basic Components
Depot: The starting and ending point for all vehicles.
Customers: Locations that require service (e.g., delivery or pickup).
Fleet: A set of vehicles available for routing, each with specific capacities.
Constraints: Limitations such as vehicle capacity, time windows, maximum route length, etc.
Variants of VRP
The basic VRP has numerous extensions and variants to model real-world complexities:
Capacitated VRP (CVRP): Each vehicle has a limited carrying capacity.
VRP with Time Windows (VRPTW): Customers must be serviced within specific time frames.
VRP with Pickup and Delivery (VRPPD): Items must be picked up from specific locations and delivered to others.
Split Delivery VRP (SDVRP): A customer's demand can be split across multiple vehicles.
VRP with Multiple Depots (MDVRP): There are multiple depots from which vehicles can start and end their routes.
Stochastic VRP: Elements like demand or travel times are uncertain and modeled probabilistically.
Electric VRP (E-VRP): Considers electric vehicles with constraints like battery capacity and charging stations.
Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) Comparision:
Real-World Considerations
Implementing VRP solutions in practice involves addressing several additional complexities:
Dynamic Routing: Adjusting routes in real-time in response to traffic conditions, cancellations, or new orders.
Driver Regulations: Complying with labor laws and driver working hours.
Geographical Constraints: Navigating areas with restricted access or specific traffic rules.
Multi-Objective Optimization: Balancing multiple objectives like cost, time, and customer satisfaction.
Integration with Other Systems: Synchronizing VRP solutions with inventory management, order processing, and customer relationship systems.
Metaheuristic algorithms like Genetic Algorithms (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) are effective for solving Vehicle Routing Problems (VRPs) because they are designed to handle complex, large-scale optimization problems that have multiple variables and constraints.
Metaheuristics for VRP:
Ant Colony Optimization (ACO): Inspired by how ants find the shortest paths, this method uses "pheromones" to guide the search for good solutions.
Tabu Search: A technique that avoids revisiting previously explored solutions by keeping track of moves that are temporarily forbidden (tabu).
Iterated Local Search: A method that repeatedly applies local search, finding a nearby solution, and then modifies it to explore new areas.
Simulated Annealing: A technique based on how materials cool down slowly to find a state of minimal energy, which helps avoid getting stuck in local solutions.
Why Use Metaheuristics for VRPs?
Scalability: Metaheuristics can solve large-scale problems with many customers and vehicles.
Flexibility: They adapt to different constraints and objectives (e.g., minimizing costs or balancing workload).
Efficiency: Provide near-optimal solutions quickly, even when the problem is complex
PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. - PART 2 [Example 2] 1.) Initialize Population [Current Iteration (t) = 0] Population Size = 4; 𝑥𝑖 : (i = 1,2,3,4) and (t = 0) 𝑥1 =1.3; 𝑥2=4.3; 𝑥3=0.4; 𝑥4=−1.2 2.) Fitness Function u...
Cuckoo Search Algorithm - Metaheuristic Optimization Algorithm What is Cuckoo Search Algorithm? Cuckoo Search Algorithm is a Meta-Heuristic Algorithm. Cuckoo Search Algorithm is inspired by some Cuckoo species laying their eggs in the nest of other species of birds. In this algorithm, we have 2 bird Species. 1.) Cuckoo birds 2.) Host Birds (Other Species) What if Host Bird discovered cuckoo eggs? Cuckoo eggs can be found by Host Bird. Host bird discovers cuckoos egg with Probability of discovery of alien eggs. If Host Bird Discovered Cuckoo Bird Eggs. The host bird can throw the egg away. Abandon the nest and build a completely new nest. Mathematically, Each egg represent a solution and it is stored in the host bird nest. In this algorithm Artificial Cuckoo Birds are used. Artificial Cuckoo can lay one egg at a time. We will replace New and better solutions with less fit solutions. It means eggs that are more similar to host bird has opportunity to de...
Particle swarm optimization (PSO) What is meant by PSO? PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. How PSO will optimize? By Improving a Candidate Solution. How PSO Solve Problems? PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). The population of Candidate Solutions (i.e., Particles). What is Search Space in PSO? It is the range in which the algorithm computes th...
Particle Swarm Optimization (PSO) is a p opulation-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. PSO is a computational method that Optimizes a problem. PSO searches for Optima by updating generations. It is popular is an intelligent metaheuristic algorithm. In Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. After a number of iterations agents / particles will find out optimal solution in the search space. Q. What is PSO? A. PSO is a computational method that Optimizes a problem. Q. How PSO will optimize? A. By Improving a Candidate Solution. Q. How PSO Solve Problems? A. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to ...
Local Binary Pattern Introduction to Local Binary Pattern (LBP) Q. What is Digital Image? A. Digital images are collections of pixels or numbers ( range from 0 to 255). Q. What is Pixel? A. Pixel is the smallest element of any digital image. Pixel can be categorized as Dark Pixel and Bright Pixel. Dark pixels contain low pixel values and bright pixels contain high pixel values. Q. Explain Local Binary Pattern (LBP)? A. Local binary pattern is a popular technique used for image processing. We can use the local binary pattern for face detection and face recognition. Q. What is LBP Operator? A. LBP operator is an image operator. We can transform images into arrays using the LBP operator. Q. How LBP values are computed? A. LBP works in 3x3 (it contain a 9-pixel value ). Local binary pattern looks at nine pixels at a time. Using each 3x3 window in the digital image, we can extract an LBP code. Q. How to Obtain LBP operator value? A. LBP operator values can be obtained by ...
Whale Optimization Algorithm Code Implementation Whale Optimization Algorithm Code Files function obj_fun(test_fun) switch test_fun case 'F1' x = -100:2:100; y=x; case 'F2' x = -10:2:10; y=x; end end function [LB,UB,D,FitFun]=test_fun_info(C) switch C case 'F1' FitFun = @F1; LB = -100; UB = 100; D = 30; case 'F2' FitFun = @F2; LB = -10; UB = 10; D = 30; end % F1 Test Function function r = F1(x) r = sum(x.^2); end % F2 Test Function function r = F2(x) r = sum(abs(x))+prod(abs(x)); end end function Position = initialize(Pop_Size,D,UB,LB) SS_Bo...
Grey Wolf Optimization Algorithm (GWO) Grey Wolf Optimization Grey Wolf Optimization Algorithm is a metaheuristic proposed by Mirjaliali Mohammad and Lewis, 2014. Grey Wolf Optimizer is inspired by the social hierarchy and the hunting technique of Grey Wolves. What is Metaheuristic? Metaheuristic means a High-level problem-independent algorithmic framework (develop optimization algorithms). Metaheuristic algorithms find the best solution out of all possible solutions of optimization. Who are the Grey Wolves? Wolf (Animal): Wolf Lived in a highly organized pack. Also known as Gray wolf or Grey Wolf, is a large canine. Wolf Speed is 50-60 km/h. Their Lifespan is 6-8 years (in the wild). Scientific Name: Canis Lupus. Family: Canidae (Biological family of dog-like carnivorans). Grey Wolves lived in a highly organized pack. The average pack size ranges from 5-12. 4 different ranks of wolves in a pack: Alpha Wolf, Beta Wolf, Delta Wolf, and Omega Wolf. How Grey Wolf Optimiza...
Grey Wolf Optimization Algorithm Numerical Example Grey Wolf Optimization Algorithm Steps 1.) Initialize Grey Wolf Population. 2.) Initialize a, A, and C. 3.) Calculate the fitness of each search agent. 4.) 𝑿_𝜶 = best search agent 5.) 𝑿_𝜷 = second-best search agent 6.) 𝑿_𝜹 = third best search agent. 7.) while (t<Max number of iteration) 8.) For each search agent update the position of the current search agent by the above equations end for 9.) update a, A, and C 10.) Calculate the fitness of all search agents. 11.) update 𝑿_𝜶, 𝑿_𝜷, 𝑿_𝜹 12.) t = t+1 end while 13.) return 𝑿_𝜶 Grey Wolf Optimization Algorithm Numerical Example STEP 1. Initialize the Grey wolf Population [Initial Position for each Search Agent] 𝒙_(𝒊 ) (i = 1,2,3,…n) n = 6 // Number of Search Agents [ -100, 100] // Range Initial Wolf Position 3.2228 4.1553 -3.8197 4.2330 ...
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