Explain with the help of an example that greedy strategy doesnot always yield optimal solution for optimisation problems
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- . A issue has property if its subproblems can be solved optimally. overlapping subproblems optimal substructure memorization greedyThe branching part of the branch and bound algorithm that Solver uses to solve integer optimization models means that the algorithm [a] creates subsets of solutions through which to search[b] searches through only a limited set of feasible integer solutions [c] identifies an incumbent solution which is optimal [d] uses a decision tree to find the optimal solution 2. The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model. [a] True [b] FalseHow does duality influence the analysis of optimization problems with inequality constraints?
- This characteristic is met by a problem if it is feasible to develop an optimum solution for it by first creating optimal solutions for its subproblems. a) Subproblems that overlap; b) substructure that's optimum; c) memorization; d) greedyBoth the Principle of Optimality (Optimal Substructure) and Insufficient Overlapping Subproblems are valid inputs for dynamic programming. To see how difficult it is to meet these two criteria, consider the case of All-Pairs Shortest Paths.Insufficient Overlapping Subproblems and the Principle of Optimality (Optimal Substructure) are dynamic programming questions. As an example, consider All-Pairs Shortest Paths.
- What is the difference between greedy algorithm and optimal solution. List at least three pros and cons of each solution.If it is possible to construct an optimal solution for a problem by constructing optimal solutions for its subproblems, then the problem possesses the specified property. a) Overlapping subproblems; b) optimal substructure; c) memorization; d) greedyB. If a Genetic Algorithm suffers from local solution problem, what do you suggest to achieve global optimal solution?
- Algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are best fit for Greedy. For example consider the Fractional Knapsack Problem. Cook is going on an excursion and requirements to apply for between locale and between state travel e-passes. It requires A minutes to fill each between region e-pass application and B minutes for each between state e-pass application. His excursion is given to you as a paired string S of length N where 0 signifies crossing starting with one locale then onto the next area (which needs a between region e-pass), and a 1 indicates crossing starting with one state then onto the next (which needs a between state e-pass). Figure out the all-out opportunity Cooks needs to spend on filling the different structures. Demonstrate the coding behavior.In an optimal A* search, a- describe the problem of a heuristic function that overestimates the cost. How does it effect the solution? Give an example. b-is a heuristic method that underestimates the cost admissible? How does it effect the solution? Give an exampleMachine Learning Problem Perform the optimization problem of finding the minimum of J(x) = (2x-3)2 by: (i) defining theta, J(theta), h(theta) as defined in the Stanford Machine Learning videos in Coursera; (ii) plotting J(theta) vs theta by hand then use a program (iii) determining its minimum using gradient descent approach starting from a random initial value of theta = 5. Perform the search for the minimum using the gradient descent approach by hand calculations, i.e., step 1, step 2, etc. showing your work completely