Quick Answer: Is The Optimal Solution Unique?

What is the optimal objective value?

Optimal Value: In an optimization problem were the objective function is to be maximized the optimal value is the least upper bound of the objective function values over the entire feasible region..

What is feasible solution in greedy method?

General method: Given n inputs choose a sub- set that satisfies some constraints. – A subset that satisfies the constraints is called a feasible solution. – A feasible solution that maximises or min- imises a given (objective) function is said to be optimal.

Why can’t solver find a feasible solution?

Solver could not find a feasible solution The message tells you that your optimization modeling problem doesn’t have an answer. As a practical matter, when you see this message, it means that your set of constraints excludes any possible answer. … No optimal value for the objective function exists.

What is optimal basic feasible solution?

An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.

Is branch and bound greedy?

Branch and bound is an algorithm design paradigm which is generally used for solving combinatorial optimization problems. … Greedy Algorithm for Fractional Knapsack. DP solution for 0/1 Knapsack. Backtracking Solution for 0/1 Knapsack.

How do you know if a solution is feasible?

If the result of a requirement is within the bounds of the requirement, the result is requirement-feasible. If the result is outside the bounds of the requirement, the solution is requirement-infeasible. The OptQuest Engine makes finding a feasible solution its highest priority.

Is branch and bound optimal?

The Branch and Bound (BB or B&B) algorithm is first proposed by A. H. Land and A. G. Doig in 1960 for discrete programming. It is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization.

What is the difference between basic solution and basic feasible solution?

Definition 1. The vector x∗ is a a basic solution if: (a) All equality constraints are tight; (b) Among the constraints that are tight at x∗, n of them are linearly independent. 2. If x∗ ∈ P is a basic solution, we say that it is a basic feasible solution.

What is slack variable in optimization?

In an optimization problem, a slack variable is a variable that added to an inequality constraint to transform it into an equality. … As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the simplex algorithm requires them to be positive or zero.

Is backtracking better than brute force?

It is useless, for example, for locating a given value in an unordered table. When it is applicable, however, backtracking is often much faster than brute force enumeration of all complete candidates, since it can eliminate many candidates with a single test.

Why do some problems have multiple optimal feasible solution?

The multiple optimal solutions will arise in a linear program with more than one set of basic solutions that can minimize or maximize the required objective function. … Therefore, it can be said that the total cost or total profit will remain identical for different sets of allocation in an assignment problem.

How do you prove a solution is optimal?

If there is a solution y to the system AT y = cB such that AT y ≤ c, then x is optimal. By = cB and AT y ≤ c. m i=1 aijyi = ci. are obeyed, then x and y must be optimal.

Are greedy algorithms optimal?

A greedy algorithm is a simple, intuitive algorithm that is used in optimization problems. The algorithm makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem. However, in many problems, a greedy strategy does not produce an optimal solution. …

What is basic feasible solution in LPP?

In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a corner of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS.

Which is better backtracking or branch and bound?

Branch-and-Bound is used for solving Optimisation Problem. In backtracking, the state space tree is searched until the solution is obtained. In Branch-and-Bound as the optimum solution may be present any where in the state space tree, so the tree need to be searched completely. Backtracking is more efficient.