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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 vertex of the polyhedron of feasible solutions.
For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0. For example, if there is a graph G which contains vertices u and v , an optimization problem might be "find a path from u to v that uses the fewest edges".
However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).
The possible results of Phase I are either that a basic feasible solution is found or that the feasible region is empty. In the latter case the linear program is called infeasible. In the second step, Phase II, the simplex algorithm is applied using the basic feasible solution found in Phase I as a starting point.
A solution is an assignment from items to bins. A feasible solution is a solution in which for each bin the total weight of assigned items is at most . The solution's profit is the sum of profits for each item-bin assignment. The goal is to find a maximum profit feasible solution.
Its solution is whichever combination of taxis and customers results in the least total cost. Now, suppose that there are four taxis available, but still only three customers. This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the ...
B will denote the best solution found so far, and will be used as an upper bound on candidate solutions. Initialize a queue to hold a partial solution with none of the variables of the problem assigned. Loop until the queue is empty: Take a node N off the queue. If N represents a single candidate solution x and f(x) < B, then x is the best ...
A. The feasible set {b+L} ∩ K is bounded, and intersects the interior of the cone K. B. We are given in advance a strictly-feasible solution x^, that is, a feasible solution in the interior of K. C. We know in advance the optimal objective value, c*, of the problem. D. We are given an M-logarithmically-homogeneous self-concordant barrier F ...