The value of any group of decision variables that meet all constraints (i.e. all pre constraints and post constraints) of a linear programming is called a feasible solution of the linear programming, and the set of all feasible solutions is called theFeasible region(similar to the definition field of a function), marked as K.
Chinese name
feasible solution
Foreign name
feasible solution
Scope of application
Mathematical Science
Definition
The problem of finding the maximum or minimum value of a linear objective function under linear constraints
The problem of finding the maximum or minimum value of a linear objective function under linear constraints is collectively referred to as the linear programming problem.A feasible solution is also called a feasible point or an allowable solution. One of the basic concepts of mathematical programming is a solution (point) that satisfies all constraints in mathematical programming.[1]
Basic feasible solution
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(basic feasible solution)
(basic feasible solution)
Basic feasible solutionAlso calledFeasible pointorPermissive solution, is an important concept of linear programming.staylinear programming problem The basic solution satisfying the nonnegative constraint condition is calledBasic feasible solution, short forBasic feasible solution。If there is a feasible solution to a linear programming problem, there must be a basic feasible solution, and the feasible solution is a basic feasible solutionSufficient and necessary conditionsIs: the column vector of the coefficient matrix corresponding to its non-zero component is linearly independent.The basic feasible solutions correspond to the poles in the feasible region and are finite.If there is a bounded optimal solution, then at least one basic feasible solution is the optimal solution.
Fundamental solution
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Find a base in the coefficient matrix of constraint equations, make the non base variable of this base zero, and then solve the m-elementLinear equationsThen we can get the unique solution, which is called linear programmingFundamental solution。
Optimal solution
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Optimal solutionIt is usually defined as the best solution that can be achieved technically without sacrificing any overall goal and sub goals.It represents the ideal solution that can be achieved by all the general goals and sub goals.In fact, such solutions rarely exist.The inherent internal factors of engineering problems always contain various contradictions. Due to the limitation of scientific level, many design factors and system constraints are not well understood;Many criteria.For example, social interrelationships, quality of life, ecology, and interests and hobbies are not easy to determine, let alone quantify.However, labor, equipment, financial resources and time are always limited in the design or planning of engineering systems.Therefore, the optimization process only produces a "most satisfactory solution" that can be achieved under the design and process constraints.
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The feasible solution is the solution that meets the constraint conditions. The non basic variable of the basic solution corresponding to the base vector is zero. The basic solution is not necessarily the feasible solution, and the feasible solution is not necessarily the basic solution. The solution that is both the feasible solution and the basic solution is the basic feasible solution. The optimal solution is the solution that makes the objective function reach the optimal value in the basic feasible solution.
