Feasible solution

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A feasible solution is a candidate solution that satisfies all specified constraints.

A feasible solution is a candidate solution that satisfies every constraint in an optimization problem. Feasibility answers whether a solution is allowed; it does not determine whether the solution is best. section 1.3

Feasible solutions fit into the broader search for useful candidates:

• An optimal solution is feasible and gives the best objective-function value. section 1.3
• A near-optimal solution is feasible and performs well without necessarily being best. section 1.3
• Optimization algorithms search feasible regions, balancing exploration of new regions with exploitation of promising ones. section 1.5

Conference ticket pricing

A conference organizer chooses ticket price x. The price must remain between lower and upper bounds, while expected demand and profit depend on x. Any price within the bounds is a feasible candidate; maximizing profit identifies the optimal candidate. section 1.3.1

Figure 1.3 Feasible solutions fall within the constraints of the problem. A feasible search space may display a combination of global, strong local, and weak local minima.

Use the search-space figure to distinguish the feasible region from global, strong local, and weak local minima. section 1.3

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Defines feasibility and contrasts it with optimality, near-optimality, and search, without developing an implementation procedure.

Examples

Uses a conference ticket-price problem with demand, costs, profit, and price bounds.

What you can do after

Evaluate candidate solutions by checking constraint satisfaction separately from objective-function quality.

How it connects

Connects feasible solutions to constraints, objective functions, decision variables, optimization, search spaces, and optimal solutions.

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Also explained in

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  Bayesian Optimization in ActionA feasible point or solution is a candidate assignment that satisfies all constraints in a constrained optimization problem.

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Related concepts

• infeasible pointcontrasts with · An infeasible point is a candidate input that violates at least one constraint and therefore cannot be accepted as a solution.
• optimal solutionincludes · An optimal solution is a feasible solution that achieves the best objective value among the alternatives considered.
• feasible regionpart of · A feasible region is the set of points or variable assignments that satisfy all constraints of an optimization problem.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.