Optimal solution
An optimal solution is a feasible solution that achieves the best objective value among the alternatives considered.
Grokking AI Algorithms, Second Edition
An optimal solution is a solution that performs best according to the criterion used to evaluate solutions to a problem.
- How it is used
- Frames solution quality as a criterion for comparing answers produced by search and optimization algorithms.
- How deep it goes
- Defines optimality, contrasts it with good-enough answers, and traces selection of the shortest tour without covering formal proofs.
- Examples
- Uses maze paths, knapsack selections, and ant tours compared by steps, value, or total distance.
- What you can do after
- Evaluate solutions by an explicit criterion and recognize when an algorithm finds an acceptable result without guaranteeing optimality.
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Statistics Every Programmer Needs
An optimal solution is a feasible assignment of decision variables that gives the best objective value under the problem's optimization direction.
- How it is used
- Optimizes feature selection while respecting cost, year, and distribution constraints.
- How deep it goes
- Explains solver inputs and interprets success, assignments, selection count, and objective value without deriving optimization algorithms.
- Examples
- Demonstrates binary feature selection yielding twelve selected features and a priority score of 17.6.
- What you can do after
- Apply it via SciPy's linprog to obtain and inspect a constrained decision-variable assignment.
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Grokking Algorithms, Second Edition
An optimal solution is a feasible solution that achieves the best possible objective value for an optimization problem.
- How it is used
- Uses optimal solutions to compare exact optimization with fast but sometimes approximate greedy choices.
- How deep it goes
- Explains exhaustive enumeration, local-versus-global choices, and unused capacity, but stops short of detailing the complete exact algorithm.
- Examples
- Illustrates the idea with knapsack items, classroom schedules, a diamond, furniture packing, and trip planning.
- What you can do after
- Evaluate whether a result is globally optimal, merely approximate, or produced by a locally optimal choice.
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Related concepts
- optimizationproduced by · Optimization is the systematic selection or adjustment of values, actions, or system designs to improve a specified objective, often subject to constraints.
- particle swarm optimizationproduced by · Particle swarm optimization is a population-based optimization method in which candidate solutions adjust their positions using individual and collective search information.
- stagnationused by · Stagnation is a search condition in which successive iterations or generations produce little or no meaningful improvement toward a better solution.
- greedy algorithmcontrasts with · A greedy algorithm builds a solution incrementally by choosing the locally best available option at each step, without generally accounting for all future consequences or revising prior choices.
- feasible solutionkind of · A feasible solution is an assignment of decision-variable values that satisfies all specified constraints and bounds.
- backtrackingproduced by · Backtracking is a technique that returns to earlier decisions or states along a path to reconsider choices, explore alternatives, or reconstruct a solution.
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