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Algorithm selection chooses an algorithm for a particular problem instance using information available before or during its solution. The available candidates form an algorithm portfolio. John R. Rice's 1976 treatment formalized the relationship between problem descriptions, descriptive features, algorithms and performance criteria.^[ref]

An original runtime example shows the potential benefit. Suppose algorithms $A$ and $B$ take $(2,20)$ and $(10,3)$ seconds on two equally likely instance types. Always choosing $A$ gives mean $11$ seconds; always choosing $B$ gives $6.5$ seconds. A selector that reliably recognizes both types and chooses the faster algorithm gives mean $2.5$ seconds before selection overhead. If computing its features and choosing costs another second, the total becomes $3.5$ seconds. The gain comes from complementary performance, not from either candidate being universally faster.

The hypothetical $2.5$-second result assumes perfect decisions. A real selector can misclassify instances, spend time extracting features or encounter inputs unlike its training examples. Its complete measured runtime includes those costs. Looking up the faster solver after both have finished supplies a useful comparison bound, but does not itself implement an online choice.

Algorithm configuration instead searches settings of a parameterized target algorithm. The two ideas can be combined by selecting among configured candidates, provided the evaluation states what was tuned, what was selected and which instances were reserved for testing.

John Rischard Rice was a computer scientist and mathematician whose work included numerical approximation, elliptic partial differential equations and mathematical software. Purdue's memorial identifies his full name and records that he led the development of the ELLPACK elliptic-problem software.^[ref]

His algorithm selection work separates a problem instance, its descriptive features, candidate algorithms and the performance criterion used to choose between them. The institutional technical-report record is dated 1975; the later chapter is dated 1976.^[ref] Thus choosing an algorithm is itself a computational decision, not simply declaring one program universally best.

For an original example, suppose two candidates in an algorithm portfolio take $1$ and $5$ seconds, with relative errors $10^{-2}$ and $10^{-6}$ on one stipulated instance. If the rule is to minimize runtime subject to error at most $10^{-3}$, only the second candidate qualifies. Relaxing the tolerance to $10^{-1}$ makes the first candidate the faster admissible choice. The ranking changes because the stated task changes; the four values are chosen examples, not measured solver performance.

A real selector must obtain usable problem features and include selection overhead in its evaluation. Choosing after observing every candidate's completed result is a comparison bound, not automatically an implementable advance decision. This distinction connects numerical software to empirical tests of how its performance varies across inputs.