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An algorithm portfolio combines several candidate algorithms or algorithm runs to exploit differences in their performance. It includes a policy for choosing or allocating work, rather than merely naming a collection. A parallel algorithm portfolio runs candidates concurrently; a sequential algorithm portfolio allocates time on one processor. The original 2001 study compared these approaches and restart strategies on specified distributions of search problems.^[ref]

Consider invented runtimes $A=(1,30)$ seconds and $B=(30,1)$ seconds on two equally likely instance types. Either algorithm alone has mean $15.5$ seconds. Perfect per-instance algorithm selection would take one second before selection overhead. Running both on independent full-speed processors and stopping at the first answer also takes one second under this model, but uses two processors.

For a different policy, run $A$ for at most five seconds, then start $B$ if needed. The two completion times become $1$ and $5+1=6$ seconds, giving mean $3.5$ seconds. This invented sequential algorithm portfolio saves time relative to either fixed choice, without matching the two-processor wall time.

Complementary runtimes make these examples work. If all candidates are slow on the same instances, diversity in names supplies no such benefit. Compare wall time, total computing work and overhead separately, and test the allocation policy on new instances. The best completed run chosen retrospectively is a comparison bound, not automatically an implementable selector.

An algorithm portfolio schedule specifies how computational resources are assigned to members of an algorithm portfolio over time. For a sequential algorithm portfolio, it states which algorithm receives each time interval, whether interrupted work is resumed or discarded, and when computation stops. A parallel algorithm portfolio also needs a processor allocation and a rule for accepting and combining results. Listing candidate algorithms alone does not specify a schedule.

An original interleaving example makes the distinction between processor time and elapsed time explicit. Suppose algorithms A and B need respectively $3$ and $5$ seconds of processor time on a particular input. Give A one second, then B one second, repeating while preserving both states and stopping at the first accepted result. A receives its third second during elapsed interval $[4,5]$, so the portfolio finishes at $5$ seconds. At that point A has used $3$ processor-seconds and B has used $2$. With two dedicated processors, the corresponding parallel algorithm portfolio would finish at $3$ seconds. These calculations assume no algorithm portfolio switching overhead and no resource contention.

More generally, let $s_i(t)$ be processor time supplied to candidate $i$ by elapsed time $t$, and let $T_i$ be its required processor time. In the resumable, interference-free model, the completion time isDiscarding a state on every interruption changes this model: separate short runs do not necessarily accumulate into one longer run. The original portfolio study compared parallel, interleaved and restart execution precisely because these are different policies.^[ref]

Choose an objective before comparing algorithm portfolio schedules: expected value of running time, probability of finishing by a deadline, and total computing work need not favor the same allocation. A schedule chosen using retrospective runtimes also requires evaluation on inputs that did not determine the schedule.

A sequential algorithm portfolio allocates one processor's time among candidate algorithms or runs. Its algorithm portfolio schedule determines which candidate runs, when to switch and whether an interrupted run is resumed or abandoned. The original portfolio study compared single-processor interleaving and restart policies with parallel execution.^[ref]

Consider original runtimes $A=(2,12)$ seconds and $B=(8,3)$ seconds on two equally likely input types. Either fixed choice has mean $7$ or $5.5$ seconds. Run $A$ for at most four seconds, then start $B$ if $A$ has not finished. The two completion times are $2$ and $4+3=7$ seconds, so the scheduled mean is $4.5$ seconds. The schedule succeeds because the candidates have complementary performance.

Algorithm portfolio switching overhead can erase that gain. If the switch costs $3$ seconds whenever it occurs, the second completion time becomes $10$ seconds and the mean becomes $6$ seconds, worse than always running $B$. The cost must be charged to the actual switching events, rather than added equally to every instance.

A timeout also does not say that the interrupted candidate would never solve the input. Resuming preserves previous search work only if the implementation supports it; restarting begins a different run. Record budgets, state retention, random seeds and the final stopping rule when reporting a sequential portfolio's performance. A good schedule on measured inputs still needs evaluation on unused inputs.