Learn German: Er erklärt, dass der Algorithmus den täglichen Ablauf optimieren werde. - He explains that the algorithm will optimize the daily routine.

werde is the Konjunktiv I (Subjunctive I) form of werden for the third-person singular (matching der Algorithmus). We use it here to indicate reported speech, showing that we are just repeating someone else's claim. If we used the normal indicative wird, it would sound like we are confirming it as a guaranteed fact.

I usually see würde used for the subjunctive. Why isn't it würde here?

You generally only fall back on Konjunktiv II (like würde) for reported speech if the Konjunktiv I form is identical to the normal present tense form. Since the normal present tense is wird and the Konjunktiv I is werde, they are clearly different. Because there is no confusion, we use the "true" reported speech form: werde.

Could we write this reported speech sentence without the word dass?

Yes! A very common and elegant way to report speech in German is to drop dass and use standard main-clause word order. If you did that, the conjugated verb would move to the second position: Er erklärt, der Algorithmus werde den täglichen Ablauf optimieren.

Why are the verbs in the order optimieren werde at the end?