Rewriting the example sentence as:
The process falls back on a move randomly chosen from among all the acceptable solutions generated from the neighborhood and reaches global optimum very slowly.
might explain why "reclines" was used in the posted example. However "reclines" does not share the idiomatic usage of "fall back on" and needs to be replaced. Possible alternatives to "recline" include
- fall back on meaning "to begin to use someone or something held in reserve" The Free Dictionary, 2.,
- default to meaning to choose an option when no information is available to make a more specific choice, TFD, noun, 4. used as a verb, or
- degenerate to to mean decline in function from an original state (TFD).
In the rewritten example above, "process" is the only noun or noun phrase in the sentence with nominative case. "Move", "all the solutions" and "neighborhood" appear as indirect objects of a preceding verb or past participle and have dative case. Dative case is not used for the subject of a verb, leaving "process" as the subject of "reaches".
The original example sentence posted requires slightly different analysis. "When" introduces a subordinate clause containing "is" as the verb (which should be "are" to match with "solutions"). Subordinate clauses can take a trailing comma to indicate their status, so inserting a comma after "neighborhood" should clarify that "when ... neighborhood" is a subordinate clause and not the subject of "reaches".