This paper proposes a framework for time-efficiently finding multiple answers that meet multiple logical constraints and are Pareto-optimal for multiple objective functions. The proposed framework determines a set of optimal answers by iteratively replacing a set of definite clauses. Clause replacement is performed using a SAT solver consisting of equivalent transformation rules (ETRs). An ETR replaces a definite clause with one or more clauses while preserving the declarative meaning of the union of the original clause and problem clauses. To efficiently find optimal answers, in this paper, we define a new class of ETRs that are generated based on the evaluation results of a multi-objective genetic algorithm (MOGA), and propose a method for generating ETRs that belong to the new class. ETRs belonging to the new class help to replace definite clauses according to user objectives such as cost--benefit performance, reliability, and financial constraints. Thus, a SAT solver that uses the new ETR class in addition to extant ETR classes can preferentially replace definite clauses that produce the optimal answer for user objectives. Experimental results indicate that the proposed framework can significantly reduce the computation time and memory usage necessary to determine a set of optimal answers for user objectives.