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jMetaISP is a framework for dynamic multi-objective Big Data optimization. It combines the jMetal multi-objective framework with the Apache Spark cluster computing system to allow the solving of dynamic optimization problems from a number of external streaming data sources in Big Data contexts. In this paper, we describe the current status of the jMetaISP project, focusing mainly in its design and internal architecture, with the aim of offering a comprehensive view of its main features to interested researchers. Among the covered features, we describe the main components of a jMetalSP application, including dynamic problems, dynamic algorithms, streaming data sources, and data consumers. For practical purposes, we describe two test cases to illustrate how to address dynamic combinatorial and dynamic continuous optimization problems by using the proposed framework.