As modern software systems expand in scale and complexity, the challenges associated with their modeling and formulation grow increasingly intricate. Traditional approaches often fall short in effectively addressing these complexities, particularly in tasks such as design pattern detection for maintenance and assessment, as well as code refactoring for optimization and long-term sustainability. This growing inadequacy underscores the need for a paradigm shift in how such challenges are approached and resolved. This paper presents Analytical Software Engineering (ASE), a novel design paradigm aimed at balancing abstraction, tool accessibility, compatibility, and scalability. ASE enables effective modeling and resolution of complex software engineering problems. The paradigm is evaluated through two frameworks Behavioral-Structural Sequences (BSS) and Optimized Design Refactoring (ODR), both developed in accordance with ASE principles. BSS offers a compact, language-agnostic representation of codebases to facilitate precise design pattern detection. ODR unifies artifact and solution representations to optimize code refactoring via heuristic algorithms while eliminating iterative computational overhead. By providing a structured approach to software design challenges, ASE lays the groundwork for future research in encoding and analyzing complex software metrics.