Executing large test suites is time and resource consuming, sometimes impossible, and such test suites typically contain many redundant test cases. Hence, test case minimization is used to remove redundant test cases that are unlikely to detect new faults. However, most test case minimization techniques rely on code coverage (white-box), model-based features, or requirements specifications, which are not always (entirely) accessible by test engineers. Code coverage analysis also leads to scalability issues, especially when applied to large industrial systems. Recently, a set of novel techniques was proposed, called FAST-R, relying solely on test case code for test case minimization, which appeared to be much more efficient than white-box techniques. However, it achieved a comparable low fault detection capability for Java projects, thus making it challenging in practice. In this paper, we propose ATM (AST-based Test case Minimizer), a similarity-based, search-based test case minimization technique, taking a specific budget as input, that also relies exclusively on the source code of test cases but attempts to achieve higher fault detection through finer-grained similarity analysis and a dedicated search algorithm. ATM transforms test case code into Abstract Syntax Trees (AST) and relies on four tree-based similarity measures to apply evolutionary search, specifically genetic algorithms, to minimize test cases. We evaluated the effectiveness and efficiency of ATM on a large dataset of 16 Java projects with 661 faulty versions using three budgets ranging from 25% to 75% of test suites. ATM achieved significantly higher fault detection rates (0.82 on average), compared to FAST-R (0.61 on average) and random minimization (0.52 on average), when running only 50% of the test cases, within practically acceptable time (1.1-4.3 hours, on average, per project version), given that minimization is only occasionally applied when many new test cases are created (major releases). Results achieved for other budgets were consistent.