Large Language Models (LLMs) are used for Register-Transfer Level (RTL) code generation, but they face two main challenges: functional correctness and Power, Performance, and Area (PPA) optimization. Iterative, feedback-based methods partially address these, but they are limited to local search, hindering the discovery of a global optimum. This paper introduces REvolution, a framework that combines Evolutionary Computation (EC) with LLMs for automatic RTL generation and optimization. REvolution evolves a population of candidates in parallel, each defined by a design strategy, RTL implementation, and evaluation feedback. The framework includes a dual-population algorithm that divides candidates into Fail and Success groups for bug fixing and PPA optimization, respectively. An adaptive mechanism further improves search efficiency by dynamically adjusting the selection probability of each prompt strategy according to its success rate. Experiments on the VerilogEval and RTLLM benchmarks show that REvolution increased the initial pass rate of various LLMs by up to 24.0 percentage points. The DeepSeek-V3 model achieved a final pass rate of 95.5\%, comparable to state-of-the-art results, without the need for separate training or domain-specific tools. Additionally, the generated RTL designs showed significant PPA improvements over reference designs. This work introduces a new RTL design approach by combining LLMs' generative capabilities with EC's broad search power, overcoming the local-search limitations of previous methods.