The use of low-cost multi-core processors that target small-scale parallelism of several or several tens of processing units has recently spread to general-purpose personal computers. As part of this trend, research on converting evolutionary computation to parallel processing on multi-core processors has begun. In our research, we place importance on proposing multi-core processor architectures from the viewpoint of evolutionary computation and on proposing indices for identifying chips that exhibit high affinity with evolutionary computation from among existing multi-core processors. This paper takes a first step in this direction by focusing on local memory built into a multi-core processor and proposing a specification that allows the contents of local memory in any core to be directly accessed by any other core without using main memory. We describe a desktop comparison with single-core processors and general multi-core processors and show that a speed-up effect should be expected with the proposed specification for both fine-grain and coarse-grained parallelization techniques. We also describe an evaluation on actual multi-core processor for the case of fine-grain parallelization and show that the speed-up effect is also useful in reducing energy consumption.