Regression testing is the process of retesting a system after it or its environment has changed. Many techniques aim to find the cheapest subset of the regression test suite that achieves full coverage. More recently, it has been observed that the tester might want to have a range of solutions providing different trade-offs between cost and one or more forms of coverage, this being a multi-objective optimisation problem. This paper further develops the multi-objective agenda by adapting a decomposition-based multi-objective evolutionary algorithm (MOEA/D). Experiments evaluated four approaches: a classic greedy algorithm; non dominated sorting genetic algorithm II (NSGA-II); MOEA/D with a fixed value for a parameter c; and MOEA/D in which tuning was used to choose the value of c. These used six programs from the SIR repository and one larger program, VoidAuth. In all of the experiments MOEA/D with tuning was the most effective technique. The relative performance of the other techniques varied, although MOEA/D with fixed c outperformed NSGA-II on the larger programs (Space and VoidAuth).