Slow relaxation due to dense packing encumbers the simulation of a variety of many particle systems like, for instance, collapsed polymers (folded proteins) or structural glasses. We propose to overcome this problem by a new algorithm, assigning each particle a fourth space coordinate and treating an expanded ensemble of systems of which the one with all fourth coordinates equal to zero is the physical system. An application of this simulation strategy to the coil-globule transition of homopolymers using the bond-fluctuation model reveals a hitherto unfound first-order liquid to solid transition of the collapsed globule.