In many real-world scenarios, agents are involved in optimization problems. Since most of these scenarios are over-constrained, optimal solutions do not always satisfy all agents. Some agents might be unhappy and ask questions of the form “Why does solution S not satisfy property P ?”. We propose CMAOE, a domain-independent approach to obtain contrastive explanations by: (i) generating a new solution S′ where property P is enforced, while also minimizing the differences between S and S′; and (ii) highlighting the differences between the two solutions, with respect to the features of the objective function of the multi-agent system. Such explanations aim to help agents understanding why the initial solution is better in the context of the multi-agent system than what they expected. We have carried out a computational evaluation that shows that CMAOE can generate contrastive explanations for large multi-agent optimization problems. We have also performed an extensive user study in four different domains that shows that: (i) after being presented with these explanations, humans’ satisfaction with the original solution increases; and (ii) the constrastive explanations generated by CMAOE are preferred or equally preferred by humans over the ones generated by state of the art approaches.