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Since optimal strategies ensure that agents negotiate optimally, finding optimal strategies for negotiation agents that have incomplete information is an important and challenging issue. In this study, we use estimation of distribution algorithms (EDAs) to find optimal strategies for a bilateral negotiation with incomplete information between two competitive negotiation agents by coevolving both the agents' strategies. Agents coevolve optimal negotiation strategies for both parties through an evolutionary learning process in which a coevolutionary interaction is performed by directly matching and interacting agents of one population with those of the other population through random pairing. Even though there have been studies on finding negotiation strategies using evolutionary approaches, there are very few works on effectively finding the global optimal solution. Finding both parties' optimal strategies is difficult because simple EDAs suffer from premature convergence and their search capability deteriorates during coevolution. To solve these problems, we previously proposed the dynamic diversity controlling EDA (D C-EDA), which has a novel dynamic diversity controlling capability. However, it suffers from the problem of population reinitialization that leads to a computational overhead. To reduce the computational overhead and to achieve further improvements in terms of solution accuracy, we have proposed an improved D2C-EDA (ID2C-EDA) by adopting a local neighborhood search. Favorable empirical results support the effectiveness of the proposed ID2CEDA.