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This paper presents a collaborative procedure for multiobjective global routing. Our procedure takes multiple global routing solutions, which are generated independently (e.g., by one router that runs in different modes concurrently or by different routers running in parallel), as input. It then performs multiobjective optimization based on Pareto algebra and quickly generates multiple global routing solutions with a tradeoff between the considered objectives. The user can control the number of generated solutions and the degree of exploring the tradeoff between them by constraining the maximum allowable degradation in each objective. This paper then considers the following three multiobjective case studies: 1) minimization of interconnect power and wirelength; 2) minimization of routing congestion and wirelength; and 3) minimization of wirelength with respect to the (finite-capacity) routing resources. The maximum allowable degradation in wirelength is specified in all cases. Our multiobjective procedure runs in only a few minutes for each of the International Symposium on Physical Design 2008 benchmarks, even the unroutable ones, which imposes a tolerable overhead in the design flow. In our simulations, we demonstrate the effectiveness of our procedure using five modern academic global routers.