Barrier coverage with wireless sensors aims at detecting intruders who attempt to cross a specific area, where wireless sensors are distributed remotely at random. This paper considers limited-power sensors with adjustable ranges deployed along a linear domain to form a barrier to detect intruding incidents. We introduce three objectives to minimize: 1) total power consumption while satisfying full coverage; 2) the number of active sensors to improve the reliability; and 3) the active sensor nodes' maximum sensing range to maintain fairness. We refer to the problem as the tradeoff barrier coverage (TBC) problem. With the aim of obtaining a better tradeoff among the three objectives, we present a multiobjective optimization framework based on multiobjective evolutionary algorithm (MOEA)/D, which is called problem specific MOEA/D (PS-MOEA/D). Specifically, we define a 2-tuple encoding scheme and introduce a cover-shrink algorithm to produce feasible and relatively optimal solutions. Subsequently, we incorporate problem-specific knowledge into local search, which allows search procedures for neighboring subproblems collaborate each other. By considering the problem characteristics, we analyze the complexity and incorporate a strategy of computational resource allocation into our algorithm. We validate our approach by comparing with four competitors through several most-used metrics. The experimental results demonstrate that PS-MOEA/D is effective and outperforms the four competitors in all the cases, which indicates that our approach is promising in dealing with TBC.