A key traffic engineering problem in the Open Shortest Path First (OSPF)-based network is the determination of optimal link weights. From the network operators' point of view, there are two approaches to determining a set of link weights: Start-time Optimization (SO) and Run-time Optimization (RO). We previously presented a Preventive Start-time Optimization (PSO) scheme that determines an appropriate set of link weights at start time. It can counter both unexpected network congestion and network instability and thus overcomes the drawbacks of SO and RO, respectively. The previous work adopts a preventive start-time optimization algorithm with limited candidates, named PSO-L (PSO for Limited candidates). Although PSO-L relaxes the worst-case congestion, it does not confirm the optimal worst-case performance. To pursue this optimality, this paper proposes a preventive start-time optimization algorithm with a wide range of candidates, named PSO-W (PSO for Wide-range candidates). PSO-W upgrades the objective function of SO that determines the set of link weights at start time by considering all possible single link failures; its goal is to minimize the worst-case congestion. Numerical results via simulations show that PSO-W effectively relaxes the worst-case network congestion compared to SO, while it avoids the network instability caused by the run-time changes of link weights caused by RO. At the same time, PSO-W yields performance superior to that of PSO-L.