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In our previous study we proposed an optimization-based collision avoidance method for multi-car elevator systems where more than one car is installed in every shaft. However, it has two drawbacks. The one is that undesirable operation called reversal occurs, i.e. on-board passengers travel in the opposite direction to their destination floors. The other is that the system may enter a livelock state and become unable to serve passengers. Therefore, in this study we will improve the collision avoidance method so that neither reversal nor livelock occurs. Then, its effectiveness will be examined by computer simulation.