1. A task allocation optimization system for a multi-core processor including a plurality of cores, comprising: accumulative response time calculating logic configured to calculate a response time of each of a plurality of tasks which are core allocation decision targets, and outputs an accumulative value of the calculated response time as an evaluation function value which is an index representing excellence of a task allocation; searching logic configured to search for a task allocation from which a good evaluation function value is calculated based on the evaluation function value; and high evaluation candidate holding logic configured to hold a candidate having a good evaluation function value among a plurality of task allocation candidates searched by the searching logic; wherein: one or more of the calculating logic, the searching logic, and the holding logic are implemented by a processor; the searching logic includes: branching logic configured to generate a sub problem by allocating a task to a core in order of from a task with a high priority to a task with a low priority, and bounding logic configured to calculate a bound value of the evaluation function value permissible to the sub problem, and performs a bounding operation to stop an unnecessary core allocation candidate search using the calculated bound value of the evaluation function value, and the bounding logic includes fixed task accumulative response time calculation instructing logic configured to calculate the bound value using the evaluation function value calculated using a task already allocated to a core.