In this paper, we propose a framework for obtaining the optimal solution of an elevator operation problem by applying Branch-and-Bound method, where it is assumed that all information ahout the passengers are given. The problem is solved by determining the assignments of passengers to elevators and the processing order of passengers for each elevator. The validity of an existing rule to decide a car service is examined by comparing the results with the optimal one.

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In this paper, an approach to complement legacy rules for the elevator operation is proposed. The approach is derived from the analysis that the elevator operation in the real world often obeys a heuristic rule, and such a rule can be divided into a legacy rule and ad-hoc rules. In the approach, ad-hoc rules are represented as polysemous rules, and a Genetics-Based Machine Learning (GBML) method is applied to acquire such rules. Here, a polysemous rule encodes, not a set of environments' states as the well-known if-then rule does, but a relative attribute vector of an arbitrary elevator. The elevator selection rule based on polysemous rules is simple: if there is a polysemous rule which matches one of attribute vectors of the elevators, select the elevator which corresponds to the matching vector; otherwise select an elevator according to a legacy rule. In computer illustrations, the GBML method is applied to 3 traffic patterns formed by the system's users. It is shown that the resultant polysemous rules seem to complement an existing (legacy) operational rule. Furthermore, polysemous rules, which are selected among those acquired by the GBML method, are successfully applied to harder problems with more elevators than those used in learning.

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: In this paper, we present a modified dynamic programming (DP) method. The method is basically the same as the value iteration method (VI), a representative DP method, except the preprocess of a system's state transition model for reducing its complexity, and is called the dynamic programming on reduced models (DPRM). That reduction is achieved by imaginarily considering causes of the probabilistic behavior of a system, and then cutting off some causes with low occurring probabilities. In computational illustrations, VI, DPRM, and the real-time Q-learning method (RTQ) are applied to elevator operation problems, which can be modeled by using Markov decision processes. The results show that DPRM can compute quasi-optimal value functions which bring more effective allocations of elevators than value functions by RTQ in less computational times than VI. This characteristic is notable when the traffic pattern is complicated.