Elevator Scheduling Using Branch-and-Bound Optimization
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Solution Overview
Problem
Existing elevator scheduling methods fail to effectively optimize average waiting time (AWT) under reassignment policies due to high computational complexity and uncertainty in passenger destinations and arrival times, especially in large building systems.
Innovation Solution
A method combining the Empty the System Algorithm by Dynamic Programming (ESA-DP) with a branch-and-bound process to evaluate and optimize car assignments, using a search tree to determine globally optimal solutions for elevator scheduling under reassignment policies, accounting for statistical expectations of waiting times and pairwise delays.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If a reassignment policy is used to optimize elevator scheduling, then the average waiting time is significantly reduced, but the computational complexity increases due to the need to evaluate multiple possible assignments
Solution Approach 1:
The patent segments the solution space into a search tree structure where each node represents a partial assignment of hall calls to cars. The branch-and-bound algorithm systematically explores this segmented space by dividing it into branches (possible assignments) and bounding them (evaluating and pruning suboptimal paths), thereby managing computational complexity while finding optimal solutions.
Solution Approach 2:
The patent applies preliminary action by using the ESA-DP method to evaluate solution vectors before full optimization. This preliminary evaluation provides initial bounds and identifies promising branches early in the search process, reducing the overall computational burden of the branch-and-bound algorithm by focusing resources on likely optimal paths.
2Measurement precision
If the ESA-DP method is used to determine exact waiting time estimates, then the accuracy of scheduling decisions is improved, but the computational resources required increase
Solution Approach 1:
The patent applies partial action by using ESA-DP not for all possible assignments, but only for evaluating solution vectors at critical nodes in the branch-and-bound search tree. This selective application of the computationally intensive ESA-DP method provides sufficient accuracy for decision-making while significantly reducing overall computational resource consumption compared to applying it universally.
3Reliability
If all possible future states of the system are considered in scheduling decisions, then the robustness of the schedule is improved, but the complexity of the scheduling algorithm increases
Solution Approach 1:
The patent introduces the search tree as an intermediary structure that systematically organizes and explores future system states. Rather than directly analyzing all possible future states, the search tree mediates this complexity by providing a structured framework for incremental exploration, where each level represents a decision point and branches represent possible future configurations.
Data Source
AI summary
A method schedules cars of an elevator system. Each possible assignment of a set of hall calls to a set of cars is represented by a solution vector maintained as a node in a search tree. Each solution vector is evaluated using an ESA-DP process according to an immediate policy to determine initially a best solution. A branch-and-bound process is applied to each solution vector using the initial best solution and the search tree to determine a globally optimal solution for scheduling the cars according to a reassignment policy.