Elevator Scheduling via Quadratic Semi-Assignment Optimization
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Solution Overview
Problem
Conventional elevator scheduling algorithms, such as the nearest car and immediate assignment methods, fail to optimize average waiting time (AWT) due to their computational simplicity and inability to reconsider assignments based on changing conditions, leading to suboptimal distribution of elevator cars and increased passenger dissatisfaction.
Innovation Solution
The development of a Semi-Assignment Problem (SAP) approach using a Quadratic Semi-Assignment Problem (QSAP) formulation, which approximates cumulative waiting time through pairwise delays and employs a branch and bound algorithm with spectral relaxations to optimize car assignments, allowing for continuous reassignment of passengers and improved AWT.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the nearest car algorithm is used for elevator scheduling, then computational complexity is low (O(CN)), but average waiting time is very far from optimal and cars are poorly positioned
Solution Approach 1:
The patent implements dynamic reassignment of passengers to elevator cars based on changing conditions. Instead of fixed immediate assignments, the system continuously evaluates and reassigned passengers as cars approach and conditions change, allowing the scheduling to adapt dynamically rather than being static
Solution Approach 2:
The system uses feedback from car positions, passenger assignments, and waiting times to continuously improve scheduling decisions. The quadratic semi-assignment program incorporates feedback about current system state to optimize reassignment decisions, creating a closed-loop control system that learns from past assignments
2Productivity
If immediate assignment mode is used, then computational complexity is CN and assignments are made quickly, but the scheduler cannot revise assignments when situations change, resulting in suboptimal AWT
Solution Approach 1:
The system transitions from static immediate assignment to dynamic reassignment. As elevator cars approach and conditions change, the system continuously reassesses passenger assignments rather than committing permanently, allowing adaptive optimization while maintaining computational efficiency through the quadratic semi-assignment formulation
Solution Approach 2:
The system performs preliminary assignments but maintains the capability to revise them. The quadratic semi-assignment program prepares initial assignments efficiently while preserving the option to reassign based on subsequent conditions, combining the benefits of quick decision-making with flexible optimization
3Loss of time
If reassignment mode is used to continuously reconsider assignments, then AWT is reduced significantly, but computational complexity becomes exponential making exhaustive enumeration infeasible
Solution Approach 1:
The patent changes the mathematical formulation from a general combinatorial optimization problem to a quadratic semi-assignment program. This parameter change in the problem structure allows efficient solution methods while maintaining the ability to capture complex interactions between passenger assignments and car positions
Solution Approach 2:
The system replaces exhaustive enumeration mechanical search with an optimized quadratic semi-assignment program. This substitution uses mathematical programming techniques to achieve near-optimal assignments without the exponential computational burden of checking all possible solutions
Data Source
AI summary
System and methods for controlling a movement of elevator cars of an elevator system. Determine, for each elevator car, an individual waiting time of accommodating each hall call. Determine, for each pair of hall calls assigned to each elevator car, a pairwise delay over the individual waiting time of each hall call in the pair caused by a joint assignment of the elevator car to accommodate the pair of the hall calls. Approximate a cumulative waiting time of an assignment of the elevator cars. Determine the assignment of the elevator cars using a branch and bound algorithm using spectral relaxations based on a generalized eigenvalue and spectral branching that assigns the plurality of hall calls to the elevator cars to minimize the approximated cumulative waiting time. Use a controller for controlling the movement of the elevator cars according to the assignment.