Time-Optimal Scheduling of Tasks with Shared and Dynamically Constrained Energy Systems

Abstract

This article addresses the minimum-time scheduling of sequential tasks requiring energy (or a similar resource)from shared, dynamically constrained systems. Practical applications of this problem include human operations with fatigue and rest cycles, among others. The goal is to jointly optimize task execution order and power allocation to the tasks, balancing execution speed with necessary recovery periods and task transition times. We present a generic Mixed-Integer Nonlinear Programming (MINLP) formulation of the problem, propose a heuristic solution method based on a Genetic Algorithm (GA), and demonstrate its use in a numerical example on efficient execution of a two-exercise workout. The numerical example shows that the proposed heuristic method rapidly produces a solution within 0.9% of the one obtained via the MINLP solver SCIP.