A Multi-Objective Perspective on Performance Assessment and Automated Selection of Single-Objective Optimization Algorithms

We build upon a recently proposed multi-objective view onto performance measurement of single-objective stochastic solvers. The trade-off between the fraction of failed runs and the mean runtime of successful runs \textendash both to be minimized \textendash is directly analyzed based on a study on algorithm selection of inexact state-of-the-art solvers for the famous Traveling Salesperson Problem (TSP). Moreover, we adopt the hypervolume indicator (HV) commonly used in multi-objective optimization for simultaneously assessing both conflicting objectives and investigate relations to commonly used performance indicators, both theoretically and empirically. Next to Penalized Average Runtime (PAR) and Penalized Quantile Runtime (PQR), the HV measure is used as a core concept within the construction of per-instance algorithm selection models offering interesting insights into complementary behavior of inexact TSP solvers. \textbullet The multi-objective perspective is naturally generalizable to multiple objectives. \textbullet Proof of relationship between HV and the PAR in the considered bi-objective space. \textbullet New insights into complementary behavior of stochastic optimization algorithms.