  Evolutionary algorithms (EAs) have emerged as a predominant approach for
addressing multi-objective optimization problems. However, the theoretical
foundation of multi-objective EAs (MOEAs), particularly the fundamental aspects
like running time analysis, remains largely underexplored. Existing theoretical
studies mainly focus on basic MOEAs, with little attention given to practical
MOEAs. In this paper, we present a running time analysis of strength Pareto
evolutionary algorithm 2 (SPEA2) for the first time. Specifically, we prove
that the expected running time of SPEA2 for solving three commonly used
multi-objective problems, i.e., $m$OneMinMax, $m$LeadingOnesTrailingZeroes, and
$m$-OneJumpZeroJump, is $O(\mu n\cdot \min\{m\log n, n\})$, $O(\mu n^2)$, and
$O(\mu n^k \cdot \min\{mn, 3^{m/2}\})$, respectively. Here $m$ denotes the
number of objectives, and the population size $\mu$ is required to be at least
$(2n/m+1)^{m/2}$, $(2n/m+1)^{m-1}$ and $(2n/m-2k+3)^{m/2}$, respectively. The
proofs are accomplished through general theorems which are also applicable for
analyzing the expected running time of other MOEAs on these problems, and thus
can be helpful for future theoretical analysis of MOEAs.
