Carsten Witt’s research while affiliated with Technical University of Denmark and other places

Estimation of distribution algorithms (EDAs) are general-purpose optimizers that maintain a probability distribution over a given search space. This probability distribution is updated through sampling from the distribution and a reinforcement learning process which rewards solution components that have shown to be part of good quality samples. The compact genetic algorithm (cGA) is a non-elitist EDA able to deal with difficult multimodal fitness landscapes that are hard to solve by elitist algorithms. We investigate the cGA on the Cliff function for which it was shown recently that non-elitist evolutionary algorithms and artificial immune systems optimize it in expected polynomial time. We point out that the cGA faces major difficulties when solving the Cliff function and investigate its dynamics both experimentally and theoretically. Our experimental results indicate that the cGA requires exponential time for all values of the update strength 1/K. We show theoretically that, under sensible assumptions, there is a negative drift when sampling around the location of the cliff. Experiments further suggest that there is a phase transition for K where the expected optimization time drops from $n^{\Theta (n)}$ to $2^{\Theta (n)}$.

Stagnation detection has been proposed as a mechanism for randomized search heuristics to escape from local optima by automatically increasing the size of the neighborhood to find the so-called gap size, i. e., the distance to the next improvement. Its usefulness has mostly been considered in simple multimodal landscapes with few local optima that could be crossed one after another. In multimodal landscapes with a more complex location of optima of similar gap size, stagnation detection suffers from the fact that the neighborhood size is frequently reset to 1 without using gap sizes that were promising in the past. In this paper, we investigate a new mechanism called radius memory which can be added to stagnation detection to control the search radius more carefully by giving preference to values that were successful in the past. We implement this idea in an algorithm called SD-RLSm$^{\text {m}}$ and show compared to previous variants of stagnation detection that it yields speed-ups for linear functions under uniform constraints and the minimum spanning tree problem. Moreover, its running time does not significantly deteriorate on unimodal functions and a generalization of the Jump benchmark. Finally, we present experimental results carried out to study SD-RLSm$^{\text {m}}$ and compare it with other algorithms.

Constrained single-objective problems have been frequently tackled by evolutionary multi-objective algorithms where the constraint is relaxed into an additional objective. Recently, it has been shown that Pareto optimization approaches using bi-objective models can be significantly sped up using sliding windows (Neumann and Witt, ECAI 2023). In this paper, we extend the sliding window approach to 3-objective formulations for tackling chance constrained problems. On the theoretical side, we show that our new sliding window approach improves previous runtime bounds obtained in (Neumann and Witt, GECCO 2023) while maintaining the same approximation guarantees. Our experimental investigations for the chance constrained dominating set problem show that our new sliding window approach allows one to solve much larger instances in a much more efficient way than the 3-objective approach presented in (Neumann and Witt, GECCO 2023).

Pareto optimization using evolutionary multi-objective algorithms such as the classical GSEMO algorithm has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good approximations is the population size of the algorithms which grows with the number of trade-offs that the algorithms encounter. In this paper, we introduce a sliding window speed up technique for recently introduced algorithms. We prove that our technique eliminates the population size as a crucial factor negatively impacting the runtime of the classical GSEMO algorithm and achieves the same theoretical performance guarantees as previous approaches within less computation time. Our experimental investigations for the classical maximum coverage problem confirms that our sliding window technique clearly leads to better results for a wide range of instances and constraint settings.

We prove that Simulated Annealing with an appropriate cooling schedule computes arbitrarily tight constant-factor approximations to the minimum spanning tree problem in polynomial time. This result was conjectured by Wegener (Automata, Languages and Programming, ICALP, Berlin, 2005). More precisely, denoting by $n, m, w_{\max }$, and $w_{\min }$ the number of vertices and edges as well as the maximum and minimum edge weight of the MST instance, we prove that simulated annealing with initial temperature $T_0 \ge w_{\max }$ and multiplicative cooling schedule with factor $1-1/\ell$, where $\ell = \omega (mn\ln (m))$, with probability at least $1-1/m$ computes in time $O(\ell (\ln \ln (\ell ) + \ln (T_0/w_{\min }) ))$ a spanning tree with weight at most $1+\kappa$ times the optimum weight, where $1+\kappa = \frac{(1+o(1))\ln (\ell m)}{\ln (\ell ) -\ln (mn\ln (m))}$. Consequently, for any $\epsilon >0$, we can choose $\ell$ in such a way that a $(1+\epsilon )$-approximation is found in time $O((mn\ln (n))^{1+1/\epsilon +o(1)}(\ln \ln n + \ln (T_0/w_{\min })))$ with probability at least $1-1/m$. In the special case of so-called $(1+\epsilon )$-separated weights, this algorithm computes an optimal solution (again in time $O( (mn\ln (n))^{1+1/\epsilon +o(1)}(\ln \ln n + \ln (T_0/w_{\min })))$), which is a significant speed-up over Wegener’s runtime guarantee of $O(m^{8 + 8/\epsilon })$. Our tighter upper bound also admits the result that in some situations a hybridization of simulated annealing and the ${(1 + 1)}$ EA can lead to stronger runtime guarantees than either algorithm alone.

Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good approximations is the population size of the algorithms which grows with the number of trade-offs that the algorithms encounter. In this paper, we introduce a sliding window speed up technique for recently introduced algorithms. We prove that our technique eliminates the population size as a crucial factor negatively impacting the runtime and achieves the same theoretical performance guarantees as previous approaches within less computation time. Our experimental investigations for the classical maximum coverage problem confirms that our sliding window technique clearly leads to better results for a wide range of instances and constraint settings.