TY - JOUR A1 - Shi, Feng A1 - Schirneck, Friedrich Martin A1 - Friedrich, Tobias A1 - Kötzing, Timo A1 - Neumann, Frank T1 - Reoptimization time analysis of evolutionary algorithms on linear functions under dynamic uniform constraints JF - Algorithmica : an international journal in computer science N2 - Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical (1+1) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the (1+(λ,λ))GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small. Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-605295 SN - 0178-4617 SN - 1432-0541 VL - 82 IS - 10 SP - 3117 EP - 3123 PB - Springer CY - New York ER - TY - GEN A1 - Kötzing, Timo A1 - Krejca, Martin Stefan T1 - First-Hitting times under additive drift T2 - Parallel Problem Solving from Nature – PPSN XV, PT II N2 - For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process - the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be nonnegative, that is, we remove unnecessary restrictions like a finite, discrete, or bounded search space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift. Y1 - 2018 SN - 978-3-319-99259-4 SN - 978-3-319-99258-7 U6 - https://doi.org/10.1007/978-3-319-99259-4_8 SN - 0302-9743 SN - 1611-3349 VL - 11102 SP - 92 EP - 104 PB - Springer CY - Cham ER - TY - GEN A1 - Kötzing, Timo A1 - Krejca, Martin Stefan T1 - First-Hitting times for finite state spaces T2 - Parallel Problem Solving from Nature – PPSN XV, PT II N2 - One of the most important aspects of a randomized algorithm is bounding its expected run time on various problems. Formally speaking, this means bounding the expected first-hitting time of a random process. The two arguably most popular tools to do so are the fitness level method and drift theory. The fitness level method considers arbitrary transition probabilities but only allows the process to move toward the goal. On the other hand, drift theory allows the process to move into any direction as long as it move closer to the goal in expectation; however, this tendency has to be monotone and, thus, the transition probabilities cannot be arbitrary. We provide a result that combines the benefit of these two approaches: our result gives a lower and an upper bound for the expected first-hitting time of a random process over {0,..., n} that is allowed to move forward and backward by 1 and can use arbitrary transition probabilities. In case that the transition probabilities are known, our bounds coincide and yield the exact value of the expected first-hitting time. Further, we also state the stationary distribution as well as the mixing time of a special case of our scenario. Y1 - 2018 SN - 978-3-319-99259-4 SN - 978-3-319-99258-7 U6 - https://doi.org/10.1007/978-3-319-99259-4_7 SN - 0302-9743 SN - 1611-3349 VL - 11102 SP - 79 EP - 91 PB - Springer CY - Cham ER - TY - GEN A1 - Kötzing, Timo A1 - Lagodzinski, Gregor J. A. A1 - Lengler, Johannes A1 - Melnichenko, Anna T1 - Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic Programming T2 - Parallel Problem Solving from Nature – PPSN XV N2 - For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts). Second, the role and realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had a surprisingly little share in this work. We analyze a simple crossover operator in combination with local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); the resulting algorithm is denoted Concatenation Crossover GP. For this purpose three variants of the wellstudied Majority test function with large plateaus are considered. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control. Y1 - 2018 SN - 978-3-319-99259-4 SN - 978-3-319-99258-7 U6 - https://doi.org/10.1007/978-3-319-99259-4_4 SN - 0302-9743 SN - 1611-3349 VL - 11102 SP - 42 EP - 54 PB - Springer CY - Cham ER -