Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically well-founded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the well-known maximum matching problem. It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Moreover, for very simple graphs it is proved that the expected optimization time of the algorithm is polynomially bounded and bipartite graphs are constructed where this time grows exponentially.

Motivated by the fact that competitive analysis yields too pessimistic results when applied to the paging problem, there has been considerable research interest in refining competitive analysis and in developing alternative models for studying online paging.In this paper, we propose a new, simple model for studying paging with locality of reference. The model is closely related to Denning's working set concept and directly reflects the amount of locality that request sequences exhibit. We use the page fault rate to evaluate the quality of paging algorithms, which is the performance measure used in practice.We develop tight or nearly tight bounds on the fault rates achieved by popular paging algorithms such as LRU, FIFO, deterministic Marking strategies and LFD. These bounds show that LRU is an optimal online algorithm, whereas FIFO and Marking strategies are not optimal in general. We present an experimental study comparing the page fault rates proven in our analyses to the page fault rates observed in practice.

The expected runtime of a simple multiobjective evolutionary algorithm for the Boolean decision space is analyzed. The algorithm uses independent hit flips as mutation operator and, therefore, searches globally. It is proved that the expected runtime is O(n") for all objective functions ( 0 , l ) " + Rm. This worstcase bound is tight and matches the worst-case bounds for fundamental evolutionary algorithms working in the scenario of single-objective Optimization. For the bicriteria problem LOTZ (Leading Ones Trailing Zeroes), it is shown that the expected runtime is O(n3). Moreover, the runtime is O ( n 3 ) with an overwhelming probability.Finally, the function x w (x', (x -2)2) that serves as a test function in the continuous decision space is adapted to the Boolean decision space, and hounds on the runtime are derived.

Multi-objective evolutionary algorithms (MOEAs) have become increasingly popular as multi-objective problem solving techniques. An important open problem is to understand the role of populations in MOEAs. We present two simple bi-objective problems which emphasise when populations are needed. Rigorous runtime analysis points out an exponential runtime gap between the population-based algorithm simple evolutionary multi-objective optimiser (SEMO) and several single individual-based algorithms on this problem. This means that among the algorithms considered, only the population-based MOEA is successful and all other algorithms fail.

Motivated by the fact that competitive analysis yields too pessimistic results when applied to the paging problem, there has been considerable research interest in refining competitive analysis and in developing alternative models for studying online paging. The goal is to devise models in which theoretical results capture phenomena observed in practice.In this paper we propose a new, simple model for studying paging with locality of reference. The model is closely related to Denning's working set concept and directly reflects the amount of locality that request sequences exhibit. We demonstrate that our model is reasonable from a practical point of view.We use the page fault rate to evaluate the quality of paging algorithms, which is the performance measure used in practice. We develop tight or nearly tight bounds on the fault rates achieved by popular paging algorithms such as LRU, FIFO, deterministic Marking strategies and LFD. It shows that LRU is an optimal online algorithm, whereas FIFO and Marking strategies are not optimal in general. We present an experimental study comparing the page fault rates proven in our analyses to the page fault rates observed in practice. This is the first such study for an alternative/refined paging model.