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.

Multi-objective evolutionary algorithms (MOEAs) have become increasingly popular as multi-objective problem solving techniques. Most studies of MOEAs are empirical. Only recently, a few theoretical results have appeared. It is acknowledged that more theoretical research is needed. An important open problem is to understand the role of populations in MOEAs. We present a simple bi-objective problem which emphasizes when populations are needed. Rigorous runtime analysis point out an exponential runtime gap between a population-based algorithm (SEMO) and several single individual-based algorithms on this problem. This means that among the algorithms considered, only the populationbased MOEA is successful and all other algorithms fail.

To understand the working principles of randomized search heuristics like evolutionary algorithms they are analyzed on optimization problems whose structure is well-studied. The idea is to investigate when it is possible to simulate clever optimization techniques for combinatorial optimization problems by random search. The maximum matching problem is well suited for this approach since long augmenting paths do not allow immediate improvements by local changes. It is known that randomized search heuristics like simulated annealing, the Metropolis algorithm, the (1+1) EA and randomized local search efficiently approximate maximum matchings for any graph; however, there are graphs where they fail to find maximum matchings in polynomial time. In this paper, we examine randomized local search (RLS) for graphs whose structure is simple. We show that RLS finds maximum matchings on trees in expected polynomial time.

The expected runtime of a simple multi-objective evolutionary algorithm for the Boolean decision space is analyzed. The algorithm uses independent bit flips as mutation operator and, therefore, searches globally. It is proved that the expected runtime is O(n/sup n/) for all objective functions {0,1}/sup n/ /spl rarr/ R/sup m/. This worst-case 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(n/sup 3/). Moreover, the runtime is O(n/sup 3/) with an overwhelming probability.

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.

Any B/sub 2/-formula of size /spl Lscr/ can be transformed into a branching program of size O(e/spl Lscr//sup 1+/spl epsi//)for arbitrary E>0. The presented proof is based on a technique due to R. Cleve (1991) to simulate balanced algebraic formulas of size s by algebraic straight-line programs that employ a constant number of registers and have length O(s/sup 1+/spl epsi//). The best previously known simulation of B2-formulas of size C by branching programs achieves a branching program size of O(/spl Lscr//sup 1.195/).