Heinz Schmitz

Metaheuristics in the service industry

A Bicriteria Traveling Salesman Problem with Sequence Priorities.- Metaheuristics for Tourist Trip Planning.- Solving Fuzzy Multi-Item Economic Order Quantity Problems via Fuzzy Ranking Functions and Particle Swarm Optimization.- Fixed and Variable Toll Pricing in Road Networks with Direct Search Meta-Heuristics.- Scatter Search for locating a treatment plant and the necessary transfer centers in a reverse network.- Variable Neighbourhood Descent for Planning Crane Operations in a Train Terminal.- Design and Analysis of Evolutionary Algorithms for the No-wait Flow-shop Scheduling Problem.- Metaheuristics for the Index Tracking Problem.- A Hybrid Algorithm for Vehicle Routing of Less-Than-Truckload Carriers.

Languages of Dot-Depth 3/2

We prove an effective characterization of languages having dot-depth 3/2. Let B3/2 denote this class, i.e., languages that can be written as finite unions of languages of the form u0L1u1L2u2 ... Lnun, where ui ∈ A* and Li are languages of dot-depth one. Let F be a deterministic finite automaton accepting some language L. Resulting from a detailed study of the structure of B3/2, we identify a pattern P (cf. Fig. 2) such that L belongs to B3/2 if and only if F does not have pattern P in its transition graph. This yields an NL-algorithm for the membership problem for B3/2. n nDue to known relations between the dot-depth hierarchy and symbolic logic, the decidability of the class of languages definable by Σ2-formulas of the logic FO[<, min,max, S, P] follows. We give an algebraic interpretation of our result.

Approximability and hardness in multi-objective optimization

We study the approximability and the hardness of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). Our contributions are: - We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions. - These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results. - We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP). n nAs a consequence we see that in contrast to single-objective problems (where the solution notions coincide), the situation is more subtle for multiple objectives. So it is important to exactly specify the NP-hardness notion when discussing the complexity of multi-objective problems.

Uniformly Defining Complexity Classes of Functions

We introduce a general framework for the definition of function classes. Our model, which is based on polynomial time nondeterministic Turing transducers, allows uniform characterizations of FP, FPNP, counting classes (#·P, #·NP, #·coNP, GapP, GapPNP), optimization classes (max·P, min·P, max·NP, min·NP), promise classes (NPSV, #few·P, c#·P), multivalued classes (FewFP, NPMV) and many more. Each such class is defined in our model by a certain family of functions. We study a reducibility notion between such families, which leads to a necessary and sufficient criterion for relativizable inclusion between function classes. As it turns out, this criterion is easily applicable and we get as a consequence e.g. that there are oracles A, B, such that min.PA (nsubseteq) #·NPA, and max.NPB (nsubseteq) c#·coNPB (note that no structural consequences are known to follow from the corresponding positive inclusions).

Decidable Hierarchies of Starfree Languages

We introduce a strict hierarchy {LnB} of language classes which exhausts the class of starfree regular languages. It is shown for all n ≥ 0 that the classes LnB have decidable membership problems. As the main result, we prove that our hierarchy is levelwise comparable by inclusion to the dot-depth hierarchy, more precisely, LnB contains all languages having dot-depth n + 1/2. This yields a lower bound algorithm for the dot-depth of a given language. The same results hold for a hierarchy {LnL} and the Straubing-ThErien hierarchy.

Level 5/2 of the Straubing-Thérien Hierarchy for Two-Letter Alphabets

We prove an effective characterization of level 5/2 of the Straubing-Therien hierarchy for the restricted case of languages defined over a two-letter alphabet.

Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages

The purpose of this paper is to provide efficient algorithms that n decide membership for classes of several Boolean hierarchies for n which efficiency (or even decidability) were previously not known. n We develop new forbidden-chain characterizations for the single n levels of these hierarchies and obtain the following results: n - The classes of the Boolean hierarchy over level

UNIFORM CHARACTERIZATIONS OF COMPLEXITY CLASSES OF FUNCTIONS

Sigma_1

Multiobjective Disk Cover Admits a PTAS

of the n dot-depth hierarchy are decidable in

A complexity analysis and an algorithmic approach to student sectioning in existing timetables

NL