Abstract—The paradigmatic shift from a Web of manual interactions to a Web of programmatic interactions driven by Web services is creating unprecedented opportunities for the formation of online Business-to-Business (B2B) collaborations. In particular, the creation of value-added services by composition of existing ones is gaining a significant momentum. Since many available Web services provide overlapping or identical functionality, albeit with different Quality of Service (QoS), a choice needs to be made to determine which services are to participate in a given composite service. This paper presents a middleware platform which addresses the issue of selecting Web services for the purpose of their composition in a way that maximizes user satisfaction expressed as utility functions over QoS attributes, while satisfying the constraints set by the user and by the structure of the composite service. Two selection approaches are described and compared: one based on local (task-level) selection of services and the other based on global allocation of tasks to services using integer programming. Index Terms—Web services, quality of service, service composition, integer programming. æ 1

. Since 1985 various evolutionary approaches to multiobjective optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of different methods available to date are mostly qualitative and restricted to two approaches. In this paper an extensive, quantitative comparison is presented, applying four multiobjective evolutionary algorithms to an extended 0/1 knapsack problem. 1 Introduction Many real-world problems involve simultaneous optimization of several incommensurable and often competing objectives. Usually, there is no single optimal solution, but rather a set of alternative solutions. These solutions are optimal in the wider sense that no other solutions in the search space are superior to them when all objectives are considered. They are known as Pareto-optimal solutions. Mathematically, the concept of Pareto-optimality can be defined as follows: Let us consider, without loss of generality, a multio...

The Multiple Knapsackproblem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. We are given a set of n items and m bins (knapsacks) such that each item i has a profit p(i) and a size s(i), and each bin j has a capacity c(j). The goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins. MKP is a special case of the Generalized Assignment problem (GAP) where the profit and the size of an item can vary based on the specific bin that it is assigned to. GAP is APX-hard and a 2-approximation for it is implicit in the work of Shmoys and Tardos [26], and thus far, this was also the best known approximation for MKP. The main result of this paper is a polynomial time approximation scheme for MKP. Apart from its inherent theoretical interest as a common generalization of the well-studied knapsack and bin packing problems, it appears to be the strongest special case of GAP that is not APX-hard. We substantiate this by showing that slight generalizations of MKP that are very restricted versions of GAP are APX-hard. Thus our results help demarcate the boundary at which instances of GAP becomeAPX-hard. An interesting and novel aspect of our approach is an approximation preserving reduction from an arbitrary instance of MKP to an instance with O(log n) distinct sizes and profits.

Test functions are commonly used to evaluate the effectiveness of different search algorithms. However, the results of evaluation are as dependent on the test problems as they are on the algorithms that are the subject of comparison. Unfortunately, developing a test suite for evaluating competing search algorithms is difficult without clearly defined evaluation goals. In this paper we discuss some basic principles that can be used to develop test suites and we examine the role of test suites as they have been used to evaluate evolutionary search algorithms. Current test suites include functions that are easily solved by simple search methods such as greedy hill-climbers. Some test functions also have undesirable characteristics that are exaggerated as the dimensionality of the search space is increased. New methods are examined for constructing functions with different degrees of nonlinearity, where the interactions and the cost of evaluation scale with respect to the dimensionality of...

Quality of Service (QoS) control is considered an important user demand and therefore receives wide attention, especially in the areas of computer networks and real-time multimedia systems. In this paper we present an QoS management scheme that enables us to quantitatively measure QoS, and to analytically plan and allocate resource. In this model, available system resources are apportioned across multiple applications such that the net utility that accrues to the end-users of those applications is maximized. In [26, 27], we primarily work with “continuous ” QoS dimensions, and assumed that the ’utility ’ gained by improvements along a QoS dimension were always representable by concave functions. In this paper, we relax both assumptions. One, we deal with discrete set of QoS operating points. Two, we make no assumptions about the concavity of the utility functions. Using these as the basis, we tackle the problem of maximizing system utility by allocating a single finite resource to satisfy the QoS requirements of multiple applications along multiple QoS dimensions. We present two nearoptimal algorithms to solve this problem. The first yields an allocation within a known bounded distance from the optimal solution, and the second yields an allocation whose distance from the optimal solution can be explicitly controlled by the QoS manager. We compare the run-times of these near-optimal algorithms and their solution quality relative to the optimal allocation, which in turn is computed using dynamic programming. These detailed evaluations provide practical insight into which of these algorithms can be used online in real-time systems.

Emerging spread spectrum high-speed data networks utilize multiple channels via orthogonal codes or frequency-hopping patterns such that multiple users can transmit concurrently. In this paper, we develop a framework for opportunistic scheduling over multiple wireless channels. With a realistic channel model, any subset of users can be selected for data transmission at any time, albeit with different throughputs and system resource requirements. We first transform selection of the best users and rates from a complex general optimization problem into a decoupled and tractable formulation: a multi-user scheduling problem that maximizes total system throughput and a control-update problem that ensures long-term deterministic or probabilistic fairness constraints. We then design and evaluate practical schedulers that approximate these objectives.

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A capacitated covering IP is an integer program of the form min{cx|Ux ≥ d, 0 ≤ x ≤ b, x ∈ Z +}, where all entries of c, U, and d are nonnegative. Given such a formulation, the ratio between the optimal integer solution and the optimal solution to the linear program relaxation can be as bad as ||d||∞, even when U consists of a single row. We show that by adding additional inequalities, this ratio can be improved significantly. In the general case, we show that the improved ratio is bounded by the maximum number of non-zero coefficients in a row of U, and provide a polynomial-time approximation algorithm to achieve this bound. This improves the previous best approximation algorithm which guaranteed a solution within the maximum row sum times optimum. We also show that for particular instances of capacitated covering problems, including the minimum knapsack problem and the capacitated network design problem, these additional inequalities yield even stronger improvements in the IP/LP ratio. For the minimum knapsack, we show that this improved ratio is at most 2. This is the first non-trivial IP/LP ratio for this basic problem. Capacitated network design generalizes the classical network design problem by introducing capacities on the edges, whereas previous work only considers the case when all capacities equal 1. For capacitated network design problems, we show that this improved ratio depends on a parameter of the graph, and we also provide polynomial-time approximation algorithms to match this bound. This improves on the best previous m-approximation, where m is the number of edges in the graph. We also discuss improvements for some other special capacitated covering problems, including the fixed charge network flow problem. Finally, for the capacitated network design problem, we give some stronger results and algorithms for series parallel graphs and strengthen these further for outerplanar graphs. Most of our approximation algorithms rely on solving a single LP. When the original LP (before adding our strengthening inequalities) has a polynomial number of constraints, we describe a combinatorial FPTAS for the LP with our (exponentially-many) inequalities added. Our contribution here is to describe an appropriate

The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NP-complete combinatorial optimization problems. In particular, the subset sum, maximum cut, and minimum tardy task problems are considered. Except for the fitness function, no problem-specific changes of the genetic algorithm are required in order to achieve results of high quality even for the problem instances of size 100 used in the paper. For constrained problems, such as the subset sum and the minimum tardy task, the constraints are taken into account by incorporating a graded penalty term into the fitness function. Even for large instances of these highly multimodal optimization problems, an iterated application of the genetic algorithm is observed to find the global optimum within a number of runs. As the genetic algorithm samples only a tiny fraction of the search space, these results are quite encouraging.

Although several large sized 0-1 Knapsack Problems (KP) may be easily solved, it is often the case that most of the computational eort is used for preprocessing, i.e. sorting and reduction. In order to avoid this problem it has been proposed to solve the so-called core of the problem: A Knapsack Problem de ned on a small subset of the variables. But the exact core cannot be identi ed without solving KP, so till now approximated core sizes had to be used.