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562
Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach
 IEEE Transactions on Evolutionary Computation
, 1999
"... Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in ..."
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Cited by 515 (18 self)
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Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EA’s are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b) evaluating an individual’s fitness dependent on the number of external nondominated points that dominate it, c) preserving population diversity using the Pareto dominance relationship, and d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proofofprinciple results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware–software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Paretooptimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EA’s on the 0/1 knapsack problem. Index Terms — Clustering, evolutionary algorithm, knapsack problem, multiobjective optimization, niching, Pareto optimality.
QoSaware middleware for web services composition
 IEEE Trans. Software Eng
, 2004
"... 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 BusinesstoBusiness (B2B) collaborations. In particular, the creation of valueadded services by composi ..."
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Cited by 283 (5 self)
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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 BusinesstoBusiness (B2B) collaborations. In particular, the creation of valueadded 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 (tasklevel) 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
Multiobjective Optimization Using Evolutionary Algorithms  A Comparative Case Study
, 1998
"... . 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. I ..."
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Cited by 139 (10 self)
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. 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 realworld 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 Paretooptimal solutions. Mathematically, the concept of Paretooptimality can be defined as follows: Let us consider, without loss of generality, a multio...
A PTAS for the Multiple Knapsack Problem
, 1993
"... 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 fin ..."
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Cited by 97 (2 self)
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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 APXhard and a 2approximation 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 wellstudied knapsack and bin packing problems, it appears to be the strongest special case of GAP that is not APXhard. We substantiate this by showing that slight generalizations of MKP that are very restricted versions of GAP are APXhard. Thus our results help demarcate the boundary at which instances of GAP becomeAPXhard. 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.
Evaluating Evolutionary Algorithms
 Artificial Intelligence
, 1996
"... 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 se ..."
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Cited by 89 (14 self)
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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 hillclimbers. 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...
Opportunistic Fair Scheduling over Multiple Wireless Channels
, 2003
"... Emerging spread spectrum highspeed data networks utilize multiple channels via orthogonal codes or frequencyhopping 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 chan ..."
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Cited by 82 (4 self)
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Emerging spread spectrum highspeed data networks utilize multiple channels via orthogonal codes or frequencyhopping 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 multiuser scheduling problem that maximizes total system throughput and a controlupdate problem that ensures longterm deterministic or probabilistic fairness constraints. We then design and evaluate practical schedulers that approximate these objectives.
On Quality of Service Optimization with Discrete QoS Options
 In Proceedings of the IEEE Realtime Technology and Applications Symposium
, 1999
"... Quality of Service (QoS) control is considered an important user demand and therefore receives wide attention, especially in the areas of computer networks and realtime multimedia systems. In this paper we present an QoS management scheme that enables us to quantitatively measure QoS, and to analyt ..."
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Cited by 80 (4 self)
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Quality of Service (QoS) control is considered an important user demand and therefore receives wide attention, especially in the areas of computer networks and realtime 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 endusers 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 runtimes of these nearoptimal 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 realtime systems.
Strengthening Integrality Gaps for Capacitated Network Design and Covering Problems
"... A capacitated covering IP is an integer program of the form min{cxUx ≥ 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∞ ..."
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Cited by 59 (1 self)
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A capacitated covering IP is an integer program of the form min{cxUx ≥ 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 nonzero coefficients in a row of U, and provide a polynomialtime 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 nontrivial 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 polynomialtime approximation algorithms to match this bound. This improves on the best previous mapproximation, 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 (exponentiallymany) inequalities added. Our contribution here is to describe an appropriate
Maximizing The System Value While Satisfying Time And Energy Constraints
, 2002
"... this paper may be copied or distributed royalty free without further permission by computerbased and other informationservice systems. Permission to republish any other portion of this paper must be obtained from the Editor ..."
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Cited by 49 (4 self)
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this paper may be copied or distributed royalty free without further permission by computerbased and other informationservice systems. Permission to republish any other portion of this paper must be obtained from the Editor
A minimal algorithm for the 01 Knapsack Problem.
 Operations Research
, 1994
"... Although several large sized 01 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 socalled core of the problem: A Knapsack ..."
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Cited by 42 (10 self)
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Although several large sized 01 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 socalled 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.