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...olve a wide variety of optimization problems, given only black-box access to the tobe-optimized function. Example of such algorithms include the simulated annealing algorithm [50], genetic algorithms =-=[32]-=-, and genetic programming [53, 54]. Each of these approaches represents an active area of research unto itself, with entire conferences and hundreds of papers published every year. This thesis advance...

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...n developed that aim to solve a wide variety of optimization problems, given only black-box access to the tobe-optimized function. Example of such algorithms include the simulated annealing algorithm =-=[50]-=-, genetic algorithms [32], and genetic programming [53, 54]. Each of these approaches represents an active area of research unto itself, with entire conferences and hundreds of papers published every ...

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...ation problems, given only black-box access to the tobe-optimized function. Example of such algorithms include the simulated annealing algorithm [50], genetic algorithms [32], and genetic programming =-=[53, 54]-=-. Each of these approaches represents an active area of research unto itself, with entire conferences and hundreds of papers published every year. This thesis advances an approach that is different fr...

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...ule to solve additional test instances drawn from the same distribution. In this setting, we give bounds on the number of instances required to learn a schedule that is probably approximately correct =-=[86]-=-. We then consider an online setting in which we are fed a sequence X = 〈x1, x2, . . . , xn〉 of problem instances one at a time and must obtain a solution to each instance (via some schedule) before m...

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... problems: 1. Problem-specific theoretical analysis. Instances of this approach include the development of constant factor approximation algorithms for a wide variety of NP-hard optimization problems =-=[87]-=-, improved exponential-time algorithms [88], and analyses of algorithms for random and semi-random problems [25]. 2. Problem-specific engineering. Examples of this approach include the ongoing quest f...

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...ned by following the advice of any fixed expert for all n days. In particular, for any fixed value of Gmax, where Gmax = max1≤j≤k i=1 ��n i=1 xi � j , the randomized weighted majority algorithm (WMR) =-=[60]-=- can be used to achieve worst-case regret O �√ Gmax ln k � . If Gmax is not known in advance, a putative value can be guessed and doubled to achieve the same guarantee up to a constant factor. 2.4.2 U...

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...e novel. In particular, when the mean payoff returned by each arm is small (relative to the maximum possible payoff) our algorithm has much better performance than the recent algorithm of Auer et al. =-=[4]-=-, which is identical to our algorithm except that confidence intervals are derived using Hoeffding’s inequality. We give further discussion of related work later in this section. 129sClassical k-armed...

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...9, 21], we also consider the special case where each payoff distribution is a generalized extreme value (GEV) distribution. The motivation for studying this special case is the Extremal Types Theorem =-=[23]-=-, which singles out the GEV as the limiting distribution of the maximum of a large number of independent identically distributed (i.i.d.) random variables. Roughly speaking, one can think of the Extre...

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...a knapsack constraint. Previous work gave offline greedy approximation algorithms for this problem [56, 84], which generalized earlier algorithms for BUDGETED MAXIMUM COVERAGE [49] and MAX k-COVERAGE =-=[65]-=-. To our knowledge, none of these three problems have previously been studied in an online setting. It is worth pointing out that the online problems we consider here are quite different from online s...

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...22] [18,24] [18,∞] continued on next page. . . 118sTable 4.1 (continued from previous page) Instance SATPLAN (S2) SATPLAN (Sg) SATPLAN (original) [lower,upper] [lower,upper] [lower,upper] p20 [17,28] =-=[18,27]-=- [19,∞] p21 [20,25] [21,25] [22,∞] p22 [17,23] [18,26] [19,∞] p23 [17,25] [17,25] [18,∞] p24 [21,27] [21,28] [22,∞] p25 [20,27] [20,∞] [21,∞] p26 [19,27] [20,31] [21,∞] p27 [19,34] [20,31] [20,∞] p28 ...

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... a single step. In optimal planning, the goal is to find a plan with (provably) minimum makespan. The two winners from the optimal track of last year’s International Planning Competition were SATPLAN =-=[47]-=- and Maxplan [89]. Both planners find a minimum-makespan plan by making a series of calls to a SAT solver, where each call determines whether there exists a feasible plan of makespan ≤ k (where the va...

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... all cases, the high-level idea is to replace the unknown quantities used by OG with (unbiased) estimates of those quantities. This technique has been used in a number of online algorithms (e.g., see =-=[5, 8, 17]-=-). Specifically, for each day i and expert j, let ˆx i j ∈ [0, 1] be an estimate of x i j, such that E � ˆx i j � = γx i j + δ i for some constant δ i (which is independent of j). In order words, we r...

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...erwise. For large n, the optimal strategy is to pull arm A once and then pull arm B the remaining n − 1 times. 126s5.1.1 Related work The classical k-armed bandit problem was first studied by Robbins =-=[70]-=- and has since been the subject of numerous papers; see Berry and Fristedt [11] and Kaelbling [40] for overviews. The max variant of the k-armed bandit problem was introduced by Cicirello and Smith [1...

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...,upper] [lower,upper] p01 [5,5] [5,5] [5,5] p02 [7,7] [7,7] [7,7] p03 [8,8] [8,8] [8,8] p04 [8,8] [8,8] [8,8] p05 [9,9] [9,9] [9,9] p06 [12,12] [12,12] [12,12] p07 [13,13] [13,13] [13,13] p08 [15,17] =-=[16,17]-=- [16,∞] p09 [15,17] [15,17] [15,∞] p10 [15,15] [15,15] [15,15] p11 [16,17] [16,17] [16,∞] p12 [16,19] [17,19] [17,∞] p13 [16,18] [17,18] [17,∞] p14 [14,20] [15,19] [15,∞] p15 [18,18] [18,18] [18,18] p...

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... optimal solutions to the original minimization problem. We evaluate two versions of Brucker: the original and a modified version that uses S2. We ran both versions on the instances in the OR library =-=[10]-=- with a one hour time limit per instance, and recorded the upper and lower bounds obtained. We do not evaluate the ramp-up strategy or Sg in this context, because they were not intended to work well o...

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...ED SET COVER [44, 64], the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules [73, 78], and the problem of constructing restart schedules =-=[35, 61, 79]-=-. The problem of maximizing f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subject to a knapsack constraint [56, 84], which in turns generalizes...

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...n − 1 times. 126s5.1.1 Related work The classical k-armed bandit problem was first studied by Robbins [70] and has since been the subject of numerous papers; see Berry and Fristedt [11] and Kaelbling =-=[40]-=- for overviews. The max variant of the k-armed bandit problem was introduced by Cicirello and Smith [19, 21], whose experiments with randomized priority dispatching rules for the RCPSP/max form the ba...

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...rm B the remaining n − 1 times. 126s5.1.1 Related work The classical k-armed bandit problem was first studied by Robbins [70] and has since been the subject of numerous papers; see Berry and Fristedt =-=[11]-=- and Kaelbling [40] for overviews. The max variant of the k-armed bandit problem was introduced by Cicirello and Smith [19, 21], whose experiments with randomized priority dispatching rules for the RC...

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...lauses that is shared among successive runs on the same instance, violating this independence assumption. To generate a set of benchmark formulae, we use the instance generator supplied with blackbox =-=[46]-=- to generate 80 random logistics planning problems, using the same parameters that were used to generate the instance logistics.d from the paper by Gomes et al. [35]. 9 We then used SATPLAN to find an...

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...omains besides job shop scheduling. 107s4.1.3 Related work The ramp-up strategy was used in the original GraphPlan algorithm [13] for A.I. planning, and is conceptually similar to iterative deepening =-=[52]-=-. In the A.I. planning community, alternatives to the ramp-up strategy were investigated by Rintanen [69], who proposed two algorithms. Algorithm A runs the decision procedure on the first n decision ...

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...e expected behavior as the original version, and thus by linearity of expectation the overall worst-case regret bounds are unchanged. This approach has been used in other online algorithms (e.g., see =-=[42]-=-). 3.6.3 Online greedy algorithm In §3.1.4 we showed that the online problem considered in this chapter satisfies the sufficient conditions required by the online greedy algorithm for MIN-SUM SUBMODUL...

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... f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subject to a knapsack constraint [56, 84], which in turns generalizes BUDGETED MAXIMUM COVERAGE =-=[49]-=- and MAX k-COVERAGE [65]. Prior to our work, many of these problems had only been considered in an offline setting. For the problems that had been considered in an online setting, the online algorithm...

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...resh random seed. In particular, solvers based on chronological backtracking often exhibit heavy-tailed run length distributions, and restarts can yield order-of-magnitude improvements in performance =-=[34, 35]-=-. Pr[run not finished] Pr[run not finished] 1 0.8 0.6 0.4 0.2 satz-rand running on logistics.d (length 14) 0 0.1 1 10 100 1000 1 0.8 0.6 0.4 0.2 time (s) satz-rand running on logistics.d (length 13) 0...

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...of a heuristic may vary by orders of magnitude across seemingly similar problem instances or, if the heuristic is randomized, across multiple runs on a single instance that use different random seeds =-=[33, 38]-=-. For this reason, after running a heuristic unsuccessfully for some time one might decide to suspend the execution of that heuristic and start running a different heuristic (or the same heuristic wit...

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...a standard model of social network dynamics, the total number of potential customers that are influenced by the advertisement is a submodular function of the set of agents that are initially infected =-=[48]-=-. Previous work [48] gave an algorithm for selecting a set of agents to initially infect so as to maximize the influence of an advertisement, assuming the dynamics of the social network are known. In ...

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...ED SET COVER [44, 64], the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules [73, 78], and the problem of constructing restart schedules =-=[35, 61, 79]-=-. The problem of maximizing f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subject to a knapsack constraint [56, 84], which in turns generalizes...

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...analysis. Instances of this approach include the development of constant factor approximation algorithms for a wide variety of NP-hard optimization problems [87], improved exponential-time algorithms =-=[88]-=-, and analyses of algorithms for random and semi-random problems [25]. 2. Problem-specific engineering. Examples of this approach include the ongoing quest for efficient Boolean satisfiability solvers...

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... and analyses of algorithms for random and semi-random problems [25]. 2. Problem-specific engineering. Examples of this approach include the ongoing quest for efficient Boolean satisfiability solvers =-=[91]-=-, and algorithms for solving specific operations research problems such as job shop scheduling [39]. 3. Black-box optimization. A number of algorithms have been developed that aim to solve a wide vari...

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...ze the number of intrusions that are detected by the sensors). Many sensor placement problems can be optimally solved by maximizing a monotone submodular set function subject to a knapsack constraint =-=[55]-=-. As discussed in §2.1.4, this problem is a special case of BUDGETED MAXIMUM SUBMODULAR COVERAGE. Our online algorithms could be used to select sensor placements when the same set of sensors is repeat...

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...of a heuristic may vary by orders of magnitude across seemingly similar problem instances or, if the heuristic is randomized, across multiple runs on a single instance that use different random seeds =-=[33, 38]-=-. For this reason, after running a heuristic unsuccessfully for some time one might decide to suspend the execution of that heuristic and start running a different heuristic (or the same heuristic wit...

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... . . . , U}. The optimal query strategy is simply the optimum binary search tree for the access sequence 〈OP T1, OP T2, . . . , OP Tn〉, which can be computed in O(U 2 ) time using dynamic programming =-=[51]-=-. Similarly, if we consider arbitrary τi but restrict ourselves to queries of the form 〈k, ∞〉 (so that again all queries succeed), dynamic programming can be used to compute an optimal query strategy....

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...f n days in analogy to (3.11), but only considering the days on which expert j made a prediction: max 1≤l≤M � n� w i jr i � l − i=1 n� w i jr i ei . (3.12) Generalizing previous work by Freund et al. =-=[29]-=-, Blum and Mansour [12] presented an algorithm for selecting experts in this setting whose j regret is O �√ n log M + log M � , simultaneously for each j. In fact, the algorithm of Blum and Mansour is...

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...cting restart schedules [35, 61, 79]. The problem of maximizing f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subject to a knapsack constraint =-=[56, 84]-=-, which in turns generalizes BUDGETED MAXIMUM COVERAGE [49] and MAX k-COVERAGE [65]. Prior to our work, many of these problems had only been considered in an offline setting. For the problems that had...

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...aints, also known as zero-one integer programming. On many benchmarks, pseudo-Boolean optimizers (which are usually based on SAT solvers) outperform general integer programming packages such as CPLEX =-=[2]-=-. The PB’07 evaluation included both optimization and decision (feasibility) problems from a large number of domains, including formal verification and logic synthesis, as well as various numerical an...

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... all cases, the high-level idea is to replace the unknown quantities used by OG with (unbiased) estimates of those quantities. This technique has been used in a number of online algorithms (e.g., see =-=[5, 8, 17]-=-). Specifically, for each day i and expert j, let ˆx i j ∈ [0, 1] be an estimate of x i j, such that E � ˆx i j � = γx i j + δ i for some constant δ i (which is independent of j). In order words, we r...

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...] [lower,upper] [lower,upper] p01 [5,5] [5,5] [5,5] p02 [7,7] [7,7] [7,7] p03 [8,8] [8,8] [8,8] p04 [8,8] [8,8] [8,8] p05 [9,9] [9,9] [9,9] p06 [12,12] [12,12] [12,12] p07 [13,13] [13,13] [13,13] p08 =-=[15,17]-=- [16,17] [16,∞] p09 [15,17] [15,17] [15,∞] p10 [15,15] [15,15] [15,15] p11 [16,17] [16,17] [16,∞] p12 [16,19] [17,19] [17,∞] p13 [16,18] [17,18] [17,∞] p14 [14,20] [15,19] [15,∞] p15 [18,18] [18,18] [...

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...(3.11), but only considering the days on which expert j made a prediction: max 1≤l≤M � n� w i jr i � l − i=1 n� w i jr i ei . (3.12) Generalizing previous work by Freund et al. [29], Blum and Mansour =-=[12]-=- presented an algorithm for selecting experts in this setting whose j regret is O �√ n log M + log M � , simultaneously for each j. In fact, the algorithm of Blum and Mansour is more general in that i...

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... randomized heuristic and returning the best solution obtained. Despite their simplicity, multi-start heuristics are used widely in practice, and represent the state of the art in a number of domains =-=[14, 20, 27]-=-. A max k-armed bandit strategy can be used to distribute trials among different multi-start heuristics or among different parameter settings for the same multi-start heuristic. Previous work has demo...

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...r each of the two objectives just defined, the problem introduced in this chapter generalizes a number of previously-studied problems. The problem of minimizing c (f, S) generalizes MIN-SUM SET COVER =-=[26]-=-, PIPELINED SET COVER [44, 64], the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules [73, 78], and the problem of constructing restart s...

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...edule in practice. Priority dispatching rules are therefore augmented to perform a limited amount of backtracking in order to increase the odds of producing a feasible schedule. For more details, see =-=[66]-=-. Cicirello and Smith describe experiments with randomized priority dispatching rules, in which the next activity to schedule is chosen from a probability distribution, with the probability assigned t...

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...,9] p06 [12,12] [12,12] [12,12] p07 [13,13] [13,13] [13,13] p08 [15,17] [16,17] [16,∞] p09 [15,17] [15,17] [15,∞] p10 [15,15] [15,15] [15,15] p11 [16,17] [16,17] [16,∞] p12 [16,19] [17,19] [17,∞] p13 =-=[16,18]-=- [17,18] [17,∞] p14 [14,20] [15,19] [15,∞] p15 [18,18] [18,18] [18,18] p16 [17,21] [19,22] [19,∞] p17 [19,21] [20,22] [20,∞] p18 [19,22] [19,23] [19,∞] p19 [17,22] [18,24] [18,∞] continued on next pag...

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...one to construct a single collection of sets that cover each element in a sequence of elements that arrive online [1, 7]. Likewise, our work is orthogonal to work on online facility location problems =-=[62]-=-. The main technical contribution of this chapter is to convert some specific greedy approximation algorithms into online algorithms. Recently, Kakade et al. [41] gave a generic procedure for converti...

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... τ) ∈ V × R>0 is called an action, and specifies that time τ is to be invested in activity v. A schedule is a sequence of actions. We denote by S the set of all schedules. A job is a function f : S → =-=[0, 1]-=-, where for any S ∈ S, f(S) equals the proportion of some task that is accomplished after performing the sequence of actions S. We require that a job f satisfy the following conditions (here ⊕ is the ...

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...e subsections is duplicated in the introductory sections of the corresponding chapters. The results in this thesis are based in part on five conference papers [78, 79, 80, 82, 83] and a working paper =-=[76]-=-. 1.1.1 Online algorithms for maximizing submodular functions In this chapter we develop algorithms for solving a class of online resource allocation problems, which can be described formally as follo...

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... all cases, the high-level idea is to replace the unknown quantities used by OG with (unbiased) estimates of those quantities. This technique has been used in a number of online algorithms (e.g., see =-=[5, 8, 17]-=-). Specifically, for each day i and expert j, let ˆx i j ∈ [0, 1] be an estimate of x i j, such that E � ˆx i j � = γx i j + δ i for some constant δ i (which is independent of j). In order words, we r...

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... by pulling the single best arm n times) and the expected cumulative payoff the algorithm receives on the instance. Chernoff Interval Estimation is simply the well-known interval estimation algorithm =-=[40, 57]-=- with confidence intervals derived using Chernoff’s inequality. Although various interval estimation algorithms have been analyzed in the literature and a variety of guarantees have been proved, both ...

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...cting restart schedules [35, 61, 79]. The problem of maximizing f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subject to a knapsack constraint =-=[56, 84]-=-, which in turns generalizes BUDGETED MAXIMUM COVERAGE [49] and MAX k-COVERAGE [65]. Prior to our work, many of these problems had only been considered in an offline setting. For the problems that had...

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... of selecting an appropriate schedule in three settings: offline, learning-theoretic, and online. The results in this chapter significantly generalize and extend previous work on algorithm portfolios =-=[33, 38, 68, 73, 90]-=- and restart schedules [31, 35, 61]. The problem considered in this chapter can be described formally as follows. We are 5sgiven as input a set H of (randomized) algorithms for solving some decision p...

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...n without maximal time lags (which make the problem more difficult), the resourceconstrained project scheduling problem is NP-hard and is “one of the most intractable problems in operations research” =-=[63]-=-. When maximal time lags are included, even the feasibility problem (i.e., deciding whether a feasible schedule exists) is NP-hard. Our experimental evaluation focuses on Threshold Ascent. In these ex...

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...es just defined, the problem introduced in this chapter generalizes a number of previously-studied problems. The problem of minimizing c (f, S) generalizes MIN-SUM SET COVER [26], PIPELINED SET COVER =-=[44, 64]-=-, the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules [73, 78], and the problem of constructing restart schedules [35, 61, 79]. The pro...

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...g query strategies 11sto branch and bound algorithms, which seems likely to be useful in other domains besides job shop scheduling. 1.1.4 The max k-armed bandit problem The max k-armed bandit problem =-=[19, 21]-=- can be described as follows. Imagine that you find yourself in the following unusual casino. The casino contains k slot machines. Each machine has an arm that, when pulled, yields a payoff drawn from...

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...has also been used to describe approaches that use features of instances to attempt to predict which algorithm will run the fastest on a given instance, and then simply run that algorithm exclusively =-=[59, 90]-=-. Note that in this approach there is no notion of a schedule per se. As already mentioned, we show how instance-specific features can be incorporated into our framework later in this chapter. The wor...

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...imental results. Some of the text in these subsections is duplicated in the introductory sections of the corresponding chapters. The results in this thesis are based in part on five conference papers =-=[78, 79, 80, 82, 83]-=- and a working paper [76]. 1.1.1 Online algorithms for maximizing submodular functions In this chapter we develop algorithms for solving a class of online resource allocation problems, which can be de...

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...universal schedule is optimal to within constant factors). Several papers have considered the case in which partial but not complete knowledge of the run length distribution is available. Ruan et al. =-=[71]-=- consider the case in which each run length distribution is one of m known distributions, and give a dynamic programming algorithm for computing an optimal restart schedule. The running time of their ...

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...an be incorporated into our framework later in this chapter. The works just described consider the problem of learning an algorithm portfolio from 51straining data. Recently, Gagliolo and Schmidhuber =-=[30]-=- presented an algorithm that, like our online algorithms, can be used to select algorithm portfolios on-the-fly while solving a sequence of problem instances. Their algorithm produces resource-sharing...

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...ortfolio offline given knowledge of the run length distribution of each algorithm, under the assumption that each algorithm has the same run length distribution on all problem instances. Earlier work =-=[43]-=- considered the problem of devising a schedule for combining multiple heuristics that achieves an optimal competitive ratio on a single problem instance. A recent paper by Sayag et al. [73] considered...

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... on online facility location problems [62]. The main technical contribution of this chapter is to convert some specific greedy approximation algorithms into online algorithms. Recently, Kakade et al. =-=[41]-=- gave a generic procedure for converting an α-approximation algorithm for a linear problem into an online algorithm whose α-regret is o (n), and this procedure could be applied to the problems conside...

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...es just defined, the problem introduced in this chapter generalizes a number of previously-studied problems. The problem of minimizing c (f, S) generalizes MIN-SUM SET COVER [26], PIPELINED SET COVER =-=[44, 64]-=-, the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules [73, 78], and the problem of constructing restart schedules [35, 61, 79]. The pro...

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... suspendand-resume and probabilistic schedules, are no more powerful than ordinary restart schedules (assuming the restart schedule’s performance is measured on a single problem instance). Alt et al. =-=[3]-=- gave related results, with a focus on minimizing tail probabilities rather than expected running time. 2 The universal schedule can be described as follows. All run lengths are powers of two, and as ...

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... improved performance in practice. Second, we modified the RSM heuristic to improve its performance. Instances We evaluate our approach on a set of 169 RCPSP/max instances from the ProGen/max library =-=[74]-=-. These instances were selected as follows. We first ran the heuristic LPF (the heuristic identified by Cicirello and Smith as having the best performance) 10,000 times on all 540 instances from the T...

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...p19 [17,22] [18,24] [18,∞] continued on next page. . . 118sTable 4.1 (continued from previous page) Instance SATPLAN (S2) SATPLAN (Sg) SATPLAN (original) [lower,upper] [lower,upper] [lower,upper] p20 =-=[17,28]-=- [18,27] [19,∞] p21 [20,25] [21,25] [22,∞] p22 [17,23] [18,26] [19,∞] p23 [17,25] [17,25] [18,∞] p24 [21,27] [21,28] [22,∞] p25 [20,27] [20,∞] [21,∞] p26 [19,27] [20,31] [21,∞] p27 [19,34] [20,31] [20...

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...imental results. Some of the text in these subsections is duplicated in the introductory sections of the corresponding chapters. The results in this thesis are based in part on five conference papers =-=[78, 79, 80, 82, 83]-=- and a working paper [76]. 1.1.1 Online algorithms for maximizing submodular functions In this chapter we develop algorithms for solving a class of online resource allocation problems, which can be de...

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...GraphPlan algorithm [13] for A.I. planning, and is conceptually similar to iterative deepening [52]. In the A.I. planning community, alternatives to the ramp-up strategy were investigated by Rintanen =-=[69]-=-, who proposed two algorithms. Algorithm A runs the decision procedure on the first n decision problems in parallel, each at equal strength, where n is a parameter. Algorithm B runs the decision proce...

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...imental results. Some of the text in these subsections is duplicated in the introductory sections of the corresponding chapters. The results in this thesis are based in part on five conference papers =-=[78, 79, 80, 82, 83]-=- and a working paper [76]. 1.1.1 Online algorithms for maximizing submodular functions In this chapter we develop algorithms for solving a class of online resource allocation problems, which can be de...

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...g query strategies 11sto branch and bound algorithms, which seems likely to be useful in other domains besides job shop scheduling. 1.1.4 The max k-armed bandit problem The max k-armed bandit problem =-=[19, 21]-=- can be described as follows. Imagine that you find yourself in the following unusual casino. The casino contains k slot machines. Each machine has an arm that, when pulled, yields a payoff drawn from...

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...ree settings: offline, learning-theoretic, and online. The results in this chapter significantly generalize and extend previous work on algorithm portfolios [33, 38, 68, 73, 90] and restart schedules =-=[31, 35, 61]-=-. The problem considered in this chapter can be described formally as follows. We are 5sgiven as input a set H of (randomized) algorithms for solving some decision problem. Given a problem instance, e...

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...imizing c (f, S) generalizes MIN-SUM SET COVER [26], PIPELINED SET COVER [44, 64], the problem of constructing efficient sequences of trials [22], the problem of constructing task-switching schedules =-=[73, 78]-=-, and the problem of constructing restart schedules [35, 61, 79]. The problem of maximizing f(S〈T 〉) for some fixed T > 0 generalizes the problem of maximizing a monotone submodular set function subje...

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...n optimal planning, the goal is to find a plan with (provably) minimum makespan. The two winners from the optimal track of last year’s International Planning Competition were SATPLAN [47] and Maxplan =-=[89]-=-. Both planners find a minimum-makespan plan by making a series of calls to a SAT solver, where each call determines whether there exists a feasible plan of makespan ≤ k (where the value of k varies a...

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...continued on next page. . . 118sTable 4.1 (continued from previous page) Instance SATPLAN (S2) SATPLAN (Sg) SATPLAN (original) [lower,upper] [lower,upper] [lower,upper] p20 [17,28] [18,27] [19,∞] p21 =-=[20,25]-=- [21,25] [22,∞] p22 [17,23] [18,26] [19,∞] p23 [17,25] [17,25] [18,∞] p24 [21,27] [21,28] [22,∞] p25 [20,27] [20,∞] [21,∞] p26 [19,27] [20,31] [21,∞] p27 [19,34] [20,31] [20,∞] p28 [19,27] [20,∞] [21,...

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...g schedules offline. As proved by Sayag et al. (Lemma 1 of [73]), an optimal task-switching schedule always performs as well or better than an optimal resource-sharing schedule. Independently, Petrik =-=[67]-=- and Petrik and Zilberstein [68] gave exact and approximation algorithms for computing optimal task-switching schedules and optimal resourcesharing schedules. Their algorithms are based on dynamic pro...

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...imental results. Some of the text in these subsections is duplicated in the introductory sections of the corresponding chapters. The results in this thesis are based in part on five conference papers =-=[78, 79, 80, 82, 83]-=- and a working paper [76]. 1.1.1 Online algorithms for maximizing submodular functions In this chapter we develop algorithms for solving a class of online resource allocation problems, which can be de...

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...our problem formulation captures a number of previouslystudied problems, including selection of algorithm portfolios [33, 38], selection of restart schedules [35, 61], and database query optimization =-=[9, 64]-=-. Additionally, this online algorithm forms the basis for many of the theoretical and experimental results in Chapter 3, “Combining Multiple Heuristics Online”. 2.1.1 Formal setup The problem consider...

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...ternational Planning Competition, with a one hour time limit per instance, and recorded the upper and lower bounds we obtained. To obtain an initial upper bound, we ran the satisficing planner SGPlan =-=[37]-=- with a one minute time limit. We chose SGPlan because it won first prize in the satisficing planning track of last year’s competition. If SGPlan found a feasible plan within the one minute time limit...

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...euristic makes use of chronological backtracking one could examine how much of the search tree has already been pruned. One could also leverage 103sexisting techniques for deliberation control (e.g., =-=[58, 72]-=-). Exploiting information of this sort is an interesting prospect, both from an experimental and a theoretical point of view. 3.10 Conclusions This chapter presented algorithms for combining multiple ...

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...euristic makes use of chronological backtracking one could examine how much of the search tree has already been pruned. One could also leverage 103sexisting techniques for deliberation control (e.g., =-=[58, 72]-=-). Exploiting information of this sort is an interesting prospect, both from an experimental and a theoretical point of view. 3.10 Conclusions This chapter presented algorithms for combining multiple ...

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...lems we consider here are quite different from online set cover problems that require one to construct a single collection of sets that cover each element in a sequence of elements that arrive online =-=[1, 7]-=-. Likewise, our work is orthogonal to work on online facility location problems [62]. The main technical contribution of this chapter is to convert some specific greedy approximation algorithms into o...

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...g an optimal restart schedule. The running time of their algorithm is exponential in m, and thus it is practical only when m is small (in the paper the algorithm is described for m = 2). Kautz et al. =-=[45]-=- considered the case in which, after running for some fixed amount of time, one observes a feature that gives the distribution of that run’s length. A paper by Gagliolo & Schmidhuber [31] considered t...

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... These results are especially promising given that the technique used to obtain them is domain-independent and could be applied to other branch and bound algorithms. In related work, Streeter & Smith =-=[81]-=- improved the performance of Brucker by using an iterated local search algorithm for job shop scheduling to obtain valid upper bounds and also to refine the branch ordering heuristic. To better unders...

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...ant factor approximation algorithms for a wide variety of NP-hard optimization problems [87], improved exponential-time algorithms [88], and analyses of algorithms for random and semi-random problems =-=[25]-=-. 2. Problem-specific engineering. Examples of this approach include the ongoing quest for efficient Boolean satisfiability solvers [91], and algorithms for solving specific operations research proble...

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...d on the behavior of the function τ. For most decision procedures used in practice, we expect τ(k) to be an increasing function 109sfor k ≤ OP T and a decreasing function for k ≥ OP T . Previous work =-=[75, 85]-=- has shown that this behavior is prevalent in planning domains (e.g., see the behavior of siege illustrated in Figure 4.1), and our query strategies are designed to take advantage of it. More specific...

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...d on the behavior of the function τ. For most decision procedures used in practice, we expect τ(k) to be an increasing function 109sfor k ≤ OP T and a decreasing function for k ≥ OP T . Previous work =-=[75, 85]-=- has shown that this behavior is prevalent in planning domains (e.g., see the behavior of siege illustrated in Figure 4.1), and our query strategies are designed to take advantage of it. More specific...