E. P. K. Tsang, J. E. Borrett, and A. C. M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of the AI and Simulated Behaviour Conf., pp. 203-216, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....lead to a substantial reduction of the search space when solving CSP problems. However, little is known about the application domains of the known heuristics. This work follows the call of Tsang et al. for mapping combinations of search algorithms and labelling heuristics to application domains [13]. Rather than inferring the applications domains of (known) algorithm heuristic combinations, we here advocate inferring (known or new) algorithm heuristic combinations for application domains. Our approach is to rst formalise a CSP application domain as a model family, so as to exhibit the ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of AISB'95, pp. 203-216. IOS Press, 1995.

....reduce the search space [15] However, little is said about the application domains of these heuristics, so modellers nd it dicult to decide when to apply a particular heuristic, and when not. Indeed, there is no universally best heuristic for all instances of all constraint models (see, e.g. [16]) unless NP=P. Thus, we are only told that a particular heuristic was best for the particular instances used to carry out some experiments with some particular models. Therefore, the performance of heuristics is not only model dependent but also instance dependent, i.e. for a given constraint ....

....heuristics may lead to a substantial reduction of the search space when solving CSP models. However, little is known about the application domains of the known heuristics. This work follows the call of Tsang et al. for mapping combinations of algorithms and heuristics to application domains [16]. Rather than inferring the applications domains of (known) algorithm heuristic combinations, we here advocate inferring (known or new) algorithm heuristic combinations for application domains. Our approach is to rst formalise a CSP application domain as a model family, so as to exhibit the ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. Proc. of AISB'95, pp. 203-216, 1995. IOS Press.

....of complexity to the modelling task. For instance, the choice of the constraint formulation is strongly affected by the choice of the representation of variables and values and of the solution methods. In addition, the performance of our solution methods is sensitive to the problem instances [13, 11]. Thus, modelling combinatorial optimisation problems so as to solve them in more efficient ways is a major challenge for constraint programming (CP) A research direction on redundant modelling is emerging within the CP community, especially for some classes of problems where a dual viewpoint ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of AISB'95, pp. 203--216. IOS Press, 1995.

....to use. Lobjois and Lemaitre found that SPP works very will in practice. Their results demonstrate that it is better to use the algorithm selected by SPP, then to use the best algorithm on average for all instances. Other examples of work in this area include Tsang s work on constructing maps [31], Minton s work on con guring constraint satisfaction programs [24] and Frost s work on nding the best algorithm [14] for binary problems. Model selection For a given problem, there is generally more than one way to model it as a CSP. Selecting between various models is often dicult, and ....

E. P. K. Tsang, J. E. Borrett, and A. C. M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proceedings of the AI and Simulated Behaviour Conference, pages 203{ 216, 1995.

....of (constraint) programming research is about pushing results from the instance level to the problem level, if not to the problem class level, so as to get generic results. The difficulty of mapping the right heuristic to a given problem is mainly due to the following. As shown by Tsang et al. [17], there is no universally best solver for all instances of all problems. Thus, we are only told that a particular solver is best for the particular instances used by researchers to carry out their experiments. Therefore, as also noticed by Minton [14] the performance of solvers is ....

....The finite domain constraint store for any subset problem is over a set of Boolean variables and contains an instance dependent number of binary constraints as well as a summation constraint. For binary CSPs, a family of instances is usually characterised by a tuple hn; m; p 1 ; p 2 i [17], where n is the number of variables, m is the (assumed constant) domain size for all variables, p 1 is the (assumed constant) constraint density, and p 2 is the (assumed constant) tightness of the individual constraints. In our experiments, the variable count n is the number of Boolean ....

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E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of AISB'95, pp. 203--216. IOS Press, 1995.

....of (constraint) programming research is about pushing results from the instance level to the problem level, if not to the problem class level, so as to get generic approaches. The diculty of mapping the right heuristic to a given problem is mainly due to the following. As proven by Tsang et al. [TBK:95], there is no universally best solver for all instances of all problems. Thus, we are only able to learn that a particular solver is best for the particular instances used to carry out experiments. Therefore, as also noticed by Minton [Min:96] the performance of solvers is instance dependent, ....

....solution. Thus, under this assumption, the heuristic H1 could nd a solution very easily when a solution existed; however, in the case where there was no solution, the heuristic H1 spent a long time to prove the non existence of solutions. Secondly, as proven by Minton [Min:96] and Tsang et al. [TBK:95], the heuristics are very sensitive to di erent instances of the same problem (class) This work follows the call of Tsang et al. for mapping combinations of algorithms and heuristics to application domains [TBK:95] We here focused on just one application domain, namely a class of subset ....

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E.P.K. Tsang, J.E. Borrett, & A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. Proc. of AISB'95, pp. 203-216. IOS Press. 15

....little is said about the application domain of these heuristics, so programmers find it difficult to decide when to apply a particular heuristic and when not. The difficulty of mapping the right heuristic to a given problem is mainly due to two reasons. First, as mentioned by Tsang et al. [10], there is no universally best heuristic for all problems. Thus, we are only able to learn that a particular heuristic is best for the particular benchmarks used by researchers to carry out their experiments. Second, as noticed by Minton [8] the performance of heuristics is instancedependent, ....

....in Section 2, the clp(FD) constraint store for any subset decision problem is over a set of Boolean variables and contains an instancedependent number of binary constraints as well as an optional summation constraint. For binary CSPs, instances are characterised by a tuple hn; m; p 1 ; p 2 i [10], where n is the number of variables, m is the (constant) domain size for all variables, p 1 is the constraint density, 2 and p 2 is the tightness of the individual constraints. In our experiments, the domain size m is fixed to 2 as we need only consider the Boolean domain f0; 1g in subset ....

[Article contains additional citation context not shown here]

E.P.K. Tsang, J.E. Borret, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of AISB'95, pp. 203--216. IOS Press, 1995.

....check the validity of these values we performed an approximate randomization of the test [9] with a sample of 1000 in each case, which never gave a value above t = 3:5. This provides strong statistical evidence that the minimize heuristic is better than the FF heuristic in these problem classes. [54] give results on the same problem classes seen in Figure 9, on a range of algorithm heuristic combinations. For high values of p 1 they report that FCCBJ with the FF heuristic was the best combination studied for problems near the phase transition. The fact that the minimize heuristic can do ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Hybrid Problems, Hybrid Solutions, pages 203--216. IOS Press, 1995. Proceedings of AISB-95.

.... testing on sets of homogenous problems, such as n queens or the zebra problem [8] towards attempting to classify algorithms in terms of performance on large samples of problems of varying size, topology and position in relation to the phase transition (for instance the study by Tsang, et al. [42]) Knowledge of phase transitions should eventually allow problems to be analysed before any search is undertaken, and accurate predictions about solution probability, likely difficulty, and most suitable search method to be made. However, recent studies have highlighted a phenomenon that ....

....prevalent view that champion algorithms which perform extremely well on all types of problem do not exist. Algorithms should clearly be chosen to suit the problem characteristics, based on the knowledge gained from empirical studies such as those presented here and those presented in [42]. An area for future study is a more detailed investigation of exactly how algorithm performance scales as problem size increases. We have been able to show that MAC performance scales at a better rate than FC as problems become larger, but at present the rates of increase cannot be specified ....

E. P. K. Tsang, J. Borrett, and A. C. M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In J. Hallam, editor, Proceedings AISB-95, pages 203--216. IOS Press, Amsterdam, 1995.

....of these algorithms contain random components. While tree search techniques usually completely explore the search space, repair based methods jump around the search space looking for an approximately optimal solution. Studies repeatedly show that there is no universally best algorithm for CSOP s [14]. Because of their algorithmic systematic nature, the treesearch techniques guarantee completeness, i.e. they guarantee to find a solution if there is one. However, they cannot escape from the curse of NP completeness of CSOP s [10] solving the problem will likely require exponential time in the ....

E. Tsang, J. E. Borrett, and A. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proceedings of Artificial Intelligence and Simulated Behaviour Conference, pages 203--216, 1995.

....all other static orderings. Here, we present three new dynamic variable ordering (dvo) heuristic, derived as a result of our studies of phase transition phenomena of combinatorial problems, and compare these against two existing heuristics. Tsang, Borrett, and Kwan s study of CSP algorithms [21] shows that there does not appear to be a universally best algorithm, and that certain algorithms may be preferred under certain circumstances. We carry out a similar investigation with respect to variable ordering heuristics in an attempt to determine under what conditions one heuristic dominates ....

....ruled out. A phase transition occurs inbetween when problems are critically constrained . Such problems are usually difficult to solve as they are neither obviously soluble or insoluble. Problems from the phase transition are now routinely used to benchmark CSP and satisfiability procedures [21, 4, 7]. Constrainedness can be used both to predict the position of a phase transition in solubility [22, 19, 15, 8] and, as we show in the next section, to motivate the construction of heuristics. In this section, we identify four measures which compute some aspect of constrainedness. All of these ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Hybrid Problems, Hybrid Solutions, pages 203--216. IOS Press, 1995. Proceedings of AISB-95.

....all other static orderings. Here, we present three new dynamic variable ordering (dvo) heuristics, derived as a result of our studies of phase transition phenomena of combinatorial problems, and compare these against two existing heuristics. Tsang, Borrett, and Kwan s study of CSP algorithms [22] shows that there does not appear to be a universally best algorithm, and that certain algorithms may be preferred under certain circumstances. We carry out a similar investigation with respect to dvo heuristics in an attempt to determine under what conditions one heuristic dominates another. In ....

....all possible solutions. A phase transition occurs in between when problems are critically constrained . Such problems are usually difficult to solve as they are neither obviously soluble or insoluble. Problems from the phase transition are often used to benchmark CSP and satisfiability procedures [22, 9]. Constrainedness can be used both to predict the position of a phase transition in solubility [23, 20, 16, 7, 19] and, as we show later, to motivate the construction of heuristics. In this section, we identify four measures of some aspect of constrainedness. These measures all apply to an ....

E.P.K. Tsang, J.E. Borrett, and A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Hybrid Problems, Hybrid Solutions, pages 203--216. IOS Press, 1995. Proceedings of AISB-95.

....with n variables with uniform domain size of m, there will be m n possible assignments of variables to values. The best known complete algorithms for CSP sare exponential in the worst case. Numerous studies have been performed on random CSP s, in order to measure the performance of algorithms [4, 24, 29] and to investigate the nature of problems [21, 26] Random CSP sare typically categorised using four parameters, namely hn; m; p 1 ; p 2 i, where n is the number of variables, m is the uniform domain size, p 1 is the proportion of edges in the constraint graph (i.e. the density of the constraint ....

E.P.K. Tsang, J. Borrett, and A.C.M. Kwan, An attempt to map the performance of a range of algorithm and heuristic combinations, In Proceedings AISB-95, pages 203-216, Ed. J. Hallam, IOS Press, Amsterdam, 1995.

....with n variables with uniform domain size of m, there will be m n possible assignments of variables to values. The best known complete algorithms for CSP s are exponential in the worst case. Numerous studies have been performed on random CSP s, in order to measure the performance of algorithms [4, 24, 28] and to investigate the nature of problems [21, 25] Typically, random CSP are categorised using four parameters, namely hn; m; p 1 ; p 2 i, where n is the number of variables, m is the uniform domain size, p 1 is the proportion of edges in the constraint graph (i.e. the density of the constraint ....

E.P.K Tsang, J. Borrett, and A.C.M Kwan, An attempt to map the performance of a range of algorithm and heuristic combinations, to appear in Proceedings AISB-95 (1995)

....time for each part of the project in person months (pm) is as follows: 1.1) Constrainedness in other NP complete problems (4pm) We will evaluate if constrainedness predicts the location and shape of phase transitions in the specified problem domains. Building on the work of Tsang s group [25], we will identify regions of constrainedness where particular algorithms perform best. 1.2) Constrainedness in optimization problems (4pm) We will compare the results of (1.1) for decision problems with results for the corresponding optimization problems. 1.3) Constrainedness in other ....

E. Tsang, J. Borrett and A. Kwan. An Attempt to Map the Performance of a Range of Algorithm and Heuristic Combinations. In Proceedings of the Artificial Intelligence and Simulated Behaviour Conference,

....To check the significance of these values we performed an approximate randomization version of the test (Cohen 1995) with a sample of 1000 in each case, which never gave a value above t = 3:5. This provides strong statistical evidence that minimize is better than FF in these problem classes. (Tsang, Borrett, Kwan 1995) give results on the same problem classes seen in Figure 4, on a range of algorithm heuristic combinations. For high values of p 1 they report that fc cbj with the FF heuristic was the best combination studied for problems near the phase transition. That the minimize heuristic can do better is ....

....1995a) The constrainedness of a problem depends on the ensemble from which it is drawn. We may not know the ensemble from which a real problem is drawn, so naive measurements of may mislead us. The role of problem representation must also be taken into account, as in a study such as (Borrett Tsang 1995). Further work in this area is vital if this research is to be of value in understanding and solving real problems. Conclusions We have defined a very general parameter , pronounced kappa , that measures the constrainedness of an ensemble of combinatorial problems. This generalises and ....

Tsang, E.; Borrett, J.; and Kwan, A. 1995. An attempt to map the performance of a range of algorithm and heuristic combinations. In Hybrid Problems, Hybrid Solutions, 203--216. IOS Press.

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Tsang, E.P.K., Borrett, J.E. & Kwan, A.C.M. 1995. An Attempt to Map the Performance of a Range of Algorithm and Heuristic Combinations. In Proceedings AISB95, 203-216.

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Tsang, E.P.K, Borrett, J.E. & Kwan, A.C.M. An Attempt to Map the Performance of a Range of Algorithm and Heuristic Combinations. In Proceedings AISB-95, 203-216, 1995.

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E. P. K. Tsang, J. E. Borrett, and A. C. M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. In Proc. of the AI and Simulated Behaviour Conf., pp. 203-216, 1995.

No context found.

E.P.K Tsang, J. Borrett, and A.C.M Kwan, An attempt to map the performance of a range of algorithm and heuristic combinations, to appear in Proceedings AISB-95 (1995)

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E.P.K. Tsang, J.E. Borrett, & A.C.M. Kwan. An attempt to map the performance of a range of algorithm and heuristic combinations. Proc. of AISB'95, pp. 203--216. IOS Press.

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