For a scheduling problem to minimize the makespan on parallel machines, we consider schedules wit... more For a scheduling problem to minimize the makespan on parallel machines, we consider schedules with at most one preemption. We show that in the case of two machines the problem is solvable in polynomial time. For m ≥ 3 uniform parallel machines, we measure the quality of a single preemption as the worst-case ratio of the makespan of an optimal schedule with at most one preemption over the makespan of an optimal preemptive schedule. We show that the global bound on such a ratio is 2 − 2/m.
For scheduling problems on parallel machines, the power of preemption is defined as the supremum ... more For scheduling problems on parallel machines, the power of preemption is defined as the supremum ratio of the cost of an optimal nonpreemptive schedule over the cost of an optimal preemptive schedule (for the same input), where the cost is defined by a fixed common cost function. We present a tight analysis of the power of preemption for the problem of minimizing the total completion time on m ≥ 2 uniformly related machines, showing that its value for m = 2 is equal to 1.2, and its overall value is approximately 1.39795.
For a scheduling problem to minimize the makespan on three uniform parallel machines we present a... more For a scheduling problem to minimize the makespan on three uniform parallel machines we present a parametric analysis of the quality of a schedule with at most one preemption compared to the global optimal schedule with any number of preemptions. A tight bound is derived as a function of the relative speeds of the machines, provided that two of the machines have the same speed.
We address single-machine scheduling problems for which the actual processing times of jobs are s... more We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.
International Journal of Foundations of Computer Science, Jun 1, 2007
We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs... more We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a [Formula: see text]–approximation algorithm that outputs a two-shipment schedule. We design a [Formula: see text]–approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.
Nahm's equations are solved for the cases corresponding to the spherically symmetric SU(N) monopo... more Nahm's equations are solved for the cases corresponding to the spherically symmetric SU(N) monopoles of %'ilkinson and Bais and their solutions reconstructed using his adaptation of the Atiyah-Drinfeld-Hitchin-Manin construction for self-dual gauge fields. The analysis of this class of solutions reveals the remarkably intricate structure of the construction.
For a scheduling problem to minimize the makespan on parallel machines, we consider schedules wit... more For a scheduling problem to minimize the makespan on parallel machines, we consider schedules with at most one preemption. We show that in the case of two machines the problem is solvable in polynomial time. For m ≥ 3 uniform parallel machines, we measure the quality of a single preemption as the worst-case ratio of the makespan of an optimal schedule with at most one preemption over the makespan of an optimal preemptive schedule. We show that the global bound on such a ratio is 2 − 2/m.
For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of... more For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2-1/m is tight. If the makespan of the optimal preemptive schedule is defined by the ratio of the total processing times of r < m longest jobs over the total speed of r fastest machines, we show that the tight bound on the power of preemption is 2-1/min{r,m-r}.
For scheduling problems on parallel machines, the power of preemption is defined as the supremum ... more For scheduling problems on parallel machines, the power of preemption is defined as the supremum ratio of the cost of an optimal nonpreemptive schedule over the cost of an optimal preemptive schedule (for the same input), where the cost is defined by a fixed common cost function. We present a tight analysis of the power of preemption for the problem of minimizing the total completion time on m ≥ 2 uniformly related machines, showing that its value for m = 2 is equal to 1.2, and its overall value is approximately 1.39795.
the very success of autonomic systems has inevitably led to situations where multiple autonomic m... more the very success of autonomic systems has inevitably led to situations where multiple autonomic managers need to coexist and/or interact directly or indirectly within the same system. This is evident, for example, in the increasing availability of large datacentres with multiple [heterogeneous] managers which are independently designed. Potentially, problems can arise as a result of conflict-of-interest when these managers (components) coexist. There is a growing concern that the lack of support for interoperability will become a break issue for future systems. We present an architecture-based solution to interoperability. Our approach is based on a Trustworthy Autonomic Architecture (different from traditional autonomic computing architecture) that includes mechanisms and instrumentation to explicitly support interoperability and trustworthiness. We posit that interoperability support should be designed in and integral at the architectural level, and not treated as add-ons as it cannot be reliably retro-fitted to systems. In this work-in-progress paper, we analyse the issue of interoperability and present our approach using a datacentre multi-manager scenario.
2007 IEEE Symposium on Computational Intelligence in Scheduling, 2007
ABSTRACT We discuss the application of the multilevel (ML) refinement technique to the vehicle ro... more ABSTRACT We discuss the application of the multilevel (ML) refinement technique to the vehicle routing problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL heuristic, termed the combined node-exchange composite heuristic (CNCH), is developed first to solve instances of the VRP. A ML version (the ML-CNCH) is then created, using the construction and improvement heuristics of the CNCH at each level. Experimentation is used to find a suitable combination, which extends the global view of these heuristics. Results comparing both SL and ML are presented
ABSTRACT Graph partitioning divides a graph into several pieces by cutting edges. Very effective ... more ABSTRACT Graph partitioning divides a graph into several pieces by cutting edges. Very effective heuristic partitioning algorithms have been developed which run in real-time, but it is unknown how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. Distinctive features are the transmission and modification of whole subdomains (the partitioned units) that act as genes, and the use of a multilevel heuristic algorithm to effect the crossover and mutations. Its effectiveness is demonstrated by improvements on previously established benchmarks.
We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Pro... more We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. ...
For a scheduling problem to minimize the makespan on parallel machines, we consider schedules wit... more For a scheduling problem to minimize the makespan on parallel machines, we consider schedules with at most one preemption. We show that in the case of two machines the problem is solvable in polynomial time. For m ≥ 3 uniform parallel machines, we measure the quality of a single preemption as the worst-case ratio of the makespan of an optimal schedule with at most one preemption over the makespan of an optimal preemptive schedule. We show that the global bound on such a ratio is 2 − 2/m.
For scheduling problems on parallel machines, the power of preemption is defined as the supremum ... more For scheduling problems on parallel machines, the power of preemption is defined as the supremum ratio of the cost of an optimal nonpreemptive schedule over the cost of an optimal preemptive schedule (for the same input), where the cost is defined by a fixed common cost function. We present a tight analysis of the power of preemption for the problem of minimizing the total completion time on m ≥ 2 uniformly related machines, showing that its value for m = 2 is equal to 1.2, and its overall value is approximately 1.39795.
For a scheduling problem to minimize the makespan on three uniform parallel machines we present a... more For a scheduling problem to minimize the makespan on three uniform parallel machines we present a parametric analysis of the quality of a schedule with at most one preemption compared to the global optimal schedule with any number of preemptions. A tight bound is derived as a function of the relative speeds of the machines, provided that two of the machines have the same speed.
We address single-machine scheduling problems for which the actual processing times of jobs are s... more We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.
International Journal of Foundations of Computer Science, Jun 1, 2007
We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs... more We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a [Formula: see text]–approximation algorithm that outputs a two-shipment schedule. We design a [Formula: see text]–approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.
Nahm's equations are solved for the cases corresponding to the spherically symmetric SU(N) monopo... more Nahm's equations are solved for the cases corresponding to the spherically symmetric SU(N) monopoles of %'ilkinson and Bais and their solutions reconstructed using his adaptation of the Atiyah-Drinfeld-Hitchin-Manin construction for self-dual gauge fields. The analysis of this class of solutions reveals the remarkably intricate structure of the construction.
For a scheduling problem to minimize the makespan on parallel machines, we consider schedules wit... more For a scheduling problem to minimize the makespan on parallel machines, we consider schedules with at most one preemption. We show that in the case of two machines the problem is solvable in polynomial time. For m ≥ 3 uniform parallel machines, we measure the quality of a single preemption as the worst-case ratio of the makespan of an optimal schedule with at most one preemption over the makespan of an optimal preemptive schedule. We show that the global bound on such a ratio is 2 − 2/m.
For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of... more For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2-1/m is tight. If the makespan of the optimal preemptive schedule is defined by the ratio of the total processing times of r < m longest jobs over the total speed of r fastest machines, we show that the tight bound on the power of preemption is 2-1/min{r,m-r}.
For scheduling problems on parallel machines, the power of preemption is defined as the supremum ... more For scheduling problems on parallel machines, the power of preemption is defined as the supremum ratio of the cost of an optimal nonpreemptive schedule over the cost of an optimal preemptive schedule (for the same input), where the cost is defined by a fixed common cost function. We present a tight analysis of the power of preemption for the problem of minimizing the total completion time on m ≥ 2 uniformly related machines, showing that its value for m = 2 is equal to 1.2, and its overall value is approximately 1.39795.
the very success of autonomic systems has inevitably led to situations where multiple autonomic m... more the very success of autonomic systems has inevitably led to situations where multiple autonomic managers need to coexist and/or interact directly or indirectly within the same system. This is evident, for example, in the increasing availability of large datacentres with multiple [heterogeneous] managers which are independently designed. Potentially, problems can arise as a result of conflict-of-interest when these managers (components) coexist. There is a growing concern that the lack of support for interoperability will become a break issue for future systems. We present an architecture-based solution to interoperability. Our approach is based on a Trustworthy Autonomic Architecture (different from traditional autonomic computing architecture) that includes mechanisms and instrumentation to explicitly support interoperability and trustworthiness. We posit that interoperability support should be designed in and integral at the architectural level, and not treated as add-ons as it cannot be reliably retro-fitted to systems. In this work-in-progress paper, we analyse the issue of interoperability and present our approach using a datacentre multi-manager scenario.
2007 IEEE Symposium on Computational Intelligence in Scheduling, 2007
ABSTRACT We discuss the application of the multilevel (ML) refinement technique to the vehicle ro... more ABSTRACT We discuss the application of the multilevel (ML) refinement technique to the vehicle routing problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL heuristic, termed the combined node-exchange composite heuristic (CNCH), is developed first to solve instances of the VRP. A ML version (the ML-CNCH) is then created, using the construction and improvement heuristics of the CNCH at each level. Experimentation is used to find a suitable combination, which extends the global view of these heuristics. Results comparing both SL and ML are presented
ABSTRACT Graph partitioning divides a graph into several pieces by cutting edges. Very effective ... more ABSTRACT Graph partitioning divides a graph into several pieces by cutting edges. Very effective heuristic partitioning algorithms have been developed which run in real-time, but it is unknown how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. Distinctive features are the transmission and modification of whole subdomains (the partitioned units) that act as genes, and the use of a multilevel heuristic algorithm to effect the crossover and mutations. Its effectiveness is demonstrated by improvements on previously established benchmarks.
We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Pro... more We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. ...
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Papers by Alan Soper