Pareto-optimale Schedules für Kommunikation D1.2.B/C Beitrag zum ZP-AP 1 Dr. Reiger EADS IW
Was ist ein Pareto Optimum? Man bezeichnet mit Pareto-Optimierung bzw. multikriterieller Optimierung das Lösen eines Optimierungsproblems mit mehreren Zielen, also eines multikriteriellen Problemes Ein Pareto-Optimum ist ein Zustand, in dem es nicht möglich ist, einen Aspekt besser zu stellen, ohne zugleich einen anderen Aspekt schlechter zu stellen. 2
Pareto Optima S ist der Lösungsraum zur Optimierung von 2 Parametern. Die Pareto-optimalen Lösungen sind die dunkle Kante. Das Minimum bzgl. λ T 1 z über S ist x 1 und ist minimal da λ 1 >0. Das Minimum bzgl. λ T 2 z über S ist x 2, das ist ein anderer minimaler Punkt von S, da λ 2 >0. Solide Kanten sind pareto-optimale Lösungen für 2 Parameter und deren 4 mögliche Kombinationen. 3
Modelle als Inputparameter Computational models pure pure synchronous models models partially partiallysynchronous models models asynchronous models models pure pure asynchronous models models Data Datamodels shared shareddata data access accessmodes data datatypes types process processbindings data datapartitioning Process models structures, structures, graphs graphs starting, starting, terminating, suspending, aborting aborting interrupts interrupts serializability, transactions failures, failures, vitality vitality resource resourcepreemtion WCET WCET Event models & arrival models event event / / process processbindings periodic periodic sporadic sporadic aperiodic aperiodic arbitrary arbitrary Failure models always alwayscorrect intermittently permanently time timedomain: clean cleancrash crash crash crashwith withpollution past past states stateslost lost / / accessible accessible omission omission early earlytiming / / late latetiming timing Byzantine Byzantine Failure occurrence models sporadic sporadic aperiodic aperiodic unimodal unimodal arbitrary arbitrary multimodal arbitrary arbitrary 4
Nicht-funktionale Requirements als Constraints der Optimierung Logical safety Liveness Timeliness nothing nothingbad badhappens happens set set of of invariants invariants shall shall never neverbe be violated: violated: causal causal process processordering ordering atomicity atomicity transactions mutual mutual exclusion exclusion data dataconsistency process processserializability something somethingcan canalways alwayshappen process processeventually eventuallyterminates terminatesin inthe theabsence of of conflicts conflicts no nodeadlocks no nostarvation no nolivelocks something somethinggood goodhappens happensin infinite, bounded, bounded, predictable time time real real time time timeliness timelinessconstraints earliest earliest / latest / lateststart start time time earliest earliest / latest / latestdeadline linear linear / / non nonlinear linearfunction functionof ofsystem systemstate state Dependability Security system systembehavior behaviorin inpresence presenceof of partial partial failures failures space space / time / timeredundancies combines combinessafety safetyand andliveness reliability reliability availability fault faulttolerance tolerance / / replications replications safety safety / safety / safetychains security security / / immunity immunityto toattacks process processatomicity atomicity execution-wise atomic atomiccommit commit termination-wise reliable reliablebroadcast broadcast causal causal broadcast atomic atomicbroadcast agreements consensus 5
To optimize: Multi-criteria / Multi-objective Scheduling * There are three very natural points of interest: The total working time of the IMA partition The total time that the client partitions spend waiting to be processed The same value as the last one but taking into account the client weights, i.e., the relative importance of the clients (these may be emergencies which should be treated with higher priority) * Scheduling: State-of-the-art survey and algorithmic solutions / AEOLUS Algorithmic Principles for Building Efficient Overlay Computers 6
To optimize: Multi-criteria / Multi-objective Scheduling If the objective is to meet the minimum total working time of a partition and the minimum total (weighted) waiting time of the client partitions we have a bi-objective scheduling problem with one minmax objective function and one min-sum objective function However, a very natural way of processing is so as neither ordinary nor important clients wait too long. In this case, the goal is to meet the minimum total waiting time and the minimum total weighted waiting time of the clients we have a bi-objective scheduling problem with two min-sum objective functions. 7
To optimize: Multi-objective / Multi-criteria Scheduling For IMA in time- & space partitioning scheduling is a multi-objective optimization problem on parallel machines. More formally, in the basic model we are given a set of independent jobs, J = {J 1 ; J 2 ; : : : ; J n }, and a set of parallel identical machines M = {M 1 ; M 2 ; : : : ; M m }. Each job J j (j = 1; 2; : : : ; n) has a processing time p j and a weight w j. A schedule is obtained by sequencing the jobs on machines in some order. There are two objectives: The sum of completion times Σ j C j and the sum of weighted completion times Σ j w j C j where C j denotes the completion time of job J j It is: to find (α;β)-approximate schedules, which are at most α times from the optimum for Σ j C j and β times from the optimum for Σ j w j C j 8
To optimize: Multi-objective / Multi-criteria Scheduling List of more objective functions: C max minimize makespan Σ j C j minimize sum of completion times (also in a weighted variant Σ j w j C j ) Σ j F j minimize sum of flow times (also weighted Σ j w j F j ) Σ j F j -p i minimize sum of waiting times (also weighted) Σ j T j minimize sum of tardiness (also weighted Σ j w j T j ) max Tj minimize the maximal tardiness Σ j T j +E i minimize sum of deviations from deadlines (also weighted; also in variants where jobs may be omitted altogether at a penalty) 9
Multi-Objective Optimization Using Evolutionary Algorithms Kalyanmoy Deb Convex Optimization Stephen Boyd Lieven Vandenberghe Scheduling: State-of-the-art survey and algorithmic solutions AEOLUS Algorithmic Principles for Building Efficient Overlay Computers 10