注塑成型中时间和能效调度的多目标方法外文文献翻译、中英文翻译
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A Multi-Objective Approachfor both Makespan- and Energy-EfficientScheduling in Injection MoldingKlaas D ahlmann(B)and J urgen SauerDepartment of Computing Science, University of Oldenburg,Uhlhornsweg 84, 26129 Oldenburg, Germanyklaas.daehlmann,juergen.saueruni-oldenburg.deAbstract. Recent sustainability efforts require machine schedulingapproaches to consider energy efficiency in the optimization of sched-ules. In this paper, an approach to reduce power peaks while maintain-ing the makespan is proposed and evaluated. The central concept of theapproach is to slowly equalize highs and lows in the energy input ofthe schedule without affecting the makespan through an iterative opti-mization. The approach is based on the simulated annealing algorithmto optimize machine schedules regarding the makespan and the energyinput, using the goal programming method as the objective function.Keywords: Energy efficiencyGoal programmingMulti-objectiveoptimizationSchedulingSimulated annealing1IntroductionLarge-scale facilities and devices such as industrial machines, air-condition, aswell as computer and server systems may unnecessarily load the power grid ifthey are operated in parallel and especially if they have unsteady power con-sumption. Temporarily switching offone or many appliances not essential tothe business processes may be one option to solve this problem. But, if thepower consumption of the individual is known or well documented, the appli-ances may instead be parallelized in such a way that unnecessary peak loads canbe avoided altogether without severely affecting the business processes. Espe-cially with regard to the scheduling of industrial machines, this concept mayalready be utilized at a predictive planning level to generate energetically idealschedules without sacrificing an already good makespan.This paper therefore presents an approach for the optimization of the totalenergy input while maintaining a near-optimal makespan using the example ofdiscontinuous plastics processing via injection molding machines. The approachis then examined through a combinatorial evaluation, describing, testing, andassessing different, plausible parameter settings.The challenge herein is that the injection molding cycles of different productsand machines do not have the same duration and power consumption throughoutc? Springer International Publishing AG 2016G. Friedrich et al. (Eds.): KI 2016, LNAI 9904, pp. 141147, 2016.DOI: 10.1007/978-3-319-46073-4 12142K. D ahlmann and J. Sauerthe cycle as well as the fact that the highs and lows of the energy input are notequally spaced and symmetrical.The different injection molding machines considered for this paper are shownin Table1. The steps cooling and melting start at the same time and run inparallel.Table 1. Individual steps, durations and power consumption of the injection moldingcycles of the machines considered.StepEngel victory 750/140 techEngel ES 2550/400 HLKraussMaffei KM420-2700C1DurationPowerDurationPowerDurationPowerClamping3s1.8kW7s14.08kW5s14.85kWNozzle1s1.2kW1s9.39kW1s9.9kWInjecting3s7.2kW6s56.31kW6s59.4kWDwelling3s1.2kW5s9.39kW5s9.9kWCooling11s4.22kW29s32.98kW27s34.79kWMelting7s5.98kW20s46.8kW22s49.37kWOpening3s0.32kW6s2.48kW7s2.62kWEjecting1s0.4kW3s3.13kW0s3.3kWDemolding2s0.17kW0s1.34kW0s1.41kWSet-up25min-60min-150min-These issues, both machine scheduling and energy-efficient production, havehad increased recent consideration: Multi-objective optimization approaches forjob and flow shop problems have been sucessfully used to either create the paretofront of possible solutions for an a posteriori evaluation 3,5 or to compare theresults of different local search heuristics for the special case of no-wait scheduling10. Holistic simulation and forecasting systems have been employed to examinemutual dependencies and reciprocal effects regarding the energy efficiency of theappliances 4,6 while evolutionary/genetic algorithms have been successfullyutilized for energy optimization within the context of parallel machines andcloud service scheduling 9,11, pp. 191224.2ApproachAs the scheduling of injection molding machines and jobs is based on combi-natorial and NP-hard optimization problems 1, p. 51, the trajectory-basedsimulated annealing algorithm 2,7 instead of a mathematically exact methodis chosen. The initial solution is constructed while attempting to balance pro-duction jobs on the available machines, thereby minimizing the total makespan.The main objective of the optimization is to reduce the power peaks within theinitial solution without negatively affecting the makespan while doing so.Minimizing the makespan by parallelizing as many jobs as possible increasesthe total energy input and may cause unwanted power peaks. However, tryingA Multi-Objective Approach for Scheduling in Injection Molding143to minimize energy consumption means to run as few machines as possible inparallel. In this paper, this dilemma will be counteracted by using the goal pro-gramming objective function to define aspiration levels or goals for each objectiveand subsequently attempting to find solutions to the scheduling problems con-sidered that reach these goals with the least deviation. As simulated annealingonly genereates a single solution, a posteriori objective functions are not suitedfor further consideration. Goal programming on the other hand is an a prioriobjective function that permits an equal examination of all objectives 8. Thegoal factors are relative to the initial solution, e.g. a goal factor of 1 describesa goal value that is identical to the initial solution while goal factor of 1.5 and0.5 means a goal value that is 50% larger or smaller respectively and a goalfactor of 0 describes a utopian zero value. Because the objectives considered inmulti-objective decision making are often measured on different scales (in thiscase time in seconds and energy input in watts), a subsequent standardizationof the scales is necessary to make them comparable. The solution is then ratedusing a distance function to determine the deviation between the current andthe goal values.The neighborhood function used for the simulated annealing algorithm selectsa random, active machine at the instant of time of a random power peak to shiftthe current and all future jobs one time unit towards the end, slowly resolvingpower peaks originating from unfavorable parallelization in the process.3EvaluationThe aim of the evaluation is twofold: On the one hand, different distance func-tions are evaluated in their applicability for bi-objective optimization regardingtime-based and energy-based objectives. On the other hand, as energy-efficientoptimization is a rather recent consideration, utopian and realistic goals for thepower peak are compared with regard to their feasibility. The underlying ideaof the evaluation is to systematically observe the behavior of the power peaks ofthe resulting schedules and to describe their dependency on the makespan, theobjective function as well as the structure of the initial solution.3.1MethodTo mimic the layout of the local company the machine data of which wasobtained from, two machines of each type shown in Table1 will be assumed forthe following evaluation, making a total of six machines. The simulated anneal-ing parameters remain unchanged for the entire evaluation. The algorithm startsat an initial temperature of 1 and is iteratively cooled by 1% until it reaches orfalls below the minimal temperature of 0.01. Two different initial solutions areexamined in the evaluation. The first solution assumes constant production onall machines after an initial setup time while the second solution consists of twoto four equidistant changeovers to alternative product variants on each machine144K. D ahlmann and J. Sauerduring the observation period, depending on the size of the machine. The obser-vation period itself is a single work shift of 8h for all experiments. Three commondistance functions are individually examined as objective functions for the goalprogramming method: The euclidean distance, the manhattan/taxicab distance,or the maximum/Chebyshev/chessboard distance. Moreover, six different goalsregarding the makespan are set and analyzed. A utopian goal with a makespanof zero as well as five further goals, starting at a goal identical to the initialsolutions makespan and increasing in 5% steps up to 20% more makespan.The last parameter of the evaluation is the goal factor for the power peak, withtwo different goals being compared. The first goal is the utopian goal as wellwhile the second, realistic goal is calculated based on the average power peaksof the first set of evaluations using the utopian goal. These parameters and theirassignments make a total of 72 different combinations. Each combination is thenindependently run 20 times to avoid some statistical deviation due to the randomsimulated annealing and neighborhood function.3.2ResultsThe results of the evaluation are divided into four categories, one for each com-bination of changeovers in the initial solution (with or without) and power peakgoal factor (utopian or realistic). For reference, both initial solutions, with orwithout changeovers, have a duration of 8h and a power peak of 348.3kW.Without Changeover and Utopian Power Peak Goal Factor. A utopiangoal for the makespan results in a plan that has only little improvement onthe power peak but also does not increase the makespan at all. Results frommakespan goal factor 1 depend on the chosen distance function: For the euclid-ean distance, the average power peak is identical to the solution using a utopianmakespan goal while the makespan is slightly longer. For the manhattan dis-tance, the results are identical to the utopian makespan goal. For the maximumdistance, the results are located in the same value range as those for makespangoal factor 1.1 to 1.2, as further described below. For the euclidean and the man-hatten distance, a makespan goal factor of 1.05 creates solutions that have theirpower peaks reduced by 20 to 15kW and are approximately 2min longer thanthe initial solution. For the maximum distance, the results are again in the samevalue range as those with from goal factor 1.1 to 1.2. Makespan goal factors 1.1,1.15, and 1.2 generate results that decrease the power peak by roughly 30 to40kW while increasing the makespan by about 3min.With Changeover and Utopian Power Peak Goal Factor. For the utopianmakespan goal factor 0, the results for the euclidean and manhattan distancehave their power peak reduced by about 30kW peak without affecting themakespan, while for the maximum distance, the power peak does not changemuch at all. Regarding the solutions for makespan goal factor 1, these are, incase of the manhattan distance, either identical to those obtained with a goalA Multi-Objective Approach for Scheduling in Injection Molding145factor of 0, in case of the euclidean distance slightly longer but with identicalpower peak, or, in case of the maximum distance, located in the same valuerange as all further goal factors. The average results for makespan goal factors1.05 to 1.2 have their power peaks reduced between 50 and 60kW while havingtheir makespan increased by almost 2min.Without Changeover and Realistic Power Peak Goal Factor. Whensetting realistic goals for the power peak, the results of the euclidean distanceare similar to those of the manhattan distance throughout all makespan goalfactors. For goal factors 0 and 1, the results again show just little improvementof the power peak but do not increase the makespan. For the euclidean andmanhattan distance, goal factor 1.05 results in solutions that have a roughly10kW reduced power peak, just slightly better than those generated with goalfactors 0 and 1, but have their makespan increased by about 2min. Resultsgenerated by makespan goal factors 1.1 to 1.2 have their power peaks reducedby 25 to 30kW while simultaneously having their makespan increased by about3min. The results when using the maximum distance are significantly differentfrom those described above. A utopian makespan goal creates almost no changeat all for both the power peak and the makespan. Results from goal factors 1to 1.2 have their power peaks reduced by roughly 20 to 30kW but at the sametime have their makespan increased by up to 7min.With Changeover and Realistic Power Peak Goal Factor. The resultsfor the euclidean and the manhattan distance are again comparable. Makespangoal factors 0 and 1 generate solutions with almost 30kW smaller power peakswhile not increasing the makespan of the results. Goal factors 1.05 to 1.2 reducethe power peaks of the results even further by 55 to almost 60kW, but increasethe makespan by 2min. The results generated using the maximum distance areagain different from those using the euclidean or manhattan distance. For autopian makespan goal there is again no change for neither the power peak northe makespan. For all other evaluated goal factors, the power peak is reducedby about 55 to 60kW, but the makespan progressively increases from 1min atgoal factor 1 to 9min increase at goal factor 1.2.3.3DiscussionSeveral different properties and behaviors can be derived from the evaluation:Regarding the behavior of the three distance functions examined, it is evidentthat there is no direct linear dependency between the makespan and the powerpeak. Allowing for an increase in makespan does not automatically imply aproportional reduction of the power peak. Instead, the power peaks of the solu-tion become more balanced and equalized with every iteration of the optimiza-tion, resulting in plans that cannot be further improved within the up to 20%makespan increase considered in the evaluation. This power peak limit is reachedwhen using a makespan goal factor of 1.1 or higher, in some cases even earlier.146K. D ahlmann and J. SauerContinuing on to the individual analysis of the distance functions, the behav-ior of the euclidean and manhattan distance is comparable while the resultsgenerated using the maximum distance differ significantly. In general, when com-paring the results of the euclidean and manhattan distance, using a utopianpower peak goal causes the individual solutions scatter more around the averagesolutions than they do when using a realistic power peak goal. When setting autopian makespan goal, the euclidean and manhattan distance can create resultsthat have a reduced power peak without affecting the makespan at all. Theactual amount of improvement depends on the initial solution with just a slightimprovement using a plan without changeovers to a more significant improve-ment when starting from a solution with frequent changeovers. This is because itis more difficult to move power peaks to phases of low energy input when usinga plan with constantly operating machines than it is when working with a planthat already has long phases of low energy input due to changeovers.In contrast, the results of the maximum distance differ greatly from thosedescribed above. When setting a utopian makespan goal, only the makespanwill be considered. But, as the initial solution is makespan-optimal already, themakespan cannot be further reduced, resulting in solutions that do not differmuch from the initial solution. When using a non-utopian goal for the makespanwith a utopian goal for the power peak, it is the other way around. As a utopianpower peak goal attempts to reduce the energy input by 100%, the mere 0 to20% goals set by the makespan goal factors 1 to 1.2 are never taken into account,resulting in virtually identical average solutions for all makespan goal factors.The third and last case when using the maximum distance is the setting ofrealistic, attainable goals for both the makespan and the power peak. For thesesettings, the general characteristic of the maximum distance, as described above,becomes apparent. Contrary to the euclidean and manhattan distance, the max-imum distance attempts to reach all different makespan goals, even if it does notprovide any improvement for the power peak.4ConclusionThis paper presented and evaluated an approach and its parameters to retroac-tively optimize machine schedules, improving their energy efficiency withoutsignificantly worsening the already optimal makespan. As apparent from theresults and the subsequent discussion, there is no consistently and uniformlybest setting for all situations. Rather, the decision maker setting up the opti-mization and its goals needs to know the desired extent of the results. If smallimprovements of the power peak suffice, using the euclidean or manhattan dis-tance with utopian goal
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