A multi-objective genetic algorithm for optimisation of energy consumption and shop floor production performance. International Journal of Production Economics, .

Increasing energy price and requirements to reduce emission are new challenges faced by manufacturing enterprises. A considerable amount of energy is wasted by machines due to their underutilisation. Consequently, energy saving can be achieved by turning off the machines when they lay idle for a comparatively long period. Otherwise, turning the machine off and back on will consume more energy than leave it stay idle. Thus, an effective way to reduce energy consumption at the system level is by employing intelligent scheduling techniques which are capable of integrating fragmented short idle periods on the machines into large ones. Such scheduling will create opportunities for switching off underutilised resources while at the same time maintaining the production performance. This paper introduces a model for the bi-objective optimisation problem that minimises the total non-processing electricity consumption and total weighted tardiness in a job shop. The Turn off/Turn on is applied as one of the electricity saving approaches. A novel multi-objective genetic algorithm based on NSGA-II is de- veloped. Two new steps are introduced for the purpose of expanding the solution pool and then selecting the elite solutions. The research presented in this paper is focused on the classical job shop environment, which is widely used in the manufacturing industry and provides considerable opportunities for energy saving. The algorithm is validated on job shop problem instances to show its effectiveness.


Introduction
The increasing price of energy and the current trend of sustainability have exerted new pressure on manufacturing enterprises (Kilian, 2008). Thus, the aim of many modern manufacturing companies is to reduce the energy consumption both to save cost and to become more environmentally friendly (Mouzon et al., 2007). Based on the previous research (Fang et al., 2011;Mouzon and Yildirim, 2008), the operational methods have been proved to be feasible and effective to reduce the energy consumption of manufacturing companies. This especially applies to the mass production environment where more than 85% of energy is consumed by functions that are not directly related to the production of components (Gutowski et al., 2005).
Our research has been focused on the multi-objective scheduling approaches to a typical job shop because they have not been well investigated from the perspective of energy consumption reduction. In addition, from the practical perspective, a large majority of companies have characteristics of the job shop production environment. In the authors' previous research, a job shop scheduling problem that considered minimisation of the total weighted tardiness (TWT) and total non-processing electricity consumption (Electricity Consumption and Tardiness-ECT) has been introduced (Liu et al., 2014). At that stage, the non-processing electricity consumption (NPE) only included the electricity consumption of machine tools when they stay idle. The multiobjective optimisation algorithm NSGA-II has been proved to be effective in reducing NPE by searching for the optimal processing sequence of jobs on each machine. However, the ECT problem can be better solved if the Turn off/Turn on is also applied (Mouzon, 2008). Then, the electricity consumed by switching the machine off and on should also be included in the NPE. This required a development of a new multiobjective optimisation algorithm and its corresponding scheduling techniques to optimally use both the Turn off/Turn on and Scheduling methods. In this paper, the electricity consumption model of the ECT problem is extended to integrate the electricity consumed by Turn off/ Turn on. A new Multi-objective Genetic Algorithm for Electricity Saving in Job Shop Production (GAEJP) is proposed. This algorithm is designed based on the NSGA-II algorithm which we extended with two new steps that are devised for solving the new ECT problem. The goal of the new step in the algorithm entitled "1 to n scheduling building" is Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe twofold. First it creates idle periods which are long enough to justify machine turning off, thereby creating the opportunities for switching off underutilised resources. Second it expands the pool of feasible solutions by producing multi scheduling plans for each individual in the population. A semi-active schedule building procedure is developed and used as the decoding tool together with rules to improve the generated schedules. The additional new step entitled "Family creation and individual rejection" is designed to reserve the elitist solutions within the enlarged pool of feasible schedules. The optimisation framework proposed in this paper outperforms NSGA-II in reducing electricity consumption and at the same time it keeps good values of classical scheduling objectives.
In the remaining of the paper, background and motivation for the presented research given in Section 2 are followed by the description of the research problem and the model in Section 3. In Section 4, the GAEJP developed to solve the aforementioned biobjective scheduling problem is described. Experiment results which demonstrate the effectiveness of the algorithm are described in Section 5. Section 6 presents conclusions and discussion about the future research work. Mouzon et al. (2007) indicated that in many manufacturing companies, the non-bottleneck machines are always left running idle. The authors collected the time and electricity consumption data of a four CNC machines workshop of an aircraft supplier of small parts. Based on the data, on average, the machine stays idle 16% of the time during an eight hours shift. This part of electricity belongs to the non-processing electricity consumption, and it can be reduced by adjustment of the scheduling plan. Based on an industrial case of energy bill saving of foundry, Artigues et al. (2013) generalised a parallel machines model considering energy and its cost saving. Scheduling which used a branching scheme via tree search has been used as the energy saving approach. Tang et al. (2000) and Tang and Wang (2008) investigated scheduling, production planning and batching approaches to improve the energy and cost efficiency in the iron and steel production. However, the amount of research on scheduling with environmentally-oriented objectives is still in its infancy, but shows an increasing trend. For example, Fang et al. (2011) considered reducing peak power load in a flow shop. Bruzzone et al. (2012) developed a method to modify the schedule of jobs in flexible flow shops in order to adjust to the maximum peak power constraint. Du et al. (2011) developed a preference vector ant colony system to minimise the make-span and energy consumption in a hybrid flow shop. Another work focused on the flow shop was developed by Mansouri et al. (2016). The authors modelled a sequence dependent two machine permutation flow shop with energy saving concern. A constructive heuristic was proposed to trade-off the makespan and energy consumption. Dai et al. (2014) proposed a new solution which combines genetic algorithm and simulated annealing algorithm to improve the energy efficiency within a job shop. Subaï et al. (2006) considered energy and waste reduction in the hoist scheduling problem of the surface treatment processes without changing the original productivity. Zhang et al. (2012) developed a goal programming mathematical model for the dynamic scheduling in the flexible manufacturing system, which considered the reduction of energy consumption and improvement of scheduling efficiency simultaneously. Wang et al. (2011) proposed an optimal scheduling procedure to select appropriate batch and sequence policies to improve the paint quality and decrease repaints, thereby reducing energy and material consumption in an automotive paint shop. Zanoni et al. (2014) modelled and investigated a system composed of two machines in series and three stocks. Optimal batch sizes were derived for different scenarios which resulted in the minimisation of the producing, storing and energy cost of the system. Luo et al. (2013) and Liu et al. (2015) proposed new meta-heuristics to reduce the electricity cost with the presence of time-of-use electricity prices in the hybrid flow shop and job shop environment, respectively. A comprehensive review on the development of the energy-efficient scheduling has been recently provided by Gahm et al. (2016). Kordonowy (2003) developed an approach to break the total electricity use of machining processes. Following this work and research by Mouzon (2008) and He et al. (2012), we divided the electricity consumption for a machine tool into two components: the non-processing electricity consumption (NPE) and processing electricity consumption (PE) (Liu et al., 2014). NPE is associated with the machine start-up, shut-down and idling. It can also be identified from previous works that on the system level, typical electricity saving methods include: Scheduling, Turn off/Turn on and Process Route Selection. By changing the order of jobs on machines, Scheduling method can reduce the total idle electricity consumption in a manufacturing system. The Turn off/Turn on (Mouzon, 2008) allows a machine tool to be turned off when it becomes idle for electricity saving purpose. The Scheduling and Turn off/Turn on can be applied to any type of manufacturing system to reduce the NPE. However, the Process Route Selection has a limitation that it is not applicable to workshops without alternative routes, or to workshops which have identical alternative routes for jobs. Optimisation approaches are required to enable the aforementioned three methods to be optimally used to achieve electricity consumption reduction. Dispatching rules, a genetic algorithm and a greedy randomised adaptive search procedure have been proposed by Mouzon et al. (2007) and Mouzon (2008) to optimally use the three methods to reduce both total NPE and PE for single machine and parallel machine environments. He et al. (2012) used PRS to decrease both total PE and total NPE for a flexible job shop environment.

Background and motivation
Reading the relevant literature one can conclude that employing operational research methods to reduce the total energy consumption in a typical job shop environment which do not have parallel machines has not been explored very well yet. A general model of the job shop scheduling problem that considered minimisation of TWT and the total idle electricity consumption was proposed by the authors (Liu et al., 2014). This previous work proved that in a basic job shop, the total NPE can be reduced by adjusting scheduling plans, and NSGA-II was effective in achieving this aim. However, by observing the solutions delivered by NSGA-II, it can be found that the NPE can be further reduced if the Scheduling and Turn off/Turn on are applied together in an optimal way. This led to a substantial modification of NSGA-II whose description will follow the new mathematical model for the ECT problem presented in the next section.

Notation and problem statement
The notation used in the problem statement, algorithm description and throughout the paper is as follows: The bi-objective ECT problem has been formally defined by Liu et al. (2014). However, in that research, NPE included only the electricity consumption of machines when they stay idle. In the research presented in this paper, the Turn off/Turn on is applied for electricity saving and the electricity consumed by it is included in the calculation of NPE. The first part of the model describes the The first optimisation objective is to minimise the total weighted tardiness of all jobs: The reader can refer to Pinedo (2012) for more details about the job shop model.
The second part of the ECT model describes the electricity consumption. It includes the electricity consumed by the Turn off/Turn on. A power input model for a machine M k when it processes operation O ik l assumes that each machine has three constant levels of power consumption: during idle time, when switched into run-time mode and when carrying out the actual cutting operation (Kordonowy, 2003). The input power, ( ) P t k , which a machine requires over time is defined as a stepped function represented by the red line in Fig. 1. The idle power level of a machine is defined by P k idle . The overall processing time p ik l is defined as the time interval between coolant switching on and off. The objective to reduce the total electricity consumption in the ECT problem can be realised by reducing the total non-processing electricity consumption (NPE). Hence, the objective to minimise the total NPE in a job shop to carry out a given schedule can be expressed as: if the l-th operation of job J i is processed on M k , 0 otherwise; S k r and C k r indicate the start and completion time of operation m k r on M k in schedule s,respectively. In addition to our previous model, here the Turn off/Turn on is applied to idle periods which are long enough. The idle electricity consumption by these periods are replaced by the electricity consumed by turning the machine off and then turning it back on. E k turn is the electricity consumed by Turn off/ Turn on; t k OFF is the time required to turn off machine M k and turn it back on; B k is the break-even time period of machine M k for which Turn off/Turn on is economically justifiable instead of running the machine idle, (Mouzon and Yildirim, 2008;Mouzon, 2008). Z k r is a decision variable such that = Z 1 k r if a Turn off/ Turn on is applied to the idle period following C k r , 0 otherwise. Consequently, the calculation of the NPE of machine M k can be expressed as: An example of the calculation of NPE of M k is presented in , which means it is justifiable to execute a Turn off/Turn on during the idle period between O i k l 1 1 and Then, the aforementioned value is multiplied by the idle power level of machine M k to obtain the total idle electricity consumption. Finally, the electricity consumed by the Turn off/Turn on should be summed with the idle electricity consumption to get the value of NPE. In this case, the machine has only been turned off then started again once, so the NPE is calculated as ⎡ In summary, the multi-objective optimisation problem considers minimisation of both TWT ( ( ) f s 1 ) and NPE ( ( ) f s 2 ) which is expressed by Expression (4):

A novel multi-objective genetic algorithm for optimisation of energy consumption
The goal of developed GAEJP is to create more opportunities for switching off underutilised resources while maintaining the production performance. The method for reducing the total nonprocessing electricity consumption is to integrate fragmented short idle periods into longer idle periods in the operation sequence on each machine, since this can create opportunities to execute the Turn off/Turn on. The schedule builder used at the first step is the semi-active one. The reason for building a semi-active schedule at the initial stage instead of the active one is that in a semi-active schedule normally some operations can be shifted to the left without delaying other operations (Pinedo, 2009;Yamada, 2003). This can create some idle periods which are long enough for executing Turn off/Turn on. The encoding schema and decoding procedure of the semi-active schedule builder is explained in the next sub-section.

Encoding schema and semi-active schedule builder
We adopt the operation-based encoding schema, which is known as "permutation with repetition" (Dahal et al., 2007). Each job's index number is repeated u i times ( u i is the number of operations of J i ). By scanning the permutation from left to right, the l-th occurrence of a job's index number refers to the l-th operation in the technological sequence of this job. As an illustration, let us follow an example of 3 Â 3 job shop problem provided by Liu and Wu (2008), whose data are given in Table 1. For example, job J 1 requires processing on machines M 1 , M 2 and M 3 and it takes 2, 2, and 3 time units, respectively.
One of the feasible individuals is [ ] 222333111 . Decoded by the active schedule builder (Dahal et al., 2007), the individual is transformed into a feasible schedule as depicted in Fig. 2(a). Comparatively, by employing the semi-active schedule builder (Yamada, 2003), the individual is transformed into a feasible schedule as depicted in Fig. 2(b). Normally, the initial semi-active schedule has larger TWT than the active one, but it provides more opportunity for improving the objective values. Fig. 2 shows how the improved semi-active schedule outperforms the active one in terms of TWT and the total NPE. The bottom schedule (Fig. 2(c)) is generated based on the middle schedule ( Fig. 2( . Let us assume that the due date for every job is the 10 th time unit, and that it is justifiable to execute Turn off/Turn on for each machine when the idle period is longer than 3 time units. Thus, it can be seen that the bottom schedule outperforms the other two schedules in both the total NPE and TWT. Therefore, the proposed optimisation strategy is to build a semi-active schedule at the initial stage, then to improve the schedule by performing left shift and left moving of appropriate operations. The algorithm is described in detail in the following sub-section.  Table 1 An example of a × 3 3 job shop problem.

Components of GAEJP
The flowchart of the developed GAEJP is shown in Fig. 3. The structure of the NSGA-II, our algorithm is based on is described by Deb et al. (2002). Two new steps are introduced to address the presented ECT problem which integrates Scheduling and Turn off/Turn on. The first one is labelled "1 to n schedule building". In this step, each individual in the coding space is decoded into several feasible scheduling plans (solutions) in the solution space, which have different idle periods to create opportunities for applying Turn off/Turn on. This expands the solutions pool of a chromosome. The goal of the second step "Family creation and individual rejection" is to select nondominated solutions from the solutions pool of each individual chromosome and then to further select an elitist solution among them. The operation-based order crossover operator and swap mutation operator are adopted from Liu (2013). The two new steps are explained in detail in the following sub-sections.

One to n schedule building
The 1 to n schedule building firstly transforms an individual into a semi-active schedule. All the idle periods within the schedule are evaluated to find those which are sufficiently long to allow a machine to be turned off and switched back on. Then, the shutdown action is applied to those idle periods, and this generates the first feasible solution corresponding to the individual. To improve the schedule's performance on the TWT objective, two changes to the schedule are introduced: left shift of an operation to the earliest valid time period left to its current position and left move from its current position in the schedule. First, all the operations which are allowed to be shifted left in the schedule are ranked according to defined rules. The operation with the highest rank is shifted left to the earliest idle period available for it. After the left shifting, it might be found that some operations can be moved left to further improve the performance on the TWT objective. Then all these permissible left move operations are  selected and ranked. The operation with the highest rank is moved left to its earliest possible starting time. After completing all the aforementioned steps, the algorithm performs iteratively the steps for collecting permissible left move operations, ranking, and left moving until there are no further operations which can be moved left. Then all the idle periods in the generated schedule are evaluated to find out those which are justifiable for the Turn off/Turn on. The values of the objective functions are calculated after the Turn off/Turn on is applied. In this way, the second feasible solution corresponding to the considered individual is obtained. The algorithm performs the described steps iteratively until there is no permissible left shift operation in the schedule. The flowchart of 1 to n schedule building step is given in Fig. 4, while the details of each step of the algorithm are given in the remainder of the sub-section.
Initial schedule building Employ the semi-active schedule builder to decode the individual I pt to a semi-active schedule.
Idle periods evaluation Evaluate all the idle periods within the produced schedule to find out those for which it is justifiable to apply the Turn off/Turn on and apply it to all of them. After the Turn off/Turn on, the first feasible solution which corresponds to individual I pt is obtained, denoted by s pt 1 . A previously introduced example of × 3 3 job shop is used to demonstrate the 1 to n schedule building procedure. Suppose the idle power of all machines is 1 power unit and it is justifiable to turn off then turn on a machine if the idle period is longer than 5 time units. . Initially, I pt is decoded by the semi-active schedule builder to the schedule shown in Fig. 5(a). After the Turn Off/Turn On has been applied, the resulting Gantt chart of s pt 1 is shown in Fig. 5(b).  Fig. 5(c). There is only one There is just one permissible left move operation in schedule s pt LM 1 , which is O 13 3 . It is moved left to its earliest possible starting time. After this move, there is no more available permissible left move operation within the schedule. Since the idle time on machine M 3 between O 13 3 and O 13 3 is longer than 5 time units, the Turn Off/Turn On is applied to get the schedule presented in Fig. 5(e). This is the second feasible solution for the considered individual, denoted by s pt 2 .

Objective functions calculation
The values of objective functions of s pt 2 are ( ) 21,0 . Next, the left shift and move continue until no available permissible left shift operation can be identified. Thus, the 1 to n schedule building process for the given × 3 3 job shop is completed. Following the above process,

Family creation and individuals rejection
On the completion of the 1 to n schedule building step, each individual is assigned h pt solutions, ≥ h 1 pt . The aim of the step Family creation and individual rejection is first to select the nondominated ones among the h pt solutions corresponding to each individual, and then to preserve one elitist among the selected non-dominated ones. The two steps are described in more details below. The relationship between the coding and solutions space is shown in Fig. 6. 4.2.2.1. Family creation. In this step, all solutions in the set S pt in the solution space associated with individual I pt in the coding space are compared with each other by using the non-dominated sorting method (Deb et al., 2002), which sorts the solutions into different dominance levels. Only those solutions located in the best level are preserved. The number of solutions corresponding to I pt is reduced from h pt to u pt , Each I pt is copied . Thus, the aim of the individuals rejection is to preserve the elitist in each family, keep the diversity of the population, and reduce the population size from ′ N back to N. Two types of individual rejections are defined to decide on which family members to keep for the next generation: individual rejections based on non-dominated sorting of the whole population which is followed by individual rejections in a family based on crowding distance. Individuals rejection in the population based on non-dominated sorting. The non-dominated sorting is performed on all ′ N solutions in population P t . As a result, the solutions which correspond to family members are sorted into different levels. Thus, within a family I pt , only members whose corresponding solutions are located in the lowest level are preserved, others are abandoned. For example, let us assume that there are three members in the family I pt , I pt 1 , I pt 2 and I pt 3 , and that their corresponding solutions (schedules) are s pt 1 , s pt 2 and s pt 3 . Let us further assume that based on the non-dominated sorting, s pt 1 is located in level 2, s pt 2 in level 3 and s pt 3 in level 4. In that case, only I pt 1 is preserved, while both I pt 2 and I pt 3 are abandoned. By completing this process, all the solutions of the members in a specific family are located in the same level, and the population size of P t is now equal to ′′ N , ′ ≥ ′′≥ N N N. Some members still need to be rejected from each family to reduce the population size back to N.
Individuals rejection in a family based on crowding distance. According to Deb et al. (2002), the crowding distance is an important indicator which evaluates the ability of an individual to contribute to the diversity of the population. In this step, the preserved family members whose corresponding solutions are located in the same non-dominated front are ranked by their crowding distance value. The one with the largest crowding distance is made elitist.Hence, the boundary solutions of each nondominated front are kept since they have an infinite value of crowding distance (Deb et al., 2002). In order to address the presence of families in our algorithm we propose a modified definition of boundary solutions and a modified neighbours search to choose solutions to be used in the crowding distance calculation. obtained taking first the right neighbour and then the left. This is illustrated in Fig. 8. The crowding distance of a solution is the maximum between the crowding distance calculated by using N s 1 pt v and N s 2 pt v . Each solution has at least one group of neighbours due to the existence of the preserved boundary solutions. Based on above, the two individuals from different families corresponding to the boundary solutions are preserved. In each of the remaining families, the individual with the largest crowding distance is preserved, while others are rejected. Completing this step, the population size is decreased to N.
A simplified example with the population size of 2 ( = N 2) is shown in Fig. 9 to show the family creation and individual rejection process.

Experimental results
The effectiveness of the developed GAEJP is validated based on comparison experiments. The solutions of GAEJP are compared with the solutions obtained by the traditional single objective scheduling methods and NSGA-II. Three job shop instances based on the F&T × 10 10 (Fisher and Thompson, 1963), Lawrence × 15 10 and × 20 10 (Lawrence, 1984) instances are modified to incorporate electrical consumption profiles for the machine tools. The due date for each job is defined by the TWK due date assignment method (Sabuncuoglu and Bayiz, 1999 The following values of f are set: 1.5, 1.6, 1.7, 1.8 and 1.9. These values have the trend of less tight due date. For instance, = f 1.5, represents a tight due date case which corresponds to 50% of tardy jobs. The weight of each job is randomly allocated. The time unit is a minute. Assuming that all the machine tools are automated ones, the idle power level and electricity consumed by Turn off/Turn on of each machine are generated based on the research works focused on the characterisation of machine tools' electricity consumption, such as Dahmus (2007), Drake et al. (2006), andLv et al. (2016). They provided us with reasonably defined ranges within which required values are generated randomly. A complete list of electrical characteristics data of machines used in the experiments can be found in Appendix I in Liu (2013).
To demonstrate the effectiveness of GAEJP in solving the ECT problem, the following comparison experiment is carried out. The classical job shop scheduling problem with the single objective to minimise TWT serves as the benchmark to represent the traditional approach to machine scheduling without the electricity saving consideration. Shifting Bottleneck Heuristic (SBH) and Local Search Heuristic (LSH) provided by the software LEKIN (Pinedo, 2009) are used to produce solutions. The solutions with minimum TWT are adopted. In each generated schedule, the total NPE value is calculated without using it as the objective function. Performance of SBH and LSH under different due date conditions are shown in Tables 2-4. In the next experiments, the goal is to prove superiority of GAEJP to NSGA-II in solving the ECT problem.
The parameter values used in the GAEJP obtained by tuning, are as follows: population size = N 150; crossover probability = p 1.0 c ; mutation probability = p 0.4 m ; generation = t 8000. The algorithm is   Tables 2-4, the solid points and the points with a pattern are produced by NSGA-II, and GAEJP, respectively. GAEJP achieves a considerable total NPE reduction. The NPE improvements are shown in Tables 5 and 6. Take the F&T × 10 10 job shop as an example, when = f 1.5 and the machines are turned off when the idle time is longer than 30 min, the minimum and maximum values of total NPE obtained by GAEJP are 3.5 kWh and 6.0 kWh respectively, which means that it achieved from 96.7% to 98.1% improvement in the total NPE consumption compared to the values obtained by LEKIN. With the same f value, the improvement in the total NPE compared to NSGA-II is from 90.3% to 98.0%. The TWT deterioration of GAEJP results (compared to the LEKIN results) in weighted minute for each job shop instance under different tardiness conditions are shown in Tables 7 and 8. By considering the performance in both the total NPE and TWT objectives, it can be noticed that scheduling plans delivered by GAEJP always have much smaller NPE consumption than scheduling plans delivered by NSGA-II if they have similar values of TWT. For instance, in the F&T × 10 10 job shop instance, when = f 1.6, one of the boundary solutions delivered by GAEJP is ( ) 1118minutes,12.2kWh ; comparatively, the solution obtained by NSGA-II with the closest value of TWT is ( ) 1136minutes,170kWh , which means the most of the solutions generated by NSGA-II are dominated by solutions delivered by GAEJP. This can also be observed in the given figures. Additional experiments have been carried out to investigate the effectiveness of GAEJP in reducing the NPE when different values of the minimum idle period allowing machine to be turn off are applied, namely using 20, 40, 50 and 60 min. We present the minimum improvement in NPE achieved across all runs of the algorithm (Tables 5 and 6). These solutions belonging to Pareto fronts, have the minimum compromise in TWT, i.e. they achieve at the same time minimum increase in TWT (Tables 7 and 8). Based on the experiment results, it can be concluded that GAEJP is effective in reducing the NPE at different levels of idle times on the machines allowing them to be turned off. Although in many cases smaller values of the minimum idle period allowing a machine to be turned off lead to larger improvements in NPE, one cannot     conclude that it holds all the time. For instance, the largest minimum NPE improvement compared to the LEKIN results for E-Lawrence × 20 10, = f 1. 7, was achieved when the minimum idle period for turning of the machine was 30 min. On the other hand, the compromise of TWT varies considerably when different values of the minimum idle period allowing machine to be turned off are applied. For instance, in the E-Lawrence × 15 10 job shop, = f 1. 9, the increase in TWT is only 10 when 40 min is used as the lower boundary to turn off the machines, compared to the LEKIN result, while the improvement in NPE is 75.5%. This is the best value of TWT across all five evaluated lower boundaries of idle periods. Thus, it can be concluded that for a specific job shop, it is worthy investigating which value of the minimum idle period allowing the machines to be turned off will result in the good trade-off between TWT and NPE. From the application perspective, this can provide more options for the decision maker. For example, for the E-Lawrence × 15 10 job shop, = f 1. 9, when 40 min is used to apply the turn off, the solution with 75.5% improvement in NPE and only 10 increase in TWT might be more preferable than the solution with 98.3% improvement in NPE and 647 increase in TWT (obtained by using 30 min idle period to apply the turn off).
It can be observed that GAEJP combined with Turn off/Turn on is more effective in reducing the total NPE than NSGA-II, without compromising TWT too much. For Lawrence × 15 10 and × 20 10 job shop, all solutions obtained by NSGA-II are dominated by at least one solution obtained by GAEJP, as shown in Figs. 11 and 12. For the F&T × 10 10 instance, some of the NSGA-II solutions are not dominated by any GAEJP solutions. For this instance, Pareto fronts generated by two algorithms are combined together to form new Pareto fronts, and only non-dominated solutions are preserved. It can be noticed from Fig. 10 that solutions obtained by the GAEJP take a larger proportion of the total number of solutions in TWT Increase 20  min  1957  1881  1185  493  2963  2931  1162  350  130  TWT Increase 30  min  1979  991  695  638  2465  2094  1515  659  78  max  2870  2794  1209  2811  3555  3165  3306  1131  647  TWT Increase 40  min  861  811  565  95  2385  2413  826  795  10  TWT Increase 50  min  1933  1664  1107  145  3420  1843  901  1120  31  TWT Increase 60  min  1206  744  156  232  2304  1947  1195  438  80   Table 8 The TWT increase in weighted minutes for Lawrence × 20 10.

Comparison of GAEJP and LEKIN
E-Lawrence × 20 10 f¼ 1.5 f ¼1.6 f¼ 1.7 f ¼1.8 f ¼1.9 TWT Increase 20  min  5010  4565  4420  3857  2288  TWT Increase 30  min  4898  3860  3880  3386  2738  max  9480  9008  7391  4281  5139  TWT Increase 40  min  5074  3988  4443  3808  2948  TWT Increase 50  min  4765  5358  3973  3738  2775  TWT Increase 60  min  5966  4222  4306  3205  3575 the new Pareto fronts, which means GAEJP can provide more options to the production manager. The upper part A and bottom part B of Fig. 13 show the Gantt charts of optimal schedules produced by GAEJP and NSGA-II respectively for E-F&T × 10 10 job shop instance when = f 1.5. It can be observed that the schedule produced by GAEJP has a smaller total amount of idle periods on all machines (31 idles periods on the GAEJP schedule versus 37 idle periods on the NSGA-II schedule), and in general the lengths of those idle periods are longer. This means when the varieties of jobs' components and their amounts are increasing, it is easier to place the new operations in the existing idle periods in scheduling plans produced by GAEJP. From above, the scheduling plans produced by GAEJP might be more preferable for managers when considering the real life job shop manufacturing system. An interesting question is whether the Turn off/Turn on applied to the optimisation result of NSGA-II may lead to a better result than that produced by GAEJP. However, in the case presented in Fig. 13, the original objective function values of scheduling plans produced by GAEJP and NSGA-II are ( ) 2288 min,6.0 kW h and ( ) 3595 min,170 kW h , respectively. When the Turn off/Turn on is applied to the bottom scheduling plan, the objective function values become ( ) 3595 min,14.5 kW h . Therefore, the solution delivered by GAEJP is still preferable for the production manager. A more thorough investigation of the effects of applying Turn off/Turn on to the optimisation results of NSGA-II will be investigated in the future research work.

Conclusions and future work
Reducing electricity consumption as well as keeping good performance in classical scheduling objectives gains more and more importance in modern manufacturing. The model for the Multi-objective Total Non-processing Electricity Consumption (NPE) and Total Weighted Tardiness (TWT) job shop problem which integrates Scheduling with the Turn off/Turn on of machines has been introduced. For solving this problem, the multiobjective optimisation algorithm based on NSGA-II, GAEJP, with two new steps has been developed. The performance of the algorithm has been tested on three extended versions of job shop instances which incorporate electrical consumption profiles for the machine tools. In addition, comparison experiments have been applied to demonstrate the effectiveness of GAEJP in solving the ECT problem. Firstly, the Shifting Bottleneck Heuristic and the Local Search Heuristic have been used as the single objective heuristic optimisation methods to deliver the baseline scenarios of the aforementioned job shops. The result of the comparison indicates that by applying GAEJP the total non-processing electricity consumption is decreased considerably, with an acceptable level of deterioration of the total weighted tardiness. The Pareto fronts produced by GAEJP have also been compared with those obtained by NSGA-II, which involved only the optimal schedules of jobs without applying Turn off/Turn on. It can be observed that GAEJP is more effective in reducing the total NPE than NSGA-II, without compromising its performance on TWT. Thus, the superiority of the GAEJP in solving the ECT problem has been demonstrated. In future work, the algorithm should be tested on a wider set of job shop instances to validate its general applicability. The developed GAEJP has the potential to solve other multi-objective optimisation problems. This will be explored in our future research work. More investigation into comparison of GAEJP and NSGA-II when they are used as the optimisation approach for both Scheduling and Turn off/Turn on methods will be conducted. Also, it will be investigated how to set a favourable value of the minimum idle period allowing the machines to be turned off for a specific job shop.