Implementation of a Memetic Algorithm to Optimize the Loading of

Kilns for the Sanitary Ware Production

Natalia Palomares

, Rony Cueva

, Manuel Tupia

and Mariuxi Bruzza

Department of Engineering, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, Lima, Peru

Faculty of Hospitality and Tourism, Universidad Laica “Eloy Alfaro” de Manabí, C. Universitaria S/N, Manabí, Ecuador

Keywords: Memetic Algorithm, Combinatorial Optimization, Artificial Intelligence, Scheduling, Production Planning.

Abstract: One of the most important aspects to be considered in the production lines of sanitaries is the optimization in

the use of critical resources such as kilns (industrial furnaces) due to the complexity of their management

(they are turned on twice a year) and the costs incurred. The manufacturing processes of products within these

kilns require that the capacity be maximized by trying to reduce downtime. In this sense, Artificial Intelligence

provides bioinspired and evolutionary optimization algorithms which can handle these complex variable

scenarios, the memetic algorithms being one of the main means for task scheduling. In present investigation,

and based on previous works of the authors, a memetic algorithm is presented for optimization in the loading

of kilns starting from a real production line.

1 INTRODUCTION

The never-ending competition among the companies

from the ceramic and sanitary ware manufacturing

industry has prompted these companies to seek to

improve their quality and efficiency in the production

process, so as to increase their revenues and minimize

losses (Porras, 2018). The use of computer solutions

is a fine example of this quest. However, although

these focus on several aspects such as staff

management, storage, sales records and so on, there

is still a gap in the optimization of the manufacturing

process stages.

This is the case of the firing stage that takes the

longest and lacks a strategy for an optimum selection

of pieces to be loaded into the kiln. As a result a

bottleneck occurs in the process. The variety of

models to be manufactured, number of pieces, colors

as well as demand, weight and volume constraints (of

kiln cars and kilns) makes pieces selection a

challenge (Leon, Cueva, Tupia & Paiva Dias, 2019).

This problem does not only emerge in the sanitary

ware manufacturing industry but also in others fields

where products composed of several parts are

https://orcid.org/0000-0001-5279-4613

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https://orcid.org/0000-0002-1470-8515

manufactured and assembled. That is why several

researches have been conducted to develop

algorithm-based solutions that generate good results

within reasonable times.

The most commonly used type of algorithms in

these cases are metaheuristic ones. Within this

category the genetic algorithm is the preferred one

because of its simplicity. However, recent researches

have shown that memetic algorithms produce positive

solutions in a lower number of evaluations but with

better quality.

This paper has taken into account the

aforementioned and puts forward the design and the

implementation of a memetic algorithm that

generates a selection of pieces prioritizing those that

take advantage of the capacity of the kilns and kiln

cars weight and volume, considering the demand of

product sets. This algorithm was then calibrated to

improve it and, finally, was compared to a genetic

algorithm to determinate which was the best suited to

tackle this type of problem.

The memetic algorithm (MA) was chosen because

of its advantages like exploitation of problem-

knowledge (Moscato & Cotta, 2003) and improved

Palomares, N., Cueva, R., Tupia, M. and Bruzza, M.

Implementation of a Memetic Algorithm to Optimize the Loading of Kilns for the Sanitary Ware Production.

DOI: 10.5220/0008875203050312

In Proceedings of the 12th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2020) - Volume 2, pages 305-312

ISBN: 978-989-758-395-7; ISSN: 2184-433X

305

procedures for local search, which lead to a faster

convergence and a statistically better solution (Wrona

& Pawełczyk, 2013). In addition, it’s easy to

implement and more efficent and efective than

traditional evolutionary algorithms (Zhang, Sun, &

Wang, 2009). And the genetic algorithm its used to

compared it to the MA because it’s one of the most

used algorithms to solve combinatorial optimization

problems due to its robust nature and how easy it is to

implement (Zhang, Sun, & Wang, 2009).

This paper is organized in the following manner:

Section 2 addresses the issues and their impact on the

industry; Section 3 displays the problem state-of-the-

art; Section 4 introduces the proposed algorithm and

finally Section 5 deals with the numeric

experimentation this algorithm went through. In the

end, the project conclusions will be introduced.

2 PROBLEM DESCRIPTION

2.1 Current Situation

The sanitary ware manufacturing sector is

characterized by a wide variety of products offered in

different models, colors and sizes (Regalado, Maroto,

Ruiz, & García del Río, 2011). Items may be

composed of one or more pieces. Products of the

same model and color pooled into sets are sold.

That is why – and because of the increase of data

volume required to manage the value change – the

sanitary ware manufacturing industry has

increasingly used computer solutions aligned to the

industry´s characteristics (Ceramic Industry, 2015).

Nevertheless, many of them are not focused on the

optimization of the production process itself.

This process has several stages, including firing,

which lasts the longest (Diaz, 2004). Within this

stage, the selection of pieces is the most important

step, which is quite complex since there are several

factors to be considered such as demand, variety of

models to be manufactured, number of pieces

comprised, colors, products sets as well as weight and

volume constraints in kiln cars and kilns.

Kilns used in sanitary ware manufacturing are

rectilinear channels oriented to continuous

production (Gómez Gutiérrez, C., 2010) where kiln

cars are introduced. These cars have plates or shelves

where pieces are put so that they don’t stick together

(Rhodes, 2004). In this paper, these specific places

where pieces are put are called compartments.

The lack of a strategy for an optimum selection of

pieces causes a bottleneck. And this bottleneck is the

problem to be solved (Monzon, Cueva, Tupia &

Bruzza, 2019).

2.2 Impact on the Sanitary Ware

Manufacturing Industry

The lack of a selection strategy results in choosing

pieces of only one model or color as well as the

production delay of other models.

Under other circumstances, pieces of different

models and colors are chosen but do not form any set,

thus delaying subsequent stages of assembly and

packaging. This also causes delayed production,

affecting selling and as a result only a few complete

models are in storage but with a huge amount of

incomplete sets and loose pieces as well. As a

consequence, clients are not timely serviced and

supply takes too long, sells are lost, and in addition

fines for delays, higher storage cost and

underutilization of the production capacity occur

(Savsar & Abdulmalek, 2008).

3 BRIEF SUMMARY OF

STATE-OF-THE-ART

The current issue regarding the selection of pieces

stage is of a combinatorial optimization type, known

as the knapsack problem, which is highly complex

and is considered as NP-difficult (Fuentes, Vélez,

Moreno, Martínez & Sánchez, 2015). The knapsack

problem consists of selecting a set of items that meet

the constraints and generate the greatest benefit

(Dorta, León, Rodríguez & Rojas, 2003).

Other industries, such as foundries and factories

that produce a vast array of products composed of

several parts to be later assembled, also pose similar

difficulties (Tupia, Cueva & Guanira, 2017). This is

the cause for researches have been conducted that

although they do not exactly cover the same problem,

they intend to solve similar problems (Koblasa,

Vavrousek, & Manlig, 2017) (Baiqing, Haixing,

Shaobu, Yifei, & Fei, 2016). The solutions proposal

they put forward is the use of metaheuristics that have

the advantage to be not specific to a problem but

provide good solutions within a reasonable time

(Blum & Roli, 2003).

Among the proposed metaheuristics, the most

commonly used method with the best results is the

genetic algorithm (Liu, Pan & Chai, 2015) (Duda &

Stawowy, 2013). This algorithm was developed by

Holland and is inspired in Charles Darwin’s theory of

evolution (Holland, 1992); among its advantages are

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

306

simplicity, global perspective and intrinsic processing

(Deb, 2004).

This method has been used to solve similar

problems. For example, Liu, Pan & Chai put forward

a specialized genetic algorithm (SGA) for the

grouping of work orders, taking into account factors

such as deadline, priority and demand (Liu, Pan &

Chai, 2015). Wang, Ma, Luo & Qin introduced a new

HGA-OVNS metaheuristics, which is the

hybridization of the genetic algorithm, the Variable

Neighborhood Search (VNS) and the Optimization

Based Learning (OBL) to deal with the production

planning problem in an assembly plant (Wang, Ma,

Luo & Qin, 2016). Duda & Stawowy developed a

genetic algorithm to optimize the selection of alloys

and products to be manufactured in a foundry (Duda

& Stawowy, 2013). In all the researches mentioned,

the genetic algorithm was compared to other

algorithms and even with commercial software. The

outcome was that the genetic algorithm showed a

better performance and generated better quality

solutions.

Another algorithm successfully used in similar

issues is the memetic one, which combines Local

Search with genetic operators (Alba & Dorronsoro,

2005), balancing the exploration skills of

evolutionary algorithms with the exploitation skills of

the local search (Krasnogor & Smith). That is why, a

lower number of evaluations is required to find top

quality optima and solutions (Baesler & Palma,

2014).

4 PROPOSED ALGORITHMS

4.1 Data Structure

A structure is required that specifies which pieces will

be loaded into the kiln. Each of the pieces will be

placed in a different compartment, and there may be

several pieces of the same type in the selected group.

Therefore, the solution’s structure has been

defined as a 2-dimensional matrix (compartment x

kiln car). See Figure 1.

Figure 1: Solution data structure.

Each row is identified with a specific

compartment: the first row contains all the pieces that

will be placed in compartment 1; the second row, the

compartment 2 and so on. In the case of the columns,

each column represents a kiln car: column 1

represents the kiln car 1; column 2, kiln car 2 and so

on.

The value within each of the cells is the code of

the piece that will go in a specific compartment and

in a specific kiln car. For example: in Figure 1, value

y represents a piece with code y that has been placed

in the compartment 3 in the first kiln car. The value 0

has been placed in empty compartments.

4.2 Proposed Memetic Algorithm

The pseudocode of the memetic algorithm is the

following:

Figure 2: Memetic Algorithm.

This algorithm takes as the initial parameter the

population generated by a GRASP algorithm and it

extracts the best solution (currentBest) from this

population.

Then, it generates a new population (newPop)

through the application of crossover operators,

mutation and local search in the current population

(pop).

Afterwards, it unifies the previous population

with the new one to obtain another population with

the best solution from both, and seeks the best

solution of this population for any improvement with

respect to the previous generation; if no improvement

is seen, the gNoImprovement counter will be

increased.

Implementation of a Memetic Algorithm to Optimize the Loading of Kilns for the Sanitary Ware Production

307

Finally, the algorithm checks if the no

improvement generation limit is reached. If so, the

conclusion is that the population degenerated (i.e., it

comes to a standstill in a local optimun) so that it will

be restored.

This process will be repeated until complying with

any of the stop conditions: reaching the maximun

number of generations or exceeding the deadline.

4.3 Brief Discussion of the Algorithm

The operators used in the memetic algortihm are

below:

Selection operator: it chooses individuals to be

affected by the recombination operator and chooses

the solutions the local search will be applied to. For

the selection the roulette method is used, allocating

each solution a circular sector of the roulette

proportional to its fitness value in such a manner that

when spinning it the best solutions will have a higher

likelihood. The roulette implemented has a binary

search and in the worst case scenario it will require

O(log n) comparisons to find the selected value

(Lipowski & Lipowska, 2012).

Recombination operator: used to make up a new

population. It uses individuals chosen by the selection

operator and takes the crossover rate as its parameter,

which determines the number of times to be applied.

To carry out the operation the uniform recombination

will be applied, thus generating a random number

between 0 and 1 for each element that is part of the

solution. If this number is lower than p

, the element of

the first father is then allocated to the first son and that

of the second father to the second son, otherwise the

allocation will be reversed (Magalhaes-Mendes, 2013).

Mutation operator: it slightly modifies a solution;

using a mutation rate and a randomly generated value

from 0 to 1; if the generated value is lower than the

rate (mutationRate), the operator will be applied. The

mutation will replace an item assigned by another one

that fits in the same compartment.

Local search operator: it uses the k-opt heuristics

that replaces k elements present in the current

solution with others that are not part thereof. Based

on the Ishibuchi, Tanigaki, et al. research, this search

will be conducted each gLs iteration, and will be

applied to a reduced number of individuals from the

population (determined by probLs variable) and will

only visit nLs neighbors (Ishibuchi, et. al, 2013).

4.3.1 Generation of a New Population

Figure 3 shows the pseudocode of the function that

generates a new population.

Figure 3: Generate new population.

4.3.2 Updating of Population

Once the new population (newPop) is generated, this

will be unified by the current (pop) one, selecting the

best elements of both populations to form a group

composed of the same number of individuals as the

current population.

The addition strategy is chosen because it is fast,

does not require a population of a high number of

offspring and ensures that values of the target

function do not get worse (Datoussaid, Verlinden &

Conti, 2002).

4.3.3 Restoration of Population

A small percentage is preserved with the best

solutions of the current population and the remainder

is disposed. To complete the population, new

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

308

solutions are generated through the GRASP

algorithm, these will be mutated before they are

added up to the population.

4.4 Mathematical Model

The target function chooses the selection of pieces

that maximize demand satisfaction, kiln volume and

kiln car weigh capacity use. The target function is:

 

∗

∑



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



(1)

where:

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(4)

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,

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(5)

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

:1.. (6)







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,0

,

10100

(7)

Equation 2, defines sum of selected pieces

considering penalties (m). Equation 3, establishes the

average priority of piece y is equal to the average

priority of the set it belongs to, which is the average

priority of requests and considers the amount

requested, the proximity of delivery and the customer

priority level (as defined in Equation 4). Equation 5,

constraints the number of pieces y considered in the

sum in SP to the necessary amount to satisfy the

demand. Equation 7 defines a function that returns an

integer value between 0 to 10 according to demand

pending to be satisfied.

Table 1: Variables definition.

CV, CW,

Coefficients that add up 1 and represent

the importance of volume factor, weight

and demand.

MaxKilnVol Maximum kiln volume.

MaxCarW Maximum weight supported by kiln car.

MaxCPrior Maximum value of the addition of

priorities of pieces that can be loaded

into a kiln car.

, H

, D

Compartment i’s dimensions (width,

height and depth)

W Number of kiln cars

N Number of compartments in kiln car.

Y Number of different types of pieces.

S Number of different types of sets.

P Amount of orders.

Volume of piece placed in the

compartment i of kiln car w.

Weight of piece placed in the

compartment i in kiln car w.

, H

Width, height and depth of piece placed

in the compartment i in kiln car w.

It is 0 if no piece of type y has been

loaded. Otherwise, it is 1.

Average priority of piece y.

SAP

Average priority of requested set s.

It is 1 if piece y belongs to product d.

Otherwise, it is 0

It is 1 if product d belongs to set s.

Otherwise, it is 0

It is 1 if order p is a set s’s order.

Otherwise, it is 0

iwy

It is 1 if piece y is placed in compartment

i in kiln car w. Otherwise, it is 0

Amount requested in order p.

Level of proximity of delivery date p.

Integer value between 1 to 5, with 5

being the closest one.

Customer priority level of order p.

Integer value between 1 to 3, with 3

being the most important.

Amount of pieces of y-type taken into

account in the sum of priorities.

miss

Amount of pieces y pending to be kilned

in order to fulfil the orders.

maxMiss Maximum missing amount per piece

type.

Solutions generated must comply with the

following restrictions:

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,∀∈

(8)

Implementation of a Memetic Algorithm to Optimize the Loading of Kilns for the Sanitary Ware Production

309





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

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

(9)

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

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,

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,





∀∈∀∈

(10)

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

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,

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∀∈∀∈

(11)

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,

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



,

∀∈∀∈

(12)



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





1,∀∈,∀∈

(13)

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















,∀∈

(14)

Equations 8 and 9 constrain the weight to be borne

by a car and the total volume to be loaded into the

kiln. Equations 10, 11 and 12 indicate that the piece

must fit in the compartment it is placed. Equation 13

ensures that up to one piece is placed in each

compartment. Equation 14 checks that the amount of

pieces y allocated to the compartments do not exceed

the initial number of pieces y pending to be kilned.

The only constrains not considered in this paper

are baking time required per piece and color

combinations per selected group, which consist of not

allowing in a selection certain combination of colours

because the resulting pieces might not end up with the

expected colours. These constraints could be added in

future works.

5 NUMERIC

EXPERIMENTATION

The developed algorithm was compared to a genetic

algorithm, which takes as its starting point the same

initial population as the memetic one and uses the

same roulette method with binary search as selection

operator, as well as: crossover method, crossover rate

and stop conditions. With a slightly different

application of the mutation process where the number

of solutions to be mutated is a fixed proportion of the

population and the solutions selected are chosen with

the roulette method.

Before comparing them, the memetic (MA) and

genetic algorithms (GA) were calibrated in order to

get better results. In this process, real data about kiln,

kiln cars and products was used as well as 40 orders

lists that were generated randomly. Using each

combination of the parameter values, the algorithms

were applied to each of the order lists 40 times and

the average fitness for each combination was

calculated. As a result, the parameters were set on the

following values:

Table 2: Parameters values.

Stage Parameter MA GA

Crossover Crossover Rate 65% 65%

Crossover probability 70% 70%

Mutation Mutation rate 6% 7%

Local search Generation interval

(gLs)

Application rate

(probLS)

Neighbors visited

(nLs)

100

Restoration /

Depuration

Percentage preserved 7% 10%

Alpha 0.4

The purpose of the comparison was to determine

which of them was the best suited for this type of

problems.

The data used in the comparison was extracted

from the results of 40 tests conducted with different

datasets. Each test was repeated 10 times for each

algorithm and based on this data the average value of

the algorithms’ performance was calculated.

Every test included the same type of sets, products

and pieces, changing only the orders’ files. We can

see fitness results on figure 4:

Figure 4: Fitness test results.

After conducting the ANOVA test, it was

determined that the difference between the two

algorithms was not significant, so that it was

concluded that both provide solutions of the same

quality level.

In addition, other tests were run changing the

amount of generations and the time to analyze the

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

310

behavior of the algorithm in two aspects (showed on

table 3 and 4 respectively):

 How long do algorithms take to reach the 99%

of their optimum value?

Table 3: Average comparison values.

Memetic Genetic

Min Max Min Max

Generations 54.33 69.17 180.39 208.65

Time

(seconds)

29.40 32.37 105.29 121.26

 How long does the genetic algorithm require to

reach the same performance than the memetic

one?

Table 4: Average comparison values.

Min Max

Generations 249.20 459.89

Seconds 176.22 312.99

Figure 5: Behavior comparison by generations.

Figure 6: Behavior comparison by execution time.

6 CONCLUSIONS

A memetic algorithm was proposed as a method to

solve the selection of pieces issue in the firing stage

of the sanitary ware production. This algorithm was

chosen because of its similarities to the genetic one –

the most commonly used method for this type of

problems – and because it shows the same exploration

skills but a higher capacity of exploitation when

incorporating the local search.

After calibrating these algorithms to improve the

solutions generated, it was determined that the

difference between the solutions obtained for the

algorithm was not significant, so that we can conclude

that both provide solutions of the same quality level.

Additionally, it was found that the memetic

algorithm takes a smaller number of generations to

reach 99% of the optimum value while it requires a

shorter execution time than the genetic one. For this

reason, this method should be recommended to

sectors and industries where obtaining a good

solution in a short amount of time is vital.

In conclusion, this research offers a valid solution

for the pieces selection into the problem at sanitary

ware manufacturing industry. This solution is fast and

it’s adapted to the industry necessities and can be

applied in other fields where products composed of

several parts are manufactured and assembled. In

addition, this research takes into account multiple

factors related to demand such as client’s priority,

delivery dates and required amounts of products

while many others only consider a subset of this ones.

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Alba, E., & Dorronsoro, B., 2005. The

exploration/exploitation tradeoff in dynamic cellular

genetic algorithms. IEEE transactions on evolutionary

computation, 9(2), 126-142.

Baesler, F., & Palma, C., 2014. Multiobjective parallel

machine scheduling in the sawmill industry using

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