Solving Many-Objective Optimization Problems Using Selection

Hyper-Heuristics

Adeem Ali Anwar

, Guanfeng Liu

and Xuyun Zhang

School of Computing, Macquarie University, Sydney, NSW, Australia

Keywords:

Hyper-Heuristic, Many-Objective Optimization, Knapsack Problem, Job-Shop Scheduling Problem.

Abstract:

To effectively solve discrete optimization problems, meta-heuristics and heuristics have been used but their

performance suffers drastically in the cross-domain applications. Hence, hyper-heuristics (HHs) have been

used to cater to cross-domain problems. In literature, different HHs and meta-heuristics have been applied to

solve the Many-objective Job-Shop Scheduling problem (MaOJSSP) and Many-objective Knapsack problem

(MaOKSP) but the results are not convincing. Furthermore, no researchers have tried to solve these problems

as cross-domain together using HHs. Additionally, the considered HH known as the cricket-based selection

hyper-heuristic (CB-SHH) has not applied to any variation of the Job-shop scheduling problem (JSP) and the

knapsack problem (KSP). This paper compares the performance of recently proposed HHs named CB-SHH,

H-ACO, MARP-NSGAIII, and meta-heuristics named MPMOGA, MOEA/D on MaOKSP, MaOJSSP and

benchmark problems. The performance of state-of-the-art HHs and meta-heuristics have been compared using

hypervolume (HV) and µ norm. The main contribution of the paper is to effectively solve the MaOJSSP and

MaOKSP using HHs and to prove the effectiveness of the best HHs on benchmark problems. It is proven

through experiments that the CB-SHH is the best-performing algorithm on 44 out of 48 instances across all

datasets and is the best cross-domain algorithm across the datasets.

1 INTRODUCTION

On the basis of objective functions, optimization

problems develop to discover the best possible solu-

tion. The objective functions are either maximized

or minimized depending on the speciﬁc problem at

hand. Depending on how many objective functions

are involved, there are several kinds of optimization

challenges. The primary focus of single-objective op-

timization problems (SOOPs) is the single-objective

function. Multiple but less than four objective

functions are taken into account in multi-objective

optimization problems (MOOPs), and lastly many-

objective optimization problems (MaOOPs) are those

which have four or more objective functions (Anwar

and Younas, 2020).

With the help of area experts, meta-heuristics

have successfully been used to solve computation-

ally hard optimization issues. These meta-heuristics,

however, frequently run into trouble when the prob-

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lem is slightly altered. This challenge is addressed

by hyper-heuristics (HHs), which give a cross-domain

method for solving various optimization difﬁculties

with little need for customization. The two primary

categories of HHs are generation HHs and selection

HHs. Based on the kind of search space, categories

are created. The process of choosing the best low-

level heuristics (LLHs) for a particular optimization

issue is automated by the selection HHs. Whereas,

generation HHs automate the processes for creating

LLHs (Drake et al., 2020). In the selection HHs,

LLHs are selected using high-level techniques. LLHs

can be recombination operators, meta-heuristics, etc

(Drake et al., 2020).

JSSP is common in a variety of industrial and

technical management sectors, such as the fabrica-

tion of printed circuit boards, the supply chains for

the clothing industry, and cloud computing. In JSSPs,

a group of tasks must go through a predetermined

number of processes, and an industrial factory must

decide the best sequence in which these procedures

are carried out on the available equipment to meet

predetermined goals (Liu et al., 2021). To optimize

certain objectives, JSSPs need the use of algorithms

194

Anwar, A., Liu, G. and Zhang, X.

Solving Many-Objective Optimization Problems Using Selection Hyper-Heuristics.

DOI: 10.5220/0012314400003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 3, pages 194-201

ISBN: 978-989-758-680-4; ISSN: 2184-433X

to choose the order of operations on each machine

while taking into account a variety of limitations (Liu

et al., 2021). The many-objective Job-Shop Schedul-

ing Problem (MaOJSSP), which has ﬁve optimiza-

tion goals of completion time, total tardiness, ad-

vance time, production cost, and machine loss, is

the subject of our study. The problem of balancing

the optimization of both time and cost targets must

be taken into consideration while designing the al-

gorithm since time and cost in MaOJSSP sometimes

clash with one another (Liu et al., 2021).

KSP is a well-known combinatorial optimization

problem. It involves a collection of things, each of

which has a weight and a value. The goal is to choose

the best goods to add to a collection while keeping

in mind that the overall weight must not go over a

certain threshold. Maximizing the combined worth

of the chosen things is the objective (Ishibuchi et al.,

2013). In this paper, we have considered the KSP with

4, 6, 8, and 10 objectives with 500 items (Ishibuchi

et al., 2013). The variations are generated from the

original problem of 2 objectives.

In literature, most of the studies based on many-

objective HHs fall behind in evaluating their HHs on

real-life applications. Moreover, the researchers have

proposed various many-objective HHs and applied

them to different real-life problems. They have con-

sidered the MaOJSSP, and MaOKSP separately and

tried to solve them through different meta-heuristics

and HHs, but their results have not been very efﬁ-

cient. Furthermore, no researchers have tried to solve

these problems as cross-domain together using HHs.

Additionally, the considered HH (CB-SHH) has not

applied to any variation of JSP and KSP.

In this paper, we have considered three different

well-known HHs, A Cricket-Based Selection Hyper-

Heuristic (CB-SHH) (Anwar et al., 2022), ACO-

based HH known as H-ACO (Rivera et al., 2023), Ge-

netic programming HH with gaussian process-based

reference adaption known as MARP-NSGAIII (Ma-

sood et al., 2022) and two meta-heuristics named as

multiple population-based genetic algorithm known

as MPMOGA (Liu et al., 2021), multi-objective evo-

lutionary algorithm based on decomposition known

as MOEA/D (Ishibuchi et al., 2013). We have applied

these HHs and meta-heuristics on two well-known

and important MaOOPs known as MaOJSSP and

MaOKSP, along with benchmark datasets of DLTZ

and WFG. To the best of our knowledge, the CB-SHH

has not been applied to MaOJSSP and MaOKSP be-

fore and no researchers have tried to solve these prob-

lems as cross-domain together.

The main contribution of the paper is to effec-

tively solve the MaOJSSP and MaOKSP problem, to

choose the best HHs for MaOJSSP, and MaOKSP and

to prove the effectiveness of the best HHs on different

benchmark problems.

In conclusion, MaOJSSP, MaOKSP, DTLZ, and

WFG are solved using HHs and meta-heuristics

known as CB-SHH, H-ACO, MARP-NSGAIII, MP-

MOGA, and MOEA/D. To choose the best cross-

domain algorithm, different evaluation measures in-

cluding Hypervolume (HV), and µ norm have been

used. Experiments show the CB-SHH is the best-

performing algorithm on 44 out of 48 instances across

all datasets and is the best cross-domain algorithm on

all the datasets.

The remaining paper structure is as follows. The

related work is discussed in Section 2. The MaOJSSP

and MaOKSP are discussed in Section 3. The HHs

and meta-heuristics are explained in Section 4. Sec-

tion 5 discusses the empirical studies, whereas the last

section presents the conclusion and future work.

2 RELATED WORK

The following section discusses the recent related

work done for many-objective HHs, MaOJSSP and

MaOKSP.

Venske et al. (Venske et al., 2022) examined the

usefulness of HH in combinatorial optimization, par-

ticularly in the context of MOEA/DD and Differen-

tial Evolution. Four selection HHs: Self-Adaptive

Differential Evolution, Probability Matching, Adap-

tive Pursuit, and Thompson Sampling were stud-

ied thoroughly. A warm-up phase and a discard

mechanism were included in the suggested method

for choosing LLHs. To solve MaOOPs, Rivera et

al. (Rivera et al., 2023) proposed HyperACO, an

HH method that combines interval outranking mod-

els with MOEAs. Greater ﬂexibility and adaptabil-

ity were possible due to HyperACO’s autonomous

search for the optimal set of outranking models to

take decision-maker preferences into account. An-

war et al. (Anwar et al., 2022) presented a sports-

based HH to solve the MaOOPs and were the ﬁrst

ones to effectively propose any sports-based HHs

and solve the MaOOPs. (Anwar et al., 2023) in-

troduced a preference-based HH to effectively solve

the MaOOPs and tested its effectiveness on various

many-objective benchmark problems.

Masood et al. (Masood et al., 2022) improved

MaOJSSP by MARP-NSGA-III, a method that in-

tegrated a Gaussian Process-based reference point

adaption mechanism. Liu et al. (Liu et al., 2021)

proposed MaOJSSP that takes ﬁve goals for man-

ufacturers’ time and cost efﬁciency into account.

Solving Many-Objective Optimization Problems Using Selection Hyper-Heuristics

195

Unique multiple populations for multiple objectives

(MPMO) framework-based genetic algorithm named

MPMOGA was suggested to simultaneously optimize

these goals. Sang et al. (Sang and Tan, 2022b) tackled

the high-dimensional green MaOJSSP. The proposed

SV-MA incorporated a ﬁtness calculation approach

based on shift-based density estimation and com-

bined the enhanced strength Pareto evolution method

(SPEA2) with variable neighborhood search. Ou et al.

(Qu et al., 2022) discussed the necessity for shop ﬂoor

schedules that concurrently take conventional goals,

energy use, and environmental considerations into ac-

count. The practical case study for MaOJSSP illus-

trated the many-objective model’s efﬁcacy in lower-

ing energy usage and enhancing sustainability on the

shop ﬂoor. Sang et al. (Sang and Tan, 2022a) stud-

ied the MaOJSSP collaborative scheduling issue (Ma-

ODFJCSP), which was essential for developing adap-

tive, ﬂexible, and green manufacturing processes. A

high-dimensional many-objective memetic algorithm

(HMOMA), combining an enhanced NSGA-III and

a local search technique, was suggested to success-

fully solve the problem. In order to solve the di-

versity problem in MOEA/D, Huang et al. (Huang

et al., 2020) suggested MOEA/D-DDC, a cooperative

evolutionary algorithm based on decomposition and

dominance. A decomposition-based population and

a dominance-based archive were used by MOEA/D-

DDC, with the decomposition-based population pro-

viding elite individuals to the archive and the archive

helping to restore the population and increase variety.

Ishibuchi et al. (Ishibuchi et al., 2013) studied the ef-

fectiveness of MOEA/D for multi-objective optimiza-

tion along with the effects of various scalarizing func-

tions. The weighted Tchebycheff and PBI functions

with the right parameter values beat the weighted sum

and PBI functions without penalty factors for two-

objective issues.

In conclusion, the researchers have proposed var-

ious many-objective HHs and applied them to differ-

ent real-life problems. Moreover, they have consid-

ered the MaOJSSP and MaOKSP separately, and tried

to solve them through different meta-heuristics and

HHs, but the results have not been very efﬁcient. Most

of the researchers focused on solving one problem,

rather than using HHs to solve multi-domain prob-

lems, which is one of the issues which is being ad-

dressed in this paper. Furthermore, no researchers

have tried to use HHs to solve the MaOJSSP and

MaOKSP through the same HHs.

In this paper, we have considered three differ-

ent well-known HHs (CB-SHH, H-ACO, MARP-

NSGAIII) and two meta-heuristics (MPMOGA,

MOEA/D) and applied them to MaOJSSP and

Figure 1: MaOJSSP.

MaOKSP, along with benchmark datasets of DLTZ

and WFG. To the best of our knowledge, the CB-SHH

has not been applied to MaOJSSP and MaOKSP be-

fore and no researchers have tried to solve these prob-

lems as cross-domain together. CB-SHH is the best-

performing algorithm on 44 out of 48 instances across

all datasets and is the best cross-domain algorithm on

all the datasets.

3 MANY-OBJECTIVE

OPTIMIZATION PROBLEMS

(MaOOPs)

In this section, the MaOOPs that are considered in

this paper are discussed. (Liu et al., 2021), (Ishibuchi

et al., 2013), (Deb et al., 2005), (Huband et al., 2005)

3.1 Many-Objective Job-Shop

Scheduling Problem (MaOJSSP)

In JSSPs, a group of tasks must go through a predeter-

mined number of processes, and an industrial factory

must decide the best sequence in which these proce-

dures are carried out on the available equipment to

meet predetermined goals (Liu et al., 2021). In Fig-

ure 1, there are four jobs and two machines. Every

job has two procedures. P

j, where i represents the

job and j represents the ranking. Jobs are allocated

to the machines based on their ranking and order. An

example of the order of processing is also shown on

the right side. In order to optimize certain objectives,

JSSPs need the use of algorithms to choose the order

of operations on each machine while taking into ac-

count a variety of limitations (Liu et al., 2021). Five

constraints are also considered. First of all, at time

0, every job is released. Second, because only one

procedure can be handled by each machine at once,

simultaneous processing is not possible. Thirdly, a

machine cannot move to another operation before the

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

196

present one is ﬁnished processing since disruptions

are not permitted during that time. Additionally, each

job’s processes need to be carried out in a speciﬁc or-

der based on a rating. Last but not least, each method

can only be executed once to prevent double process-

ing. The objectives are taken from (Liu et al., 2021)

and are represented as follows:

f unc

max

i=0

(1)

f unc

∑

i=0

max(T

−Y

, 0) (2)

f unc

∑

i=0

min(T

−Y

, 0) (3)

f unc

∑

t=1

(wt

∗ c w + st

∗ c s) (4)

f unc

∑

t=1

count

(5)

The goal is to minimize the ﬁve objectives (com-

pletion time, total tardiness, advance time, production

cost, and machine loss). Completion time is repre-

sented by T

, the Due date of a job is represented by Y

work time and sleep time are represented by wt

and

respectively. Production cost during working and

sleeping time is represented by c w and c s respec-

tively. MaOJSSP is considered with ﬁve objectives

represented by f unc. In f unc

, the maximum time

for completion of all jobs is calculated. Total tardi-

ness is denoted by f unc

. f unc

represents the total

time of the jobs that will be completed before the due

date. The cost of production during sleep and work-

ing time is represented by f unc

. f unc

calculates the

count of how many times, the machine changed from

sleeping to working mode.

3.2 Many-Objective Knapsack Problem

(MaOKSP)

The knapsack problem involves a collection of things,

each of which has a weight and a value. The goal is

to choose the best goods to add to a collection while

keeping in mind that the overall weight must not go

over a certain threshold. Maximizing the combined

worth of the chosen things is the objective (Ishibuchi

et al., 2013). KSP is stated as follows (Ishibuchi et al.,

2013):

f unc

(y) =

∑

k=1

, j = 1, 2, ..., 10

sub ject to

∑

i=1

≤ c

, i = 1, 2, ..., T

(6)

T is the number of items. p

is the proﬁt of k

item according to j knapsack. y is the binary string

of 500 bits. w

is the weight of i item according to j

knapsack. c

is the constant value that represents the

capacity. Proﬁt and weight values are generated ran-

domly between 10 and 100 and c

is the half of total

weights. The considered objectives are 4, 6, 8, and

10 with 500 items (T) and stated as follows (Ishibuchi

et al., 2013):

(y) = α f unc

(y) + (1 − α) f unc

(y)

f or j = 4, 6, 8, 10

(7)

where α is a co-relation strengths between the ob-

jectives. and its between 0 to 1.

4 ALGORITHMS FOR

COMPARATIVE STUDIES

4.1 A Cricket-Based Selection

Hyper-Heuristic (CB-SHH)

A selection HH approach called cricket-based selec-

tion hyper-heuristic (CB-SHH) is proposed by Anwar

et al. (Anwar et al., 2022) (shown in Figure 2. It

draws its inspiration from the game of cricket. The

striker and the non-striker are the only two batsmen

on the ﬁeld at once in cricket. The side with the

most runs scored wins at the end (Anwar et al., 2022).

Their objective is to score as many runs as they can

(Anwar et al., 2022). While the non-striker waits un-

til the striker has scored a particular amount of runs

before taking the strike, the striker is the player that

actively plays the ball (Anwar et al., 2022). The most

effective batters are typically given opportunities ﬁrst,

and depending on their historical scoring trends, their

future batting positions may alter. Similarly most ef-

fective LLHs are given chances at ﬁrst and the best

LLHs are decided on how they performed before (An-

war et al., 2022). For MaOOPs, CB-SHH strives to

produce well-diverse and convergent optimum solu-

tions. The method’s use of delta evaluation, which

addresses a signiﬁcant weakness of previous HHs, is

one of its important contributions. CB-SHH uses ran-

domization for exploration and a greedy technique for

exploitation. In addition, LLHs (many-objective algo-

rithms) are used to direct the CB-SHH search process

(Anwar et al., 2022).

4.2 H-ACO

This section introduces H-ACO, a cutting-edge HH

created to tackle MaOOPs by sequentially imple-

Solving Many-Objective Optimization Problems Using Selection Hyper-Heuristics

197

Figure 2: Flowchart of CB-SHH.

menting numerous MOEA/D/O variations (Rivera

et al., 2023). Decision makers (DMs) use out-

ranking models, which are frequently used in non-

compensatory H-ACO. The approach uses an Ant

Colony Optimisation (ACO) algorithm to determine

the best answer to a sequencing optimization problem

with discrete choice variables (Rivera et al., 2023). It

is made up of a high-level heuristic (HLH) (Rivera

et al., 2023). The goal functions to determine the

sequence that most closely matches the DM’s pref-

erences by evaluating the distance from the Region

of Interest (RoI) (Rivera et al., 2023). In addition,

LLHs try to ﬁnd the best compromise solution in

MaOOPs with continuous decision variables by in-

cluding outranking relations into MOEA/D/O (Rivera

et al., 2023). In this instance, the objective functions

assess the effectiveness of the proposed solutions us-

ing the outranking model, taking into account both

their strengths and weaknesses (Rivera et al., 2023).

4.3 Genetic Programming HH with

Gaussian Process-Based Reference

Adaption (MARP-NSGAIII)

MARP-NSGAIII (Masood et al., 2022) is a ge-

netic programming-based HH that uses the Gaussian

method for reference points and is designed to solve

MaOJSSP. It is an advanced version of one of the most

famous algorithms NSGA-III (Deb and Jain, 2013).

The solutions that are lost from the ﬁnal front and the

acceptable front members that couldn’t be completely

accommodated by NSGA-III are saved by MARP-

NSGA-III in a set, after ﬁnishing the non-dominated

sorting process. This method also makes use of the

simplexs’ preset positions as well as the set acquired

by NSGA-III.

Overall, Masood et al. (Masood et al., 2022)

improved MaOJSSP by MARP-NSGA-III, a method

that integrated a Gaussian Process-based reference

point adaption mechanism. Experimental compar-

isons showed that MARP-NSGA-III greatly improved

performance on a variety of benchmark datasets when

compared to well-known many-objective algorithms.

4.4 Multiple Population-Based Genetic

Algorithm (MPMOGA)

MPMOGA (Liu et al., 2021) is a genetic algorithm

based on multiple populations. MPMOGA is used

to address the MaOJSSP, which combines the advan-

tages of the MPMO (Multi-Objective Parallel Meta-

heuristic Optimisation) framework with Genetic Al-

gorithms (GA). The reason for using the MPMO

framework is based on its previous applications in

maximizing individual goals. An archive is created

within MPMOGA to keep the top-performing solu-

tions found throughout the evolutionary process. In

the crossover operation, Adaptive Selection Tech-

nique (AST) is used, which promotes co-evolution

across all populations. To further improve the cal-

iber of top solutions kept in the archive, an Adaptive

Update Strategy (AUS) is used as well.

4.5 Multi-Objective Evolutionary

Algorithm Based on Decomposition

(MOEA/D)

MOEA/D (Ishibuchi et al., 2013) is an evolution-

ary Algorithm based on Decomposition for multi-

objective optimization. This method divides a multi-

objective optimization issue into several smaller

scalar optimization problems and solves them all at

once. The computational cost in each generation is

greatly lowered since each sub-problem’s optimiza-

tion process only uses data from its nearby sub-

problems (Ishibuchi et al., 2013).

5 EMPIRICAL STUDIES

In this section, the empirical studies are discussed.

CB-SHH, H-ACO, MARP-NSGAIII, MPMOGA,

and MOEA/D have been applied on MaOJSSP,

MaOKSP, DTLZ, and WFG, and HV and µ norm

values have been calculated to provide the best algo-

rithm.

5.1 Experimental Settings

5.1.1 Datasets

For MaOJSSP, 12 datasets named as FT06, FT10,

FT20, LA01, LA05, LA10, LA15, LA20, LA25,

LA30, LA35, and LA40 have been used (JSSP

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198

Figure 3: Mean HV values on MaOJSSP, MaOKSP, DTLZ and WFG.

Dataset, 2023). All of these datasets have different

dimensionality varying from 6 jobs and 6 machines

to 30 jobs and 10 machines (Liu et al., 2021). For

MaOKSP, 4 datasets have been considered with 500

items named 4-500, 6-500, 8-500, and 10-500. 4, 6, 8,

and 10 objectives have been considered respectively.

In benchmark datasets, DTLZ 1, 3, and 6 along with

WFG 1, 3, 6, 8, and 9 have been used (Deb et al.,

2005), (Huband et al., 2005). DTLZ 1 covers how

well the algorithm converges to the hyper-plane (Deb

et al., 2005). DTLZ 3 and 6 test the algorithms’ abil-

ity to converge towards optimal solutions (Deb et al.,

2005). WFG 1 is separable and has uni modality with

convex as well as mixed geometry, whereas WFG 3,

6, and 8 are non-separable with uni modality (Huband

et al., 2005). WFG 3 has linear as well as degenerate

geometry (Huband et al., 2005). WFG 6, 8, and 9

have concave geometry (Huband et al., 2005). WFG

9 is non-separable and has multi and deceptive modal-

ity (Huband et al., 2005).

5.1.2 Parameters Selections

The values for HHs and meta-heuristics are deter-

mined with 25 generations and 1 iteration. For MaO-

JSSP the objectives are 5, whereas for MaOKSP,

DTLZ, and WFG the objectives are 4, 6, 8, and 10.

To ensure fair outcomes, 5 seeds are used in every

experiment. In WFG, the distance and position vari-

ables are both set to 5. To demonstrate the relevance

of one method over other algorithms, a T-test is uti-

lized (al pha value is 0.05).

5.1.3 Evaluation Measures

Hypervolume (HV) (Liefooghe and Derbel, 2016) is

taken into consideration while comparing the values.

HV values range from [0,1], with 1 being the best.

To check the cross-domain ability of the algorithms

µ norm (Anwar et al., 2023) are calculated. It nor-

malizes the values from [0,1] and helps in comparing

different algorithms across different problems.

5.2 Experimental Results and

Sensitivity Analyses

5.2.1 Experimental Results

The following section describes the experiments.

HV mean values and µ norm have been computed

for 48 instances across multiple datasets of MaO-

JSSP, MaOKSP, DTLZ, and WFG on MOEA/D, MP-

MOGA, MARP-NSGAIII, H-ACO, CB-SHH.

Figure 3 shows the mean HV values of MaO-

JSSP datasets (FT06, FT10, FT20, LA01, LA05,

LA10, LA15, LA20, LA25, LA30, LA35, LA40)

on MOEA/D, MPMOGA, MARP-NSGAIII, H-ACO

and CB-SHH. The CB-SHH has performed better on

all datasets except FT06, LA10, and LA25. On these

three datasets, MPMOGA has performed the best.

Moreover, it shows the mean HV values of MaOKSP

datasets (4-500, 6-500, 8-500, 10-500), CB-SHH has

outperformed the other algorithms on these datasets.

Furthermore, the benchmark datasets have been con-

sidered (DTLZ 1, 3, 6, WFG 1, 3, 6, 8, 9). CB-

SHH has outperformed all other algorithms on these

datasets except for WFG3, on this MOEA/D has out-

performed the other algorithms.

Table 1 shows the cross-domain ability of algo-

rithms and the values are calculated using a well-

known cross-domain evaluation measure named µ

norm. CB-SHH has outperformed all the remain-

ing state-of-the-art algorithms. Whereas the MP-

MOGA is the second-best-performing algorithm. Ta-

ble 2 shows the signiﬁcance of algorithms using a t-

test. CB-SHH is the best-performing algorithm out-

performing other algorithms on 83 instances out of

96 instances.

5.3 Analysis of the Best Performing

Algorithm (CB-SHH)

As meta-heuristics, CB-SHH as shown in Figure 2

employs MaOEAs because MaOOPs struggle with

Solving Many-Objective Optimization Problems Using Selection Hyper-Heuristics

199

Table 1: Values of µ norm of MaOJSSP, MaOKSP, DTLZ and WFG.

µ norm mean values

Datasets MOEA/D MPMOGA MARP-NSGAIII H-ACO CB-SHH

MaOJSSP 0.379356 0.724128 0.203776 0.311296 0.903517

MaOKSP 0.140000 0.676943 0.426615 0.271110 1

DTLZ 0.323390 0.324173 0.267647 0.441242 0.990754

WFG 0.544403 0.135912 0.122133 0.637191 0.847717

All Combined 0.346787 0.465289 0.255043 0.415210 0.935497

Algorithms Rank 4th 2nd 5th 3rd 1st

Table 2: Algorithm signiﬁcance of algorithms using t-test at alpha 0.05.

Algorithms MOEA/D MPMOGA MARP-NSGAIII H-ACO CB-SHH

MOEA/D - +5/3/-16 +13/5/-6 +5/8/-11 +1/3/-20

MPMOGA +16/3/-5 - +12/11/-1 +15/3/-6 +2/3/-19

MARP-NSGAIII +6/5/-13 +1/11/-12 - +6/3/-15 +0/0/-24

H-ACO +11/8/-5 +6/3/-15 +15/3/-6 - +1/3/-20

CB-SHH +20/3/-1 +19/3/-2 +24/0/-0 +20/3/-1 -

Table 3: Analysis over different parameters considering selected datasets.

MaOJSSP (LA05) MaOKSP DTLZ3 WFG6

Objectives p1 p2 p1 p2 p1 p2 p1 p2

4 - - RA1 RA2 RA1 RA1 RA4 RA4

5 RA1 RA1 - - - - - -

6 - - RA1 RA1 RA1 RA1 RA1 RA1

8 - - RA1 RA1 RA1 RA1 RA1 RA1

10 - - RA1 RA1 RA1 RA1 RA1 RA1

MOEAs because of the larger number of objectives.

This has an impact on how optimal solutions work.

By taking into account the non-dominated solutions

from the previous generation and an original selection

mechanism, respectively, CB-SHH manages the off-

spring development and environmental selection suc-

cessfully. Additionally, the proper balance between

an algorithm’s exploration and exploitation is crucial

to obtaining a global optimal solution and is one of

the primary factors inﬂuencing the effectiveness of

the suggested technique (Anwar and Younas, 2020).

Because they aid in expanding the search area and ad-

vancing toward the best solutions, which are deter-

mined via greedy and random mechanisms, respec-

tively. The best meta-heuristics are chosen both ran-

domly and depending on their performance. Further-

more, handling the consequences and incentive values

in the scores represents the implementation of a rein-

forcement learning approach. As a result, both ran-

domization and the greedy strategy are used. resulting

in effective exploration and exploitation of solutions.

5.3.1 Parametrical Analysis

Two different sets of parameters have been taken

as described in Table 3. CB-SHH, MPMOGA, and

MOEA/D are represented by RA1, RA2, and RA4 re-

spectively. The original and new parameters are rep-

resented by p1, and p2 respectively. In p2, the gen-

erations are changed to 30, iterations to 10, and seeds

to 10. For analysis, 13 different datasets have been

taken across multiple problems. The different param-

eters still yielded similar results with one exception

on the 4-500 dataset of MaOKSP. Where MPMOGA

performed better than the CB-SHH by a small margin.

6 CONCLUSION AND FUTURE

WORK

CB-SHH, H-ACO, MARP-NSGAIII, MPMOGA,

and MOEA/D are applied to MaOKSP, MaOJSSP and

benchmark problems (DTLZ, WFG). The JSP is con-

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

200

sidered with 5 objectives whereas the KSP, DLTZ, and

WFG are considered with 4, 6, 8, and 10 objectives

each. To the best of our knowledge, no researchers

have solved these problems as cross-domain together

and the CB-SHH has not applied to any variations of

JSP and KSP. CB-SHH is the best-performing algo-

rithm on 44 out of 48 instances across all datasets and

is the best cross-domain algorithm on all the datasets.

The CB-SHH has performed better on all datasets

except FT06, LA10 and LA25, WFG3. Whereas

on FT06, LA10, and LA25, MPMOGA has outper-

formed other algorithms and MOEA/D has the best

results on WFG3. CB-SHH handles the balance be-

tween exploration and exploitation very intelligently

which is one of the main reasons for the algorithm

outperforming others.

In the future, more real-life many-objective

benchmark problems can be added to extend the stud-

ies.

ACKNOWLEDGEMENTS

Adeem Ali Anwar is the recipient of an iMQRES

funded by Macquarie University, Australia (allocation

No. 20213183).

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