**Published at : ** 28 Jul 2023

**Volume :** **IJtech**
Vol 14, No 5 (2023)

**DOI :** https://doi.org/10.14716/ijtech.v14i5.5148

Utama, D.M., Yurifah, A., Garside, A.K., 2023. A Novel Hybrid Spotted Hyena Optimizer: An Algorithm for Fuel Consumption Capacitated Vehicle Routing Problem.

797

Dana Marsetiya Utama | Department of Industrial Engineering, University of Muhammadiyah Malang, Jl. Tlogomas No. 246, 65144 Malang, East Java, Indonesia |

Aminatul Yurifah | Department of Industrial Engineering, University of Muhammadiyah Malang, Jl. Tlogomas No. 246, 65144 Malang, East Java, Indonesia |

Annisa Kesy Garside | Department of Industrial Engineering, University of Muhammadiyah Malang, Jl. Tlogomas No. 246, 65144 Malang, East Java, Indonesia |

Abstract

Distribution activities are closely related to
the objective function of minimizing fuel consumption, which is affected by
distance and product load in transportation. This indicates the need for
optimization to improve company performance. Therefore, this study aims to
develop a new Hybrid Spotted Hyena Optimizer (HSHO) algorithm, to minimize the
total transportation and fuel costs. This was provided by applying the Large
Rank Value (LRV) procedure to convert hyena positions to travel sequences. This
also proposed a Flip and Swap rule in each iteration to improve the algorithm's
performance. Furthermore, a mathematical model was developed for the Fuel Consumption
Capacitated Vehicle Routing Problem (FCCVRP) by considering the load and FC
(fuel consumption) rates between the nodes. This indicated that several
population variations, iterations, and several nodes were used to investigate
the effectiveness of the HSHO algorithm. The results showed increased
population parameters, and HSHO iterations reduced the FCCVRP total
transportation costs. Furthermore, decreasing the fuel consumption rate between
nodes affected reduced fuel consumption. In addition, the proposed HSHO
produced a more optimal total transportation cost than the state-of-the-art
algorithm.

Capacitated vehicle routing problem; Distribution; Fuel consumption; Spotted hyena optimizer

Introduction

The supply chain reportedly plays a vital role in organizational performance (Abdulameer, Yaacob, and Ibrahim, 2020; Ibrahim *et al.* 2020), through some activities such as procurement (Deepradit *et
al.,* 2020), production scheduling (Utama *et
al.,* 2019), and transportation (Sitompul and
Horas, 2021; Benyamin, Farhad,
and
Saeid, 2021), where fuel consumption is found to be a crucial factor (Ozener and Ozkan, 2020; Norouzi, Sadegh-Amalnick,
and Tavakkoli-Moghaddam, 2017). According to Sahin *et al.* (2009), a road transportation company
in Shanghai, China, was
responsible for 67.41% of fuel consumption within the total cost. This indicated that distribution
route planning was a crucial factor to be considered in transportation activities (Utama *et
al.,* 2020a), due to significantly affecting efficiency (Utama *et
al.,* 2020c) and environmental protection (Dewi and
Utama, 2021). Subsequently, most theories state that environmental problems are influenced by
fuel consumption (Utama *et
al.,* 2021b), indicating that the transportation sector should contribute to the reduction of energy utilization. In popular routing activities, the issue of reducing fuel consumption is known as the FCCVRP (Fuel Consumption Capacitated Vehicle Routing
Problem) (Utama *et
al.*, 2021a).

This was initially
introduced by Kuo (2010), which proposed the Simulated
Annealing (SA) procedure until several studies began to provide metaheuristic
and heuristic algorithms as solution sources. The techniques utilized in these
studies included Particle Swarm (PSO) (Poonthalir and Nadarajan, 2018) and Ant Colony Optimizations (ACO) (Yao *et al.,*
2015), Genetic Algorithm (GA) (Xiong, 2010), Simulated
Annealing (SA) (Normasari *et al.,* 2019), Tabu Search (TS) (Suzuki, 2011), and the heuristic method Gaur, Mudgal,
and Singh
(2013). This indicated that the
distance to estimate fuel consumption was generally considered, although it was
still affected by the vehicle load between the nodes. In calculating fuel
consumption, loads have recently been considered in several FCCVRP studies,
indicating the development of metaheuristic algorithms such as SA (Xiao *et
al.,* 2012), as well as Novel Hybrid TS (Niu *et al.,*
2018) and Hybrid PSO (Ali and
Farida, 2021). These aligned with Zhang, Wei, and Lim (2015), where a local evolutionary
search was provided for the problem. However, some previous FCCVRP studies
assumed that the Fuel Consumption Rate (FCR) between nodes was similar,
indicating that load and FCR subsequently affected FC (fuel consumption). This
motivated several study experts to investigate the issues of the FCCVRP by
developing a model emphasizing load-based inter-node FCR. These indicate that
full load is considered by the FCR level between nodes during loading and
no-load occurrences.

Therefore, this study
aims to develop a Hybrid Spotted Hyena Optimizer (HSHO) to solve FCCVRP
problems. This is because several studies did not use the algorithm to optimize
Fuel Consumption Capacitated Vehicle Routing Problems. According to Dhiman and Kumar (2017), the inspiration obtained from
the hunting behavior of hyenas led to the development of the SHO algorithm,
which was applied in various fields (Ghafori and
Gharehchopogh, 2021), such as allocation distribution (Naderipour *et al.,* 2021), scheduling (Sahman, 2021), and transportation salesperson
problems (Nguyen *et
al.,* 2020). This indicated that the
algorithm was developed by integrating the neighborhood search procedure to
solve FCCVRP. Therefore, the following contribution is observed (1) It proposes
a new FCCVRP model balancing the payload and FCR between nodes, (2) It presents
the influential analysis of the FCR on fuel consumption, and (3) It suggests a Novel
HSHO developed from the integration of the SHO and neighborhood search
procedures, respectively. The following sections are also observed, (a) Section
2 presents assumptions and problem definition, proposed algorithm, data
collection, and experiment setup, (b) Section 3 explains the results and
discussion, and (c) Section 4 shows the conclusions and recommendations for
further studies.

Experimental Methods

Based on this study,
several assumptions of FCCVRP were observed as follows: (1) The deterministic
customer demand, (2) The FCR between nodes is affected by load weight, (3) Each
customer is served once by one vehicle, (4) Each vehicle departs and returns to
the depot, and (5) The vehicle type is homogeneous. Several notations were also
used to define the FCCVRP, as shown below:

The FCCVRP
mathematical model was also developed from the method proposed by Xiao *et al.* (2012). It was
developed by considering the node-dependent FCR. The objective function of the
proposed model is formulated in Equation (1). Constraints of the proposed
mathematical model are presented in Equations (2)-(7), with the model being
developed as follows:

Based on Equation (1), the reduction of the Total Cost (TC) was the objective function to be achieved in this study. This indicated that the fixed budgets (travel and fuel costs) were involved at the TC. Subsequently, the proposed fuel cost considered the nodal FCR, distance, price, and transported load quantity. The constraints of the FCCVRP mathematical model used were as
follows: (i) *Constraint** **(2)* ensured that each customer was only visited by one vehicle, (ii) *Constraint** **(3)* indicated that vehicles should come and go from
each customer, (iii) *Constraint
(4)* showed that a load of all vehicles was equal to the demand
from all customers, (iv) *Constraint (5)* stated that the loads did not exceed the maximum vehicle capacity, (v) *Constraint (6)* ensured that customer
demand should not be negative, and (vi) *Constraint** **(7)* was the decision variable's
binary number [0.1].

*2.2. Hybrid Spotted Hyena
Optimization (HSHO) Algorithm*

According to the hunting phase, the best and optimal spotted hyenas had
good knowledge (fitness) of prey locations. This showed that the herd created a
cluster towards the best hyena, indicating the subsequent updates of their
positions. These behaviors were modeled in Equations (14) to (16), where

Based on a discrete problem
classified as a hard non-polynomial issue, the decision variable of FCCVRP was
observed as the sequence of trips. This indicated the development of the Large
Rank Value (LRV), to convert the position of the spotted hyena vector to the
travel order. It is also an easy method to convert continuous values to the
combinatorial problem, i.e., sorting from the largest to the smallest (Utama and
Widodo, 2021). The conversion of the spotted hyena position to the
travel route is shown in Figure 1. In addition, the results of the trip
sequence for each predator were used to calculate the total distribution cost
in Equation (1).

In the attacking prey (exploitation) phase, the observations were modeled in Equation (18), where was determined as the new position of the spotted hyena. This indicated a decrease in the value of , changed with each additional iteration. It also showed that the herd moved away and closer to locate and attack the prey. When the value of |E|<1, E was subsequently generated from a variational random number [-1, 1]. In the searching phase (exploration), the spotted hyenas predictably moved away from the prey when the value of |E|>1.

According to the neighborhood search phase, an
exchange was applied to improve the algorithm performance in each iteration (Utama *et
al.,* 2020b). This indicated that two neighborhood exchange rules
were proposed in this study, namely flip and swap, where a reversal was
observed by transforming and exchanging two randomly selected position vectors
of the spotted hyenas, as shown in Figures 2 and 3, respectively. The
repetition of the neighborhood search was also suggested as 0.25 x the number
of customers in each iteration. The LRV process was also applied as regards the
conversion to a sequence of trips on each iteration. This was then compared
with the previous processes to determine the best solution in the present
iteration. In addition, algorithm 1 presented the complete Pseudo-code of the
HHSO model, whose flow chart is shown in Figure 4.

Figure 1

2.3.

The data were obtained from the
case study of a mineral water distribution company in Mojokerto, Indonesia,
where the needs of 25 customers were to be met. The demand for each customer
(Di) was between 379 and 905 kg, with the vehicle capacity (Gm) estimated to
carry 2500 kg for one transport. The price of fuel per liter was also IDR 9,400,
with the fixed cost for delivery being IDR 300,000.
Furthermore, the company had 1 Distribution Centre (DC) for customer needs, as
the distance observed between 1 DC and 25 consumers was within 0.5-52
km. The FCRs from node i to j were also observed between 0.313-0.714 L/km and
0.625-1.429 L/km when the vehicle was unloaded

According to the sensitivity
test, the transformed variables were This indicated that
the five variations of were shifted from the initial values at each
node. In cases 1/2 and 4/5, the initial value was decreased and increased by 0.1/0.05
and 1/1.5, respectively, with condition 3 completely utilizing this value. The
initial values were also
decreased and increased by 0.1/0.05 and 1/1.5 in cases 6/7 and 9/10,
respectively, with condition 8 fully using this value. In five data
variations were applied with a value range of 8500 to 10500. Furthermore, five
data variations were used for between 150000-400000, as comparisons with the
state-of-the-art algorithms were applied to test the performance of HSHO. Based
on the case study data, random parameters were generated for This indicated the
utilization of three variations, namely small (15 and 25 customers), medium (50
and 60 customers), and large (90 and 100 customers) cases, respectively. The
utilized comparison algorithm was also SA (Kuo 2010), ACO (Yao *et al.,*
2015), GA (Xiong, 2010), HPSO (Ali and
Farida, 2021), Teaching–Learning-Based Optimization
(TLBO) (Trachanatzi *et al.,* 2021). These algorithms were then operated with 200 iterations and 500
population through the Matlab 2014a software on Windows 10 AMD A12 x64-64 8GB
RAM processor.

Results and Discussion

*3.1. Effect of HSHO parameters on total transportation cost *

The results of the HSHO effects
on the total cost of transportation are presented in Table 1, where increasing
iterations and population of the algorithm reduced the TC. However, decreased
iterations and populations led to high total transportation costs. This
indicated that large population parameters and HSHO interactions were needed to
solve the FCCVRP. For a population of 500 and 200 iterations, the optimal
result of TC was generated, as six routes were produced with a total
transportation cost of 3,128,100 IDR.

**Table 1** The effects of HSHO on total transportation cost (IDR)

*3.2. Sensitivity Analysis*

The effects of the value changes towards the cost are shown in
Tables 2 and 3, respectively, where both parameters significantly affected the
total transportation budget. When the values of were increased and decreased, the total and
fuel costs were also observed to be elevated and reduced, respectively. This
indicated that the changes and the increase/decrease of both values
significantly and insignificantly influenced the fuel and fixed costs,
respectively. Therefore, the distribution company needs to minimize the values, to optimize the total transportation
cost.

**Table 2** The effect of the value change towards the cost (IDR)

**Table 3** The effect of the value change towards the cost
(IDR)

The effect of the value change towards cost is presented in Table 4, where higher and lower led to more expensive and cheaper fuel and total transportation costs, respectively. This indicated that the value had no significant effect on the fixed cost.

**Table 4** The effect of value change towards the cost (IDR)

The results of the value change towards the cost is shown in Table 5, where higher and lower values led to more expensive and cheaper transportation and fixed costs, respectively. This indicated that fuel cost had no significant effect on .

**Table 5** The effect of value change towards the cost
(IDR)

*3.3. Algorithm Comparison*

Based on this study, a comparison of the HSHO algorithm was carried out
against the SA, ACO, GA, HPSO, and TLBO algorithms. The comparative results
towards the total transportation costs are shown in Table 6, where the proposed
HSHO algorithm produced more optimal TC than the HPSO, TLBO GA, ACO, and SA
algorithms. This was subsequently confirmed from the three variants of the
trial case (small, medium, and large), which produced a better and optimal
total transportation cost.

**Table 6** Comparison of Algorithms to Total Transportation Costs (IDR)

Conclusion

This study presented the FCCVRP that considered the
load-based inter-node FCR. In this condition, a new mathematical model and
algorithm (FCCVRP and HSHO) were proposed as solution sources. Moreover, the
HSHO was a combination of the SHO algorithm with the neighborhood search
procedure. Based on the numerical experiments in the model, the changes
observed in

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