DOI: 10.3303/CET24114168 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 30 June 2024; Revised: 25 July 2024; Accepted: 24 November 2024 
Please cite this article as: Bíró T.J., Horváth A., 2024, Assigning Metaheuristics to a Logistics Problem: A Novel Classification System for 
Algorithms and Problems, Chemical Engineering Transactions, 114, 1003-1008  DOI:10.3303/CET24114168 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 114, 2024 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Min Zeng, Yee Van Fan, Xuechao Wang 

Copyright © 2024, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-12-0; ISSN 2283-9216 

Assigning Metaheuristics to a Logistics Problem: a Novel 

Classification System for Algorithms and Problems 

Tamara J. Bíró*, Adrián Horváth 

Széchenyi István University, Hungary, 9026 Győr, Egyetem tér 1. 

biro.tamara@sze.hu 

Metaheuristic algorithms applied to NP-hard problems are proven effective techniques in the field of optimization 

to ensure a good result within an acceptable calculation time. However, finding a suitable technique for 

optimizing a complex problem is not an easy task since there are hundreds of methods. The majority of 

metaheuristic research is characterized by developing a new algorithm for a task or modifying or improving an 

existing technique. The reuse of metaheuristics is small compared to the fact that up to 30+ new procedures 

can be presented in the scientific community every year. Metaheuristic algorithms have already been grouped 

in countless ways, but not based on their components and structural elements, which are responsible for the 

basic optimization performance of the given method. The grouping of the problems to be solved is also not 

typical in terms of which method can be used to solve them effectively. This paper contributes to filling this gap 

by introducing a novel classification system for algorithms and problems in terms of variables or based on the 

type of task. Two main categories were distinguished for both logistic tasks and metaheuristic algorithms: 

discrete and continuous. Linking the nature of the variables between the task and the algorithm is a significant 

step forward in choosing an efficient metaheuristic with a high probability for a logistics problem. This can 

increase the efficiency of solving logistics problems and expand the use of the latest optimization techniques. 

1. Introduction 

Due to their complexity, many logistics tasks and problems belong to NP-hard problems. For this reason, the 

literature considers metaheuristics to be the most suitable for solving these tasks (Sörensen and Glover, 2010), 

considering the priority of time and solution quality. There are hundreds of metaheuristic algorithms (Ma et al., 

2023) and thousands of articles dealing with their efficient problem-solving. However, the question arises. If 

there is a problem, how can the appropriate optimization technique and algorithm be selected for it? If there is 

such a large set containing hundreds of different algorithms, why is there little reuse of metaheuristics (Swan et 

al., 2022)? What can help professionals and industry workers to choose the right algorithm? These questions 

are the focus of this paper.  

Until now, metaheuristics and problems have not been grouped based on their components and structural 

elements, which are responsible for the basic optimization performance of the given method. Based on these, 

the problem can be formulated as follows: No framework or selection structure can assign metaheuristics to a 

problem that is most likely to solve the given problem correctly. All this is based on general information and 

schemes, not in the case of specific, special tasks. 

To make it easier to associate a metaheuristic with a specific logistics problem, the authors introduced a new 

kind of classification of logistics tasks according to characteristics important for optimization. Based on the 

variables and the nature of the problem, 2 main categories were distinguished: discrete and continuous. The 

authors also examined what kind of problems can be efficiently solved with the given algorithm based on the 

literature, and based on this, the procedures were classified into 2 main categories: metaheuristics suitable for 

solving discrete and continuous tasks were distinguished. Based on the similar classification principle of logistic 

tasks and metaheuristic algorithms, the authors believe that a metaheuristic procedure suitable for solving a 

given problem can be defined. All of this contributes to increasing practical applications and efficiency in the 

field of logistics as well. 

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The paper presents a framework based on which the most likely suitable optimization procedure can be selected 

for given variable tasks. A kind of reverse optimization is presented: a technique is not modified and adapted to 

a task, but the techniques providing a possible good solution for a task type are given, promoting the reuse and 

industrial applicability of existing metaheuristic procedures.  

The paper is structured as follows: in section 2, the literature related to the topic is reviewed. Section 3 presents 

the selection framework. In section 4, an efficiency study is described, and finally, in section 5, the paper's 

conclusions and further research directions are presented. 

2. Literature review 

Due to their NP-hard complexity, metaheuristics are often applied to logistics problems. These algorithms have 

already been used for shop scheduling tasks (Coelho and Silva, 2021) and Resource-Constrained Project 

Scheduling Problems (Pellerin et al., 2020), but they have also proposed an algorithm that can be used in any 

intelligent decision-making system as an optimization module to increase accuracy and efficiency (Keivanian 

and Chiong, 2022). According to Ezugwu et al. (2021), it is possible to identify metaheuristics that have already 

been successfully applied to several problems (for example, the Vehicle Routing Problem). It is also useful to 

define the parameter settings of the algorithm for specific tasks (Chirwa et al., 2024). There are many research 

studies to solve logistics and supply chain problems, and it is difficult to summarize the results already achieved 

in each small area and to determine the best solution technique for the given problem, the reason, and details 

of the usefulness of the procedure.  

Real optimization problems (e.g., logistics, transportation, engineering design) contain both continuous and 

discrete variables. This is also why it is difficult to assign a suitable metaheuristic to a problem since a 

metaheuristic algorithm cannot efficiently handle tasks containing mixed variables. One reason for this is that 

standard metaheuristics are designed to solve either continuous or discrete optimization problems (Talbi, 2024). 

Designing an algorithm is time-consuming and expensive, and the process itself is rarely documented (because 

of this, the process of thought is often untraceable, and it is not clear what motivated certain design decisions) 

(Swan et al., 2022). 

Finding the right metaheuristic for a specific problem is very difficult. This hinders the re-implementation of 

algorithms, although the primary goal of research is to optimize practical tasks. The work is further complicated 

by the exponential growth of papers: new research materials appear every day.  

The more frequent reuse of algorithms is further hampered by the lack of systematics for practical problems. It 

would be important to organize and classify practical problems according to aspects that can be connected to 

the operating mechanisms of algorithms. With the help of this, potentially suitable metaheuristics for a given 

problem can be selected more likely.  

The aim of this paper is to find the components between logistic problems and metaheuristics, which can be 

used to determine the algorithm that provides a possible good solution for a given task. The general goals of 

the papers are to create, improve, or compare a metaheuristic with other metaheuristics to find out which 

algorithm performs best. But it is almost impossible to tell based on the results of thousands of papers. The 

primary aim of this paper is to promote more frequent reuse of metaheuristics by applying a general scheme. 

This is necessary because the thousands of scientific works and the hundreds of metaheuristics are less valid 

in practice. Efficiency, transparency, and sustainability can also be improved by using existing techniques 

instead of creating new ones. 

3. A novel classification of logistic problems and metaheuristics 

Most logistical problems are extremely complex and complicated tasks. Optimization is crucial in countless 

areas: the proper allocation of resources, minimizing the time or distance traveled, choosing the right warehouse 

structure, and the proper placement of depots are just a few examples of the countless tasks to be solved. In 

many cases, these tasks can only be performed properly if the processes are coordinated and properly 

optimized. Figure 1 shows the structure of the framework, which helps to assign a metaheuristic with a possible 

good solution to a task. 

The steps of the modeling procedure are as follows: 1. Definition of the problem; 2. Brief description of the 

problem (goals, constraints, etc.); 3. Defining the nature of the problem (discrete or continuous); 4. Literature 

review of algorithms; 5. Identifying metaheuristics that can provide a possible good solution; 6. Selection of a 

specific algorithm; 7. Application of metaheuristics to the specific task. 

 

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Figure 1: Framework for choosing an optimization technique 

This is a new type of selection method, where the main hypothesis is that a logistics problem consisting of 

discrete or continuous variables can most likely be efficiently solved with metaheuristics that, based on the 

literature, have already been successfully applied to solving discrete or continuous tasks. Therefore, it is 

necessary to determine whether the nature of the problem is discrete or continuous. It is advisable to identify 

the goal and the most important constraints. Examples of this can be seen in Table 1. 

Table 1: Classification of logistics problems (The nature of the tasks and their most important goals and 

constraints) 

Logistical problem Description/Purpose 
Nature of the 

problem 

Determining the 

location of warehouses 

Optimizing network design by evaluating up to thousands of 

configurations and selecting the best one. 

Goal: minimizing total costs. 

Constraints: cost, distance, certain service level limits. 

Discrete 

Inventory management 

Determination of order quantities, safety stock levels, determination 

of optimal order points. 

Goal: balance between storage costs and shipping costs. 

Constraint: cost. 

Continuous 

Vehicle Routing 

Problem (VRP) 

Determination of optimal route and means of transport. 

Goal: minimize travel distance, time, or cost. 

Constraints: number and size of resources. 

Discrete 

There are hundreds of different metaheuristic algorithms, which have been classified in many different ways. 

One of the latest classification techniques was presented by Darvishpoor et al. (2023). Based on these groups, 

the authors selected a metaheuristic from each group, which was examined in terms of whether the given 

algorithm had already been successfully applied to solve discrete or continuous problems (Table 2). 

Further literature research was carried out according to the scheme below: The selected algorithms were 

examined according to how many papers deal with the given metaheuristics at some level (Database: 

ScienceDirect). Figure 2 shows the results of searching for the name of the algorithm. According to the authors' 

assumption, the more articles deal with a metaheuristic, the more data and information can be obtained from 

the papers. Therefore, the given algorithm received a + sign above 10,000 hits and a ++ sign above 100,000. 

The authors also examined whether the title of a publication included the name of the metaheuristic and the 

nature of the problem (discrete or continuous). It was considered important to see how easy or difficult it is to 

search for problems and algorithms. If a publication containing this information was found in the first-page listing 

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(metaheuristics marked with an asterisk in Figure 2), the metaheuristic was given an extra + sign. The results 

obtained in this way are included in Table 2. 

 

Figure 2: Literature statistics 

Table 2: Metaheuristics for discrete or continuous variable problems 

Metaheuristic Variable’s type (Problem) Literature results 

Genetic Algorithm (GA) discrete-continuous +++/+++ 

Artificial Immune System (AIS) discrete ++ 

Selfish Herd Optimizer (SHO) continuous  

Swine Influenza Models-Based Optimization (SIMBO) continuous  

Bacterial Colony Chemotaxis Optimization (BCCO) continuous  

Ant Colony Optimization (ACO) discrete ++ 

African Vultures Optimization Algorithm (AVOA) continuous  

Whale Optimization Algorithm (WOA) continuous + 

Grey Wolf Optimizer (GWO) continuous + 

Flower Pollination Algorithm (FPA) continuous + 

Water Cycle Algorithm (WCA) discrete +++ 

Particle Swarm Optimization (PSO) discrete ++ 

Gravitational Search Algorithm (GSA) continuous ++ 

Chemical Reaction Optimization (CRO) discrete +++ 

Sine Cosine Algorithm (SCA) discrete + 

Harmony Search (HS) discrete ++ 

Golden Ball Algorithm (GBA) discrete  

Hybrid Metaheuristic (HM) discrete + 

With the help of these data, metaheuristics that provide a possible good solution for a given task were 

determined. The list below contains one example, highlighting which algorithms are primarily recommended for 

use based on the above (+++,++): 

Problem1 - Determining the location of warehouses (nature of the problem: discrete): GA, AIS, ACO, WCA, 

PSO, CRO, SCA, HS, GBA, HM. 

Problem2 - Inventory management (nature of the problem: continuous): GA, SHO, SIMBO, BCCO, AVOA, 

WOA, GWO, FPA, GSA. 

4. Efficiency test of the selection method: Algorithm for Traveling Salesman Problem 

The Traveling Salesman Problem (TSP) is the most well-known combinatorial NP-hard optimization problem. 

Many logistics problems, such as vehicle routing, distribution and network optimization, etc., can be transformed 

into TSP (Wang and Han, 2021). TSP poses the following question: „Given a list of cities and the distances 

between each pair of cities, what is the shortest route that visits each city precisely once and returns to the initial 

city?” (Rajwar et al., 2023). The TSP is a widely researched and popular area with a wide range of practical 

applications, such as production scheduling, material flow planning problems, waste collection management 

(Pop et al., 2024), order picking problems, frequency assignment problems in communication networks, etc. 

(Jati et al., 2023). 

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A
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A

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1
4

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8
5

3
7

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2
3

9
5

2
9

2
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9
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3

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Metaheuristics
(Database: ScienceDirect, 11.10.2024)

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Using the framework, based on the steps below, the authors chose an algorithm providing a possible good 

solution (Which does not guarantee the best possible solution for the task, but that is not the goal here. The 

goal is to have a potential solution technique for a problem, even if there is not much time to choose and there 

is less loss with a medium-quality solution than the absence of a complete solution.): 

1. The problem: Travelling Salesman Problem (TSP) 

2. A brief description of the problem: Given a list of cities and the distances between each pair of cities. The aim 

is to find the shortest route that visits each city precisely once and returns to the initial city. 

3. The nature of the problem: TSP is a combinatorial problem with discrete variables. 

4.Identifying metaheuristics that can provide a possible good solution: It was necessary to identify 

metaheuristics that, based on the literature, have already effectively solved tasks of a discrete nature. (Examples 

in Table 2.) 

5. Selecting a specific algorithm: Ant Colony Optimization was chosen.  

6. Application of metaheuristics to a specific task. 

The TSP contains discrete variables, so based on the above, the Ant Colony Optimization algorithm can provide 

a possible good solution. We tested the algorithm (ACOn, programming language: Python) created on the basis 

of expert knowledge gathered from the research materials belonging to this metaheuristic for tasks with n=50 

cities (symmetric matrix). The goal was to find the shortest path based on Eq(1). 

 (1) 

Solution with ACOn: 

Best Tour: [40, 41, 18, 38, 49, 46, 19, 37, 44, 17, 4, 36, 7, 43, 6, 28, 1, 26, 33, 29, 32, 0, 31, 21, 20, 2, 45, 5, 34, 

27, 15, 48, 25, 35, 3, 13, 24, 22, 10, 9, 8, 14, 16, 42, 30, 12, 23, 47, 39, 11] 

Best Distance: 3315 

Fine-tuning the parameters can further improve the efficiency of the procedure. Table 4 shows the parameter 

data for the best result. 

Table 4: Parameter settings (ACOn) 

Parameter  Value 

num_ants 100 

num_iterations 200 

alpha 1.0 

beta 2.0 

decay_factor 0.5 

 

The results of the 20 runs are shown in Figure 3, highlighting the best result (run 11). 

 

 

Figure 3: Running results ACOn-TSP 

The metaheuristics selected using the framework effectively solved the simple TSP, a problem consisting of 

discrete variables.  

5. Conclusions 

The practical application of metaheuristics and the reuse of existing algorithms is not an easy task. In addition, 

the authors found that in countless cases in industry, events do not take place according to the predetermined 

scenario. The uncertain environment, the complex problems, and, in many cases, the conflicting tension of the 

31323100

3200

3300

3400

0 5 10 15 20 25

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Running times

  𝑑𝑖𝑗𝑥𝑖𝑗  → 

50

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𝑚𝑖𝑛 

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results expected within a short period of time led to the search for a possible solution that would facilitate and 

speed up the time devoted to optimization while ensuring an acceptable result.  

The classification of algorithms and tasks to be solved according to a similar principle was identified as a 

shortcoming. To solve these problems and shortcomings, the authors introduced a new classification principle: 

they classified both logistic problems and metaheuristics into discrete and continuous groups. They have 

developed a method that can be used to assign a metaheuristic to a logistics problem with high probability and 

be able to handle it efficiently. As a first step, the nature and variables of the problem to be solved were examined 

(discrete or continuous). After that, metaheuristics were examined based on the fact that, according to the 

literature, mostly discrete or continuous problems have already been solved effectively. Finally, metaheuristics 

were associated with the problem to be solved based on common characteristics. The classification of logistic 

problems and metaheuristics along a similar, novel principle is useful and can facilitate the choice of the 

appropriate optimization method. The authors demonstrated the suitability of the framework through a specific 

example. With the help of this, the authors supported their proposition that it has the right to categorize logistics 

tasks and algorithms according to a novel principle. A possible good framework for facilitating the decision 

process has been implemented, which can contribute to more frequent reuse of metaheuristics and their real 

industrial application, increasing efficiency and sustainability. The current research provides countless additional 

research directions and goals: assigning specific parameters to both logistics tasks and metaheuristics, 

identifying common points based on the parameters and narrowing down the possible methods that provide a 

good solution, extending the study to even more metaheuristics, solving specific logistics tasks is the framework 

with metaheuristics chosen based on. 

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