Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

An estimation of distribution algorithm for combinatorial optimization problems

This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms

A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective

Scheduling Algorithms: Challenges Towards Smart Manufacturing

Collecting, processing, analyzing, and driving knowledge from large-scale real-time data is now realized with the emergence of Artificial Intelligence (AI) and Deep Learning (DL). The breakthrough of Industry 4.0 lays a foundation for intelligent manufacturing. However, implementation challenges of scheduling algorithms in the context of smart manufacturing are not yet comprehensively studied. The purpose of this study is to show the scheduling No.s that need to be considered in the smart manufacturing paradigm. To attain this objective, the literature review is conducted in five stages using publish or perish tools from different sources such as Scopus, Pubmed, Crossref, and Google Scholar. As a result, the first contribution of this study is a critical analysis of existing production scheduling algorithms\u27 characteristics and limitations from the viewpoint of smart manufacturing. The other contribution is to suggest the best strategies for selecting scheduling algorithms in a real-world scenario

A novel hybrid archimedes optimization algorithm for energy-efficient hybrid flow shop scheduling

The manufacturing sector consumes most of the global energy and had been in focus since the outbreak of the energy crisis. One of the proposed strategies to overcome this problem is to implement appropriate scheduling, such as Hybrid Flow Shop Scheduling. Therefore, this study aims to create a Hybrid Archimedes Optimization Algorithm (HAOA) for solving the Energy-Efficient Hybrid Flow Shop Scheduling Problem (EEHFSP). It is hoped that this helps to provide new insights into advanced HAOA methods for resolving the EEHFSP as the algorithm has the potential to be a more efficient alternative. In this study, three stages of EEHFSP were considered in the problem as well as a sequence-dependent setup and removal times in the second stage. Experiments with three population variations and iterations were presented for testing the effect of HAOA parameters on energy consumption. Furthermore, ten job variations are also presented to evaluate the performance of the HAOA algorithm and the results showed that HAOA iteration and the population did not affect the removal and processing of energy consumption, but impacted that of setup and idle. The comparison of these ten cases revealed that the proposed HAOA produced the best total energy consumption (TEC) when compared to the other algorithms

Algorithms and Methods for Designing and Scheduling Smart Manufacturing Systems

This book, as a Special Issue, is a collection of some of the latest advancements in designing and scheduling smart manufacturing systems. The smart manufacturing concept is undoubtedly considered a paradigm shift in manufacturing technology. This conception is part of the Industry 4.0 strategy, or equivalent national policies, and brings new challenges and opportunities for the companies that are facing tough global competition. Industry 4.0 should not only be perceived as one of many possible strategies for manufacturing companies, but also as an important practice within organizations. The main focus of Industry 4.0 implementation is to combine production, information technology, and the internet. The presented Special Issue consists of ten research papers presenting the latest works in the field. The papers include various topics, which can be divided into three categories—(i) designing and scheduling manufacturing systems (seven articles), (ii) machining process optimization (two articles), (iii) digital insurance platforms (one article). Most of the mentioned research problems are solved in these articles by using genetic algorithms, the harmony search algorithm, the hybrid bat algorithm, the combined whale optimization algorithm, and other optimization and decision-making methods. The above-mentioned groups of articles are briefly described in this order in this book

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex con guration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases

Genetic based discrete particle swarm optimization for elderly day care center timetabling

The timetabling problem of local Elderly Day Care Centers (EDCCs) is formulated into a weighted maximum constraint satisfaction problem (Max-CSP) in this study. The EDCC timetabling problem is a multi-dimensional assignment problem, where users (elderly) are required to perform activities that require different venues and timeslots, depending on operational constraints. These constraints are categorized into two: hard constraints, which must be fulfilled strictly, and soft constraints, which may be violated but with a penalty. Numerous methods have been successfully applied to the weighted Max-CSP; these methods include exact algorithms based on branch and bound techniques, and approximation methods based on repair heuristics, such as the min-conflict heuristic. This study aims to explore the potential of evolutionary algorithms by proposing a genetic-based discrete particle swarm optimization (GDPSO) to solve the EDCC timetabling problem. The proposed method is compared with the min-conflict random-walk algorithm (MCRW), Tabu search (TS), standard particle swarm optimization (SPSO), and a guided genetic algorithm (GGA). Computational evidence shows that GDPSO significantly outperforms the other algorithms in terms of solution quality and efficiency