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

Optimization Models and Algorithms for Spatial Scheduling

Spatial scheduling problems involve scheduling a set of activities or jobs that each require a certain amount of physical space in order to be carried out. In these problems space is a limited resource, and the job locations, orientations, and start times must be simultaneously determined. As a result, spatial scheduling problems are a particularly difficult class of scheduling problems. These problems are commonly encountered in diverse industries including shipbuilding, aircraft assembly, and supply chain management. Despite its importance, there is a relatively scarce amount of research in the area of spatial scheduling. In this dissertation, spatial scheduling problems are studied from a mathematical and algorithmic perspective. Optimization models based on integer programming are developed for several classes of spatial scheduling problems. While the majority of these models address problems having an objective of minimizing total tardiness, the models are shown to contain a core set of constraints that are common to most spatial scheduling problems. As a result, these constraints form the basis of the models given in this dissertation and many other spatial scheduling problems with different objectives as well. The complexity of these models is shown to be at least NP-complete, and spatial scheduling problems in general are shown to be NP-hard. A lower bound for the total tardiness objective is shown, and a polynomial-time algorithm for computing this lower bound is given. The computational complexity inherent to spatial scheduling generally prevents the use of optimization models to find solutions to larger, realistic problems in a reasonable time. Accordingly, two classes of approximation algorithms were developed: greedy heuristics for finding fast, feasible solutions; and hybrid meta-heuristic algorithms to search for near-optimal solutions. A flexible hybrid algorithm framework was developed, and a number of hybrid algorithms were devised from this framework that employ local search and several varieties of simulated annealing. Extensive computational experiments showed these hybrid meta-heuristic algorithms to be effective in finding high-quality solutions over a wide variety of problems. Hybrid algorithms based on local search generally provided both the best-quality solutions and the greatest consistency

Machine Scheduling for Multitask Machining

Multitasking is an important part of today’s manufacturing plants. Multitask machine tools are capable of processing multiple operations at the same time by applying a different set of part and tool holding devices. Mill-turns are multitasking machines with the ability to perform a variety of operations with considerable accuracy and agility. One critical factor in simultaneous machining is to create a schedule for different operations to be completed in minimum make-span. A Mixed Integer Linear Programming (MILP) model is developed to address the machine scheduling problem. The adopted assumptions are more realistic when compared with the previous models. The model allows for processing multiple operations simultaneously on a single part; parts are being processed on the same setup and multiple turrets can process a single operation of a single job simultaneously performing multiple depths of cut. A Simulated Annealing algorithm with a novel initial solution and assignment approach is developed to solve large instances of the problem. Test cases are presented to assess the proposed model and metaheuristic algorithm

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Reducing physical ergonomic risks at assembly lines by line balancing and job rotation: A survey

Factors such as repetitiveness of work, required application of forces, handling of heavy loads, and awkward, static postures expose assembly line workers to risks of musculoskeletal disorders. As a rule, companies perform a post hoc analysis of ergonomic risks and examine ways to modify workplaces with high ergonomic risks. However, it is possible to lower ergonomic risks by taking ergonomics aspects into account right from the planning stage. In this survey, we provide an overview of the existing optimization approaches to assembly line balancing and job rotation scheduling that consider physical ergonomic risks. We summarize major findings to provide helpful insights for practitioners and identify research directions

Genetic algorithms

Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology

A survey on constructing rosters for air traffic controllers

In this survey the state-of-the-art technology and the literature to date are discussed. In particular, we will discuss the gap in the literature concerning rostering staff to tasks by qualifications, with the inclusion of restrictions on a measure of task familiarity, which is a unique consequence of the structure of ATC operations

Quantum Computing in Logistics and Supply Chain Management an Overview

The work explores the integration of quantum computing into logistics and supply chain management, emphasising its potential for use in complex optimisation problems. The discussion introduces quantum computing principles, focusing on quantum annealing and gate-based quantum computing, with the Quantum Approximate Optimisation Algorithm and Quantum Annealing as key algorithmic approaches. The paper provides an overview of quantum approaches to routing, logistic network design, fleet maintenance, cargo loading, prediction, and scheduling problems. Notably, most solutions in the literature are hybrid, combining quantum and classical computing. The conclusion highlights the early stage of quantum computing, emphasising its potential impact on logistics and supply chain optimisation. In the final overview, the literature is categorised, identifying quantum annealing dominance and a need for more research in prediction and machine learning is highlighted. The consensus is that quantum computing has great potential but faces current hardware limitations, necessitating further advancements for practical implementation