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

Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance

Multi-Objective Mission Route Planning Using Particle Swarm Optimization

The Mission Routing Problem (MRP) is the selection of a vehicle path starting at a point, going through enemy terrain defended by radar sites to get to the target(s) and returning to a safe destination (usually the starting point). The MRP is a three-dimensional, multi-objective path search with constraints such as fuel expenditure, time limits, multi-targets, and radar sites with different levels of risks. It can severely task all the resources (people, hardware, software) of the system trying to compute the possible routes. The nature of the problem can cause operational planning systems to take longer to generate a solution than the time available. Since time is critical in MRP, it is important that a solution is reached within a relatively short time. It is not worth generating the solution if it takes days to calculate since the information may become invalid during that time. Particle Swarm Optimization (PSO) is an Evolutionary Algorithm (EA) technique that tries to find optimal solutions to complex problems using particles that interact with each other. Both Particle Swarm Optimization (PSO) and the Ant System (AS) have been shown to provide good solutions to Traveling Salesman Problem (TSP). PSO_AS is a synthesis of PSO and Ant System (AS). PSO_AS is a new approach for solving the MRP, and it produces good solutions. This thesis presents a new algorithm (PSO_AS) that functions to find the optimal solution by exploring the MRP search space stochastically

An optimized field coverage planning approach for navigation of agricultural robots in fields involving obstacle areas

Technological advances combined with the demand of cost efficiency and environmental considerations has led farmers to review their practices towards the adoption of new managerial approaches, including enhanced automation. The application of field robots is one of the most promising advances among automation technologies. Since the primary goal of an agricultural vehicle is the complete coverage of the cropped area within a field, an essential prerequisite is the capability of the mobile unit to cover the whole field area autonomously. In this paper, the main objective is to develop an approach for coverage planning for agricultural operations involving the presence of obstacle areas within the field area. The developed approach involves a series of stages including the generation of field‐work tracks in the field polygon, the clustering of the tracks into blocks taking into account the in‐field obstacle areas, the headland paths generation for the field and each obstacle area, the implementation of a genetic algorithm to optimize the sequence that the field robot vehicle will follow to visit the blocks and an algorithmic generation of the task sequences derived from the farmer practices. This approach has proven that it is possible to capture the practices of farmers and embed these practices in an algorithmic description providing a complete field area coverage plan in a form prepared for execution by the navigation system of a field robot

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering