A Transportation-Scheduling System for Managing Silvicultural Projects

A silvicultural project encompasses tasks such as site-level planning, regeneration, harvest, and stand-tending treatments. An essential problem in managing silvicultural projects is to efficiently schedule the operations while considering project task due dates and costs of moving scarce resources to specific job locations. Transportation costs represent a significant portion of the total operating cost. The main difficulty in developing such a management system is finding an optimal transport schedule while handling complicated constraints, such as precedence and temporal relations among project tasks, project due dates, truck routing, weather, and other operational conditions. It is well known that finding an optimal solution to these types of problems involves high computational complexity. They are usually NP-hard. For this reason, we propose to use simulated annealing -a meta-heuristic optimization method- that interacts with a network simulation model of the system in which the precedence and temporal relations among project tasks and logistics are explicitly accounted for. The approach has been tested using data provided by a silvicultural contractor located in Alabama. The results obtained solving one instance of a small size problem with five worksites showed that the best solution could be found in less than four minutes using a personal computer with a processor Pentium III (1 GHz). A good solution for a larger problem with twenty worksites was found in thirty minutes. Also a resource analysis is performed to evaluate the impact of each resource on the best solution

The minimum cost network upgrade problem with maximum robustness to multiple node failures

The design of networks which are robust to multiple failures is gaining increasing attention in areas such as telecommunications. In this paper, we consider the problem of upgrading an existent network in order to enhance its robustness to events involving multiple node failures. This problem is modeled as a bi-objective mixed linear integer formulation considering both the minimization of the cost of the added edges and the maximization of the robustness of the resulting upgraded network. As the robustness metric of the network, we consider the value of the Critical Node Detection (CND) problem variant which provides the minimum pairwise connectivity between all node pairs when a set of c critical nodes are removed from the network. We present a general iterative framework to obtain the complete Pareto frontier that alternates between the minimum cost edge selection problem and the CND problem. Two different approaches based on a cover model are introduced for the edge selection problem. Computational results conducted on different network topologies show that the proposed methodology based on the cover model is effective in computing Pareto solutions for graphs with up to 100 nodes, which includes four commonly used telecommunication networks.publishe

Understanding Complexity in Multiobjective Optimization

This report documents the program and outcomes of the Dagstuhl Seminar 15031 Understanding Complexity in Multiobjective Optimization. This seminar carried on the series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization, and strengthening the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities. The purpose of the seminar was to bring together researchers from the two communities to take part in a wide-ranging discussion about the different sources and impacts of complexity in multiobjective optimization. The outcome was a clarified viewpoint of complexity in the various facets of multiobjective optimization, leading to several research initiatives with innovative approaches for coping with complexity

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

Matheuristic algorithms for solving multi-objective/stochastic scheduling and routing problems

In der Praxis beinhalten Optimierungsprobleme oft unterschiedliche Ziele, welche optimiert werden sollen. Oft ist es nicht möglich die Ziele zu einem einzelnen Ziel zusammenzufassen. Mehrzieloptimierung beschäftigt sich damit, solche Probleme zu lösen. Wie in der Einzieloptimierung muss eine Lösung alle Nebenbedingungen des Problems erfüllen. Im Allgemeinen sind die Ziele konfligierend, sodass es nicht möglich ist eine einzelne Lösung zu finden welche optimal im Sinne aller Ziele ist. Algorithmen zum Lösen von Mehrziel-Optimierungsproblemen, präsentieren dem Entscheider eine Menge von effizienten Alternativen. Effizienz in der Mehrzieloptimierung ist als Pareto-Optimalität ausgedrückt. Eine Lösung eines Optimierungsproblems ist genau dann Pareto-optimal wenn es keine andere zulässige Lösung gibt, welche in allen Zielen mindestens gleich gut wie die betrachtete Lösung ist und besser in mindestens einem Ziel. In dieser Arbeit werden Mehrziel-Optimierungsprobleme aus zwei unterschiedlichen Anwendungsgebieten betrachtet. Das erste Problem, das Multi-objective Project Selection, Scheduling and Staffing with Learning Problem (MPSSSL), entstammt dem Management in forschungsorientierten Organisationen. Die Entscheider in solchen Organisationen stehen vor der Frage welche Projekte sie aus einer Menge von Projektanträgen auswählen sollen, und wie diese Teilmenge von Projekten (ein Projektportfolio) mit den benötigten Ressourcen ausgestattet werden kann (dies beinhaltet die zeitliche und personelle Planung). Aus unterschiedlichen Gründen ist dieses Problem schwer zu lösen, z.B. (i) die Auswahl von Projekten unter Beachtung der beschränkten Ressourcen ist ein Rucksackproblem (und ist damit NP-schwer) (ii) ob ein Projektportfolio zulässig ist oder nicht hängt davon ab ob, man dafür einen Zeitplan erstellen kann und genügend Mitarbeiter zur Verfügung stehen. Da in diesem Problem die Mitarbeiterzuordnung zu den einzelnen Projekten einbezogen wird, muss der Entscheider Ziele unterschiedlicher Art berücksichtigen. Manche Ziele sind ökonomischer Natur, z.B. die Rendite, andere wiederum beziehen sich auf die Kompetenzentwicklung der einzelnen Mitarbeiter. Ziele, die sich auf die Kompetenzentwicklung beziehen, sollen sicherstellen, dass das Unternehmen auch in Zukunft am Markt bestehen kann. Im Allgemeinen können diese unterschiedlichen Ziele nicht zu einem einzigen Ziel zusammengefasst werden. Daher werden Methoden zur Lösung von Mehrziel-Optimierungsproblemen benötigt. Um MPSSSL Probleme zu lösen werden in dieser Arbeit zwei unterschiedliche hybride Algorithmen betrachtet. Beide kombinieren nämlich Metaheuristiken (i) den Nondominated Sorting Genetic (NSGA-II) Algorithmus, und den (ii)~Pareto Ant Colony (P-ACO) Algorithmus, mit einem exakten Algorithmus zum Lösen von Linearen Programmen kombinieren. Unsicherheit ist ein weiterer wichtiger Aspekt der in der Praxis auftaucht. Unterschiedliche Parameter des Problems können unsicher sein (z.B. der aus einem Projekt erzielte Gewinn oder die Zeit bzw. der Aufwand, der benötigt wird, um die einzelnen Vorgänge eines Projekts abzuschließen). Um in diesem Fall das ``beste'' Projektportfolio zu finden, werden Methoden benötigt, welche stochastische Mehrziel-Optimierungsprobleme lösen können. Zur Lösung der stochastischen Erweiterung (SMPSSSL) des MPSSSL Problems zu lösen, präsentieren wir eine Methode, die den zuvor genannten hybriden NSGA-II Algorithmus mit dem Adaptive Pareto Sampling (APS) Algorithmus kombiniert. APS wird verwendet, um das Zusammenspiel von Simulation und Optimierung zu koordinieren. Zur Steigerung der Performance des Simulationsprozesses, verwenden wir Importance Sampling (IS). Das zweite Problem dieser Arbeit, das Bi-Objective Capacitated Vehicle Routing Problem with Route Balancing (CVRPB), kommt aus dem Bereich Logistik. Wenn man eine Menge von Kunden zu beliefern hat, steht man als Entscheider vor der Frage, wie man die Routen für eine fixe Anzahl von Fahrzeugen (mit beschränkter Kapazität) bestimmt, sodass alle Kunden beliefert werden können. Die Routen aller Fahrzeuge starten und enden dabei immer bei einem Depot. Die Einziel-Variante dieses Problems ist als Capacitated Vehicle Routing Problem (CVRP) bekannt, dessen Ziel es ist die Lösung zu finden, die die Gesamtkosten aller Routen minimiert. Dabei tritt jedoch das Problem auf, dass die Routen der optimalen Lösung sehr unterschiedliche Fahrtzeiten haben können. Unter bestimmten Umständen ist dies jedoch nicht erwünscht. Um dieses Problem zu umgehen, betrachten wir in dieser Arbeit eine Variante des (bezeichnet als CVRPB) CVRP, welche als zweite Zielfunktion die Balanziertheit der einzelnen Routen einbezieht. Zur Lösung von CVRPB Problemen verwenden wir die Adaptive Epsilon-Constraint Method in Kombination mit einem Branch-and-Cut Algorithmus und zwei unterschiedlichen Genetischen Algorithmen (GA), (i) einem Einziel-GA und (ii) dem NSGA-II. In dieser Arbeit werden Optimierungsalgorithmen präsentiert, welche es erlauben, Mehrziel- und stochastische Mehrziel-Optimierungsprobleme zu lösen. Unterschiedliche Algorithmen wurden implementiert und basierend auf aktuellen Performance-Maßen verglichen. Experimente haben gezeigt, dass die entwickelten Methoden gut geeignet sind, die betrachteten Optimierungsprobleme zu lösen. Die hybriden Algorithmen, welche Metaheuristiken mit exakten Methoden kombinieren, waren entweder ausschlaggebend um das Problem zu lösen (im Fall des Project Portfolio Selection Problems) oder konnten die Performance des Lösungsprozesses signifikant verbessern (im Fall des Vehicle Routing Problems).In practice decision problems often include different goals which can hardly be aggregated to a single objective for different reasons. In the field of multi-objective optimization several objective functions are considered. As in single objective optimization a solution has to satisfy all constraints of the problem. In general the goals are conflicting and there will be no solution, that is optimal for all objectives. Algorithms for multi-objective optimization problems provide the decision maker a set of efficient solutions, among which she or he can choose the most suitable alternative. In multi-objective optimization efficiency of a solution is expressed as Pareto-optimality. Pareto-optimality of a solution is defined as the property that no other solution exists that is better than the proposed one in at least one objective and at least equally good in all criteria. The first application that is considered in this thesis, the Multi-objective Project Selection, Scheduling and Staffing with Learning problem (MPSSSL) arises from the field of management in research-centered organizations. Given a set of project proposals the decision makers have to select the ``best'' subset of projects (a project portfolio) and set these up properly (schedule them and provide the necessary resources). This problem is hard to solve for different reasons: (i) selecting a subset of projects considering limited resources is a knapsack-type problem that is known to be NP-hard, and (ii) to determine the feasibility of a given portfolio, the projects have to be scheduled and staff must be assigned to them. As in this problem the assignment of workers is influenced by the decision which portfolio should be selected, the decision maker has to consider goals of different nature. Some objectives are related to economic goals (e.g. return of investment), others are related to the competence development of the workers. Competence oriented goals are motivated by the fact that competencies determine the attainment and sustainability of strategic positions in market competition. In general the objectives cannot be combined to a single objective, therefore methods for solving multi-objective optimization problems are used. To solve the problem we use two different hybrid algorithms that combine metaheuristic algorithms, (i) the Nondominated Sorting Genetic Algorithm (NSGA-II), and (ii) Pareto Ant Colony (P-ACO) algorithm with a linear programming solver as a subordinate. In practice, uncertainty is another typically encountered aspect. Different parameters of the problem can be uncertain (e.g. benefits of a project, or the time and effort required to perform the single activities required by a project). To determine the ``best'' portfolio, methods are needed that are able to handle uncertainty in optimization. To solve the stochastic extension (SMPSSSL) of the MPSSSL problem we present an algorithm that combines the aforementioned NSGA-II algorithm with the Adaptive Pareto Sampling (APS) algorithm. APS is used to handle the interplay between multi-objective optimization and simulation. The performance of the simulation process is increased by using importance sampling (IS). The second problem, the Bi-objective Capacitated Vehicle Routing Problem with Route Balancing (CVRPB) arises from the field of vehicle routing. Given a set of customers, the decision makers have to construct routes for a fixed number of vehicles, each starting and ending at the same depot, such that the demands of all customers can be fulfilled, and the capacity constraints of each vehicle are not violated. The traditional objective of this problem (known as the Capacitated Vehicle Routing Problem (CVRP)) is minimizing the total costs of all routes. A problem that may arise by this approach is that the resulting routes can be very unbalanced (in the sense of drivers workload). To overcome this problem a second objective function that measures the balance of the routes of a solution is introduced. In this work, we use the Adaptive Epsilon-Constraint Method in combination with a branch-and-cut algorithm and two genetic algorithms (i) a single-objective GA and (ii) the multi-objective NSGA-II, to solve the considered problem. Prototypes of different algorithms to solve the problems are developed and their performance is assessed by using state of the art performance measures. The computational experiments show that the developed solution procedures will be well suited to solve the considered optimization problems. The hybrid algorithms combining metaheuristic and exact optimization methods, turned out to be crucial to solve the problem (application to project portfolio selection) or to improve the performance of the solution procedure (application to vehicle routing)