In project scheduling, the activity durations can often be reduced by dedicating additional resources. Time/Cost Trade-off Problem considers the compromise between the total cost and project duration. The discrete version of the problem assumes a number of time/cost pairs, so called modes, and selects a mode for each activity. In this thesis we consider the Discrete Time/Cost Trade-off Problem. We first study the Deadline Problem, i.e., the problem of minimizing total cost subject to a deadline on project duration. To solve the Deadline Problem, we propose several optimization and approximation algorithms that are based on optimal Linear Programming Relaxation solutions. We then analyze the problem of generating all efficient solutions, and propose an approach that uses the successive solutions of the Deadline Problem. Our computational results on large-sized problem instances have revealed the satisfactory behavior of our algorithms.

The growing extent and variety of present military operations forces to use the resources in hand at its best. Especially, the optimum usage and assignment of limited number of the air force resources to missions will provide a considerable advantage in the battle field. The problem of finding the feasible and optimum assignment has been known to be studied / yet performing the process faster is still a topic that captures researchers&rsquo / attention because of the computational complexity that the assignment problem involves within. In this thesis, exploring the optimal assignment of fleets/aircrafts to targets/groups of targets is going to be performed via algorithms and heuristics. As the best choice for finding the exact solution, Branch-and-Bound algorithm, which is an intelligent way of searching for the solution on a solution tree where the nodes with potential of not leading to the solution are fathomed, has been investigated and applied according to the specific problem needs. The number of nodes on the search tree increases exponentially as the problem size increases. Moreover / as the size of the assignment problem increases, attaining the solution solely by Branch-and-Bound algorithm is definitely computationally expensive due to memory and time requirements. Therefore, Genetic algorithm which can provide good solutions in a relatively short time without having computational difficulties is considered as the second algorithm. Branch-and-Bound algorithm and Genetic algorithm are separately used for obtaining the solution. Hybrid algorithms which are combinations of Branch-and-Bound and Genetic algorithms are used with heuristics for improving the results.

ABSTRACT FLEXIBLE ASSEMBLY LINE DESIGN PROBLEM WITH FIXED NUMBER OF WORKSTATIONS Barut&ccedil / uoglu, Sirin M.S. Department of Industrial Engineering Supervisor: Prof. Dr. Meral Azizoglu July 2009, 70 pages In this thesis, we study a Flexible Assembly Line Design problem. We assume the task times and equipment costs are correlated in the sense that for all tasks the cheaper equipment gives no smaller task time. Given the cycle time and number of workstations we aim to find the assignment of tasks and equipments to the workstations that minimizes the total equipment cost. We study a special case of the problem with identical task times. For the general case, we develop a branch and bound algorithm that uses powerful lower bounds and reduction mechanisms. We test the performance of our branch and bound algorithm on randomly generated test problems. The results of our experiments have revealed that we are able to solve large-sized problem instances in reasonable times.

In this dissertation, we study the single machine scheduling problem with an objective of minimizing the total completion time subject to release dates. The problem, denoted 1|rj £UCj ,was known to be strongly NP-hard and both theoretically and practically important. The focus of the research in this dissertation is to develop the efficient algorithms for solving the 1|rj|£UCj problem. This thesis contains two parts. In the first part, the theme concerns the approximation approach. We derive a necessary and sufficient condition for local optimality, which can be implemented as a priority rule and be used to construct three heuristic algorithms with running times of O(n log n). By ¡¨local optimality¡¨, we mean the optimality of all candidates whenever a job is selected in a schedule, without considering the other jobs preceding or following. This is the most broadly considered concepts of locally optimal rule. We also identify a dominant subset which is strictly contained in each of all known dominant subsets, where a dominant subset is a set of solutions containing all optimal schedules. In the second part, we develop our optimality algorithms for the 1|rj |£UCj problem. First, we present a lemma for estimating the sum of delay times of the rest jobs, if the starting time is delayed a period of time in a schedule. Then, using the lemma, partially, we proceed to develop a new partition property and three dominance theorems, that will be used and have improved the branch-and-bound algorithms for our optimization approach. By exploiting the insights gained from our heuristics as a branching scheme and by exploiting our heuristics as an upper bounding procedure, we propose three branch-and-bound algorithms. Our algorithms can optimally solve the problem up to 120 jobs, which is known to be the best till now.

<p>This thesis consists of an introduction and sevenindependent, but closely related, papers which all deal withproblems in structural optimization. In particular, we considermodels and methods for global optimization of problems intopology design of discrete and continuum structures.</p><p>In the first four papers of the thesis the nonconvex problemof minimizing the weight of a truss structure subject to stressconstraints is considered. First itis shown that a certainsubclass of these problems can equivalently be cast as linearprograms and thus efficiently solved to global optimality.Thereafter, the behavior of a certain well-known perturbationtechnique is studied. It is concluded that, in practice, thistechnique can not guarantee that a global minimizer is found.Finally, a convergent continuous branch-and-bound method forglobal optimization of minimum weight problems with stress,displacement, and local buckling constraints is developed.Using this method, several problems taken from the literatureare solved with a proof of global optimality for the firsttime.</p><p>The last three papers of the thesis deal with topologyoptimization of discretized continuum structures. Theseproblems are usually modeled as mixed or pure nonlinear 0-1programs. First, the behavior of certain often usedpenalization methods for minimum compliance problems isstudied. It is concluded that these methods may fail to producea zero-one solution to the considered problem. To remedy this,a material interpolation scheme based on a rational functionsuch that compli- ance becomes a concave function is proposed.Finally, it is shown that a broad range of nonlinear 0-1topology optimization problems, including stress- anddisplacement-constrained minimum weight problems, canequivalently be modeled as linear mixed 0-1 programs. Thisresult implies that any of the standard methods available forgeneral linear integer programming can now be used on topologyoptimization problems.</p><p><b>Keywords:</b>topology optimization, global optimization,stress constraints, linear programming, mixed integerprogramming, branch-and-bound.</p>

Thesis (doctoral)--Universität Karlsruhe, 1999.

Thèse de doctorat : SCIENCES APPLIQUEES : Metz : 1994. / 1994METZ031S. 57 REF.

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. Dimitri N. Mavris; Committee Member: Dr. Brian J. German; Committee Member: Dr. Daniel P. Schrage; Committee Member: Dr. Frederic Villeneuve; Committee Member: Dr. Michelle R. Kirby; Committee Member: Ms. Antje Lembcke. Part of the SMARTech Electronic Thesis and Dissertation Collection.

The research reported in this thesis considers the classical combinatorial optimization problem known as the Generalized Assignment Problem (GAP). Since the mid 1970's researchers have been developing solution approaches for this particular type of problem due to its importance both in practical and theoretical terms. Early attempts at solving GAP tended to use exact integer programming techniques such as Branch and Bound. Although these tended to be reasonably successful on small problem instances they struggle to cope with the increase in computational effort required to solve larger instances. The increase in available computing power during the 1980's and 1990's coincided with the development of some highly efficient heuristic approaches such as Tabu Search (TS), Genetic Algorithms (GA) and Simulated Annealing (SA). Heuristic approaches were subsequently developed that were able to obtain high quality solutions to larger and more complex instances of GAP. Most of these heuristic approaches were able to outperform highly sophisticated commercial mathematical programming software since the heuristics tend to be tailored to the problem and therefore exploit its structure. A new approach for solving GAP has been developed during this research that combines the exact Branch and Bound approach and the heuristic strategy of Tabu Search to produce a hybrid algorithm for solving GAP. This approach utilizes the mathematical programming software Xpress-MP as a Branch and Bound solver in order to solve sub-problems that are generated by the Tabu Search guiding heuristic. Tabu Search makes use of memory structures that record information about attributes of solutions visited during the search. This information is used to guide the search and in the case of the hybrid algorithm to generate sub problems to pass to the Branch and Bound solver. The new algorithm has been developed, imp lemented and tested on benchmark test problems that are extremely challenging and a comprehensive report and analysis of the experimentation is reported in this thesis.

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