Recently meta-heuristics have become a popular solution methodology, in terms of both research and application, for solving combinatorial optimization problems. Meta-heuristic methods guide simple heuristics or priority rules designed to solve a particular problem. Meta-heuristics enhance these simple heuristics by using a higher level strategy. The advantage of using meta-heuristics over conventional optimization methods is meta-heuristics are able to find good (near optimal) solutions within a reasonable computation time. Investigating this line of research is justified because in most practical cases with medium to large scale problems, the use of meta-heuristics is necessary to be able to find a solution in a reasonable time. The specific meta-heuristic studied in this research is, Meta-RaPS; Meta-heuristic for Randomized Priority Search which is developed by DePuy and Whitehouse in 2001. Meta-RaPS is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element (Moraga, 2002). To date, Meta-RaPS had been applied to different types of combinatorial optimization problems and achieved comparable solution performance to other meta-heuristic techniques. The specific problem studied in this dissertation is parameter setting of Meta-RaPS. The topic of parameter setting for meta-heuristics has not been extensively studied in the literature. Although the parameter setting method devised in this dissertation is used primarily on Meta-RaPS, it is applicable to any meta-heuristic's parameter setting problem. This dissertation not only enhances the power of Meta-RaPS by parameter tuning but also it introduces a robust parameter selection technique with wide-spread utility for many meta-heuristics. Because the distribution of solution values generated by meta-heuristics for combinatorial optimization problems is not normal, the current parameter setting techniques which employ a parametric approach based on the assumption of normality may not be appropriate. The proposed method is Non-parametric Based Genetic Algorithms. Based on statistical tests, the Non-parametric Based Genetic Algorithms (NPGA) is able to enhance the solution quality of Meta-RaPS more than any other parameter setting procedures benchmarked in this research. NPGA sets the best parameter settings, of all the methods studied, for 38 of the 41 Early/Tardy Single Machine Scheduling with Common Due Date and Sequence-Dependent Setup Time (ETP) problems and 50 of the 54 0-1 Multidimensional Knapsack Problems (0-1 MKP). In addition to the parameter setting procedure discussed, this dissertation provides two Meta-RaPS combinatorial optimization problem applications, the 0-1 MKP, and the ETP. For the ETP problem, the Meta-RaPS application in this dissertation currently gives the best meta-heuristic solution performance so far in the literature for common ETP test sets. For the large ETP test set, Meta-RaPS provided better solution performance than Simulated Annealing (SA) for 55 of the 60 problems. For the small test set, in all four different small problem sets, the Meta-RaPS solution performance outperformed exiting algorithms in terms of average percent deviation from the optimal solution value. For the 0-1 MKP, the present Meta-RaPS application performs better than the earlier Meta-RaPS applications by other researchers on this problem. The Meta-RaPS 0-1 MKP application presented here has better solution quality than the existing Meta-RaPS application (Moraga, 2005) found in the literature. Meta-RaPS gives 0.75% average percent deviation, from the best known solutions, for the 270 0-1 MKP test problems.

Composite panel structure optimization is commonly decomposed into panel optimization subproblems, with specified local loads, resulting in manufacturing incompatibilities between adjacent panel designs. Using genetic algorithms to optimize local panel stacking sequences allows panel populations of stacking sequences to evolve in parallel and send migrants to adjacent panels, so as to blend the local panel designs globally. The blending process is accomplished using the edit distance between individuals of a population and the set of migrants from adjacent panels. The objective function evaluating the fitness of designs is modified according to the severity of mismatches detected between neighboring populations. This lays the ground work for natural evolution to a blended global solution without leaving the paradigm of genetic algorithms. An additional method applied here for constructing globally blended panel designs uses a parallel decomposition antithetical to that of earlier work. Rather than performing concurrent panel genetic optimizations, a single genetic optimization is conducted for the entire structure with the parallelism solely within the fitness evaluations. A guide based genetic algorithm approach is introduced to exclusively generate and evaluate valid globally blended designs, utilizing a simple master-slave parallel implementation, implicitly reducing the size of the problem design space and increasing the quality of discovered local optima. / Ph. D.

Optimization problems of location-assignment correspond to a wide range of real situations, such as factory network design. However most of the previous works seek in most cases at minimizing a cost function. Traffic incidents routinely impact the performance and the safety of the supply. These incidents can not be totally avoided and must be regarded. A way to consider these incidents is to design a network on which multiple assignments are performed. Precisely, the problem we focus on deals with power supplying that has become a more and more complex and crucial question. Many international companies have customers who are located all around the world; usually one customer per country. At the other side of the scale, power extraction or production is done in several sites that are spread on several continents and seas. A strong willing of becoming less energetically-dependent has lead many governments to increase the diversity of supply locations. For each kind of energy, many countries expect to deal ideally with 2 or 3 location sites. As a decrease in power supply can have serious consequences for the economic performance of a whole country, companies prefer to balance equally the production rate among all sites as the reliability of all the sites is considered to be very similar. Sharing equally the demand between the 2 or 3 sites assigned to a given area is the most common way. Despite the cost of the network has an importance, it is also crucial to balance the loading between the sites to guarantee that no site would take more importance than the others for a given area. In case an accident happens in a site or in case technical problems do not permit to satisfy the demand assigned to the site, the overall power supply of this site is still likely to be ensured by the one or two available remaining site(s). It is common to assign a cost per open power plant and another cost that depends on the distance between the factory or power extraction point and the customer. On the whole, such companies who are concerned in the quality service of power supply have to find a good trade-off between this factor and their overall functioning cost. This situation exists also for companies who supplies power at the national scale. The expected number of areas as well that of potential sites, can reach 100. However the targeted size of problem to be solved is 50. This thesis focuses on devising an efficient methodology to provide all the solutions of this bi-objective problem. This proposal is an investigation of close problems to delimit the most relevant approaches to this untypical problem. All this work permits us to present one exact method and an evolutionary algorithm that might provide a good answer to this problem. / Master of Science

Composite panel structure optimization is commonly decomposed into panel optimization subproblems, with specified local loads, resulting in manufacturing incompatibilities between adjacent panel designs. Using genetic algorithms to optimize local panel stacking sequences allows panel populations of stacking sequences to evolve in parallel and send migrants to adjacent panels, so as to blend the local panel designs globally. The blending process is accomplished using the edit distance between individuals of a population and the set of migrants from adjacent panels. The objective function evaluating the fitness of designs is modified according to the severity of mismatches detected between neighboring populations. This lays the ground work for natural evolution to a blended global solution without leaving the paradigm of genetic algorithms. An additional method proposed here for constructing globally blended panel designs uses a parallel decomposition antithetical to that of earlier work. Rather than performing concurrent panel genetic optimizations, a single genetic optimization is conducted for the entire structure with the parallelism solely within the fitness evaluations. A guide based genetic algorithm approach is introduced to exclusively generate and evaluate valid globally blended designs, utilizing a simple master-slave parallel implementation, implicitly reducing the size of the problem design space and increasing the quality of discovered local optima. / Master of Science

This research explores the idea that for certain optimization problems there is a way to parallelize the algorithm such that the parallel efficiency can exceed one hundred percent. Specifically, a parallel compiler, PC, is used to apply shortcutting techniquest to a metaheuristic Ant Colony Optimization (ACO), to solve the well-known Traveling Salesman Problem (TSP) on a cluster running Message Passing Interface (MPI). The results of both serial and parallel execution are compared using test datasets from the TSPLIB.

It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems.

Thesis (PhD (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2004. / Suppose a lottery scheme consists of randomly selecting an unordered winning n-subset from a universal set of m numbers, while a player participates in the scheme by purchasing a playing set of any number of unordered n-subsets from the same universal set prior to a winning draw, and is awarded a prize if ...

<p>This thesis focuses on the development of algorithms that will allow protein design calculations to incorporate more realistic modeling assumptions. Protein design algorithms search large sequence spaces for protein sequences that are biologically and medically useful. Better modeling could improve the chance of success in designs and expand the range of problems to which these algorithms are applied. I have developed algorithms to improve modeling of backbone flexibility (DEEPer) and of more extensive continuous flexibility in general (EPIC and LUTE). I’ve also developed algorithms to perform multistate designs, which account for effects like specificity, with provable guarantees of accuracy (COMETS), and to accommodate a wider range of energy functions in design (EPIC and LUTE).</p> / Dissertation

The Ant Colony Optimization belongs into the metaheuristic methods category and it has been developing quite recently. So far it has shown its capabalities to over-perform other metaheuristic methods in quality of the solutions. This work brings analysis of the possible applications of the method on the classical optimization combinatorial problems -- traveling salesman problem, vehicle routing problem, knapsack problem, generalized assignment problem and maximal clique problem. It also deals with the practical experiments with application on several optimization problems and analysis of the time and memory complexity of such algorithms. The last part of the work is dedicated to the possibility of parallelization of the algorithm, which was result of the application of the ACO method on the traveling salesman problem. It brings analysis of the crucial operations and data synchronization issues, as well as practical example and demonstration of the parallelized version of the algorithm.

A dissertation submitted in partial ful lment of the degree of Master of Science in Engineering (Electrical) (50/50) in the Faculty of Engineering and the Built Environment Department of Electrical and Information Engineering May 2017 / Numerous applications in a wide variety of elds has resulted in a rich history of research into optimisation for scheduling. Although it is a fundamental form of the problem, the single machine scheduling problem with two or more objectives is known to be NP-hard. For this reason we consider the single machine problem a good test bed for solution algorithms. While there is a plethora of research into various aspects of scheduling problems, little has been done in evaluating the performance of the Simulated Annealing algorithm for the fundamental problem, or using it in combination with other techniques. Speci cally, this has not been done for minimising total weighted earliness and tardiness, which is the optimisation objective of this work. If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible solution schedules. It is thus of de nite practical necessity to reduce the search space in order to nd an optimal or acceptable suboptimal solution in a shorter time, especially when scaling up the problem size. This is of particular importance in the application area of packet scheduling in wireless communications networks where the tolerance for computational delays is very low. The main contribution of this work is to investigate the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo methods before running the Simulated Annealing algorithm on the pruned search space can result in overall reduced running times. The search space is divided into a number of sections and Metropolis-Hastings Markov Chain Monte Carlo is performed over the sections in order to reduce the search space for Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time and number of sections of the pre-sampling algorithm, and the run time of Simulated Annealing for minimising the percentage deviation of the nal result from the optimal solution cost. Algorithm performance is determined both by computational complexity and the quality of the solution (i.e. the percentage deviation from the optimal). We nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation from the optimal, as compared to the basic Simulated Annealing algorithm on the full search space. More importantly, we are able to reduce the complexity of nding the optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis- Hastings iterations, r inner samples and m sections. / MT 2017