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Scheduling problems and constraint satisfaction problems are generally known to be extremely hard. This thesis proposes a new evolutionary al- gorithm approach to solve a constrained-based scheduling problem. In this approach, variable orderings are evolved. The variable ordering serves as a parameter for the constraint solver. Its purpose is to determine the order in which variables are labelled by the solver. Hence the evolving individuals may be encoded as permutations. Therefore, our approach can be applied to a wider range of constraint satisfaction problems. Methods for generating the initial population of individuals based on the analysis of the precedence constraints graph are proposed. New genetic operators are presented and successfully applied. Our approach succeeded in finding a range of diverse schedules with the optimal makespan. Furthermore, multi-objective opti- mization was successfully attempted with the NSGA-II. 1

"This work presents a novel method to efficiently factorize the combination of multiple factor graphs having common variables of estimation. The fast-paced innovation in the algebraic graph theory has enabled new tools of state estimation like factor graphs. Recent factor graph formulation for Simultaneous Localization and Mapping (SLAM) like Incremental Smoothing and Mapping using the Bayes tree (ISAM2) has been very successful and garnered much attention. Variable ordering, a well-known technique in linear algebra is employed for solving the factor graph. Our primary contribution in this work is to reuse the variable ordering of the graphs being combined to find the ordering of the fused graph. In the case of mapping, multiple robots provide a great advantage over single robot by providing a faster map coverage and better estimation quality. This coupled with an inevitable increase in the number of robots around us produce a demand for faster algorithms. For example, a city full of self-driving cars could pool their observation measurements rapidly to plan a traffic free navigation. By reusing the variable ordering of the parent graphs we were able to produce an order-of-magnitude difference in the time required for solving the fused graph. We also provide a formal verification to show that the proposed strategy does not violate any of the relevant standards. A common problem in multi-robot SLAM is relative pose graph initialization to produce a globally consistent map. The other contribution addresses this by minimizing a specially formulated error function as a part of solving the factor graph. The performance is illustrated on a publicly available SuiteSparse dataset and the multi-robot AP Hill dataset."

Many real life problems can be formulated as constraint satisfaction problems <i>(CSPs)</i>. Backtracking search algorithms are usually employed to solve <i>CSPs</i> and in backtracking search the choice of branching strategies can be critical since they specify how a search algorithm can instantiate a variable and how a problem can be reduced into subproblems; that is, they define a search tree. In spite of the apparent importance of the branching strategy, there have been only a few empirical studies about different branching strategies and they all have been tested exclusively for numerical constraints. In this thesis, we employ the three most commonly used branching strategies in solving finite domain <i>CSPs</i>. These branching strategies are described as follows: first, a branching strategy with strong commitment assigns its variables in the early stage of the search as in k-Way branching; second, 2-Way branching guides a search by branching one side with assigning a variable and the other with eliminating the assigned value; third, the domain splitting strategy, based on the least commitment principle, branches by dividing a variable's domain rather than by assigning a single value to a variable. In our experiments, we compared the efficiency of different branching strategies in terms of their execution times and the number of choice points in solving finite domain <i>CSPs</i>. Interestingly, our experiments provide evidence that the choice of branching strategy for finite domain problems does not matter much in most cases--provided we are using an effective variable ordering heuristic--as domain splitting and 2-Way branching end up simulating k-Way branching. However, for an optimization problem with large domain size, the branching strategy with the least commitment principle can be more efficient than the other strategies. This empirical study will hopefully interest other practitioners to take different branching schemes into consideration in designing heuristics.

Many real life problems can be formulated as constraint satisfaction problems <i>(CSPs)</i>. Backtracking search algorithms are usually employed to solve <i>CSPs</i> and in backtracking search the choice of branching strategies can be critical since they specify how a search algorithm can instantiate a variable and how a problem can be reduced into subproblems; that is, they define a search tree. In spite of the apparent importance of the branching strategy, there have been only a few empirical studies about different branching strategies and they all have been tested exclusively for numerical constraints. In this thesis, we employ the three most commonly used branching strategies in solving finite domain <i>CSPs</i>. These branching strategies are described as follows: first, a branching strategy with strong commitment assigns its variables in the early stage of the search as in k-Way branching; second, 2-Way branching guides a search by branching one side with assigning a variable and the other with eliminating the assigned value; third, the domain splitting strategy, based on the least commitment principle, branches by dividing a variable's domain rather than by assigning a single value to a variable. In our experiments, we compared the efficiency of different branching strategies in terms of their execution times and the number of choice points in solving finite domain <i>CSPs</i>. Interestingly, our experiments provide evidence that the choice of branching strategy for finite domain problems does not matter much in most cases--provided we are using an effective variable ordering heuristic--as domain splitting and 2-Way branching end up simulating k-Way branching. However, for an optimization problem with large domain size, the branching strategy with the least commitment principle can be more efficient than the other strategies. This empirical study will hopefully interest other practitioners to take different branching schemes into consideration in designing heuristics.