On a Vehicle Routing Problem with Customer Costs and Multi Depots

The Vehicle Routing Problem with Customer Costs (short VRPCC) was developed for railway maintenance scheduling. In detail, corrective maintenance jobs for unexpected occurring failures are planned to a short time horizon. These jobs are geographically distributed in the railway net. Furthermore, dependent on the severity of the failure, it can be necessary to reduce the top speed on the track section in order to avoid safety risks or a too fast deterioration. For fatal failures, it can even be necessary to close the track section. The resulting limitations on railway service lead to penalty costs for the maintenance operator. These must be paid until the track is repaired and the restrictions are removed. By scheduling the maintenance tasks, these penalty costs can be reduced by proceeding corresponding maintenance tasks earlier. However, this may in return lead to increased costs for moving the maintenance machines and crews. For this scheduling problem, the VRPCC was developed. With it, for each maintenance vehicle and crew, a route is defined that describes the order to proceed maintenance tasks. Two kinds of costs are considered: Firstly, travel costs for machinery and crew; and secondly, penalty costs for an unsafe track condition that have to be paid for each day from failure detection to maintenance completion. To model the penalties, the novel customer costs are defined. In detail, for each maintenance activity a customer cost coefficient is given which incur for each day between failure detection and failure repair. The objective function of this problem is defined by the sum of travel costs and time-dependent customer costs. With it, the priority of customers can be taken into account without losing the sight on travel costs. This new vehicle routing problem was introduced in this thesis by a non-linear partition and permutation model. In this model, a feasible solution is defined by a partition of the job set into subsets that represent the allocation of jobs to vehicles and a permutation for each subset that represent the order of processing the jobs. Then, the start times of the jobs were calculated based on the order given by the permutations. It was taken into account that work can only be done in eight hour shifts during the night. Based on the start times, the customer cost value of each job is computed which equals to the paid penalty costs. Then, the costs of a schedule are calculated via the sum of travel costs and customer costs. To solve the VRPCC by a commercial linear programming solver, different formulations of the VRPCC as mixed-integer linear program were developed. In doing so, the start times became decision variables. It turned out that including customer costs led to problems harder to solve than vehicle routing problems where only travel costs are minimized. Further, in the thesis several construction heuristics for the VRPCC were designed and investigated. Also two local search algorithms, first and best improvement, were applied. The computational experiments showed that the solutions generated by the local search algorithm were much better than the solutions of the construction heuristics. The main part of this thesis was to design a Branch-and-Bound algorithm for the VRPCC. For this purpose, new lower bounds for the customer cost part of the objective function were formulated. The computational experiments showed that a lower bound computed from the LP relaxation of a specific bin packing problem had the best trade-off between computational effort and bound quality. For the travel cost part of the objective function, several known lower bounds from the TSP were compared. To design a Branch-and-Bound algorithm, beside efficient lower bound, also suitable branching strategies are necessary to split the problem space into smaller subspaces. In this thesis two branching strategies were developed which are based on the non-linear partition and permutation model to take advantage from the problem structure. To be more precise, new branches are generated by appending or including a job to an uncompleted schedule. Consequently, the start times can be computed directly from the so far planned jobs and more tight lower bounds can be computed for the so far unplanned jobs. By means of computational experiments, the developed Branch-and-Bound algorithms were compared with the classical approach, which means solving a mixed-integer linear program of the VRPCC by a commercial solver. The results showed that both Branch-and-Bound algorithms solved the small instances faster than the classical approach

Theoretical and computational advances in finite-size facility placement and assignment problems

The goal of this research is to develop fundamental theory and exact solution methods for the optimal placement of multiple, finite-size, rectangular facilities in presence of existing rectangular facilities, in a plane. Applications of this research can be found in facility layout (re)design in manufacturing, distribution systems, services (retail outlets, hospital floors, etc.), and printed circuit board design; where designing an efficient layout can save millions of dollars in operational costs. Main difficulty of this optimization problem lies in its continuous non-convex/non-concave feasible space, which makes it tough to escape local optimality. Through this research, novel approaches will be proposed which can be used to distill this continuous space into a finite set of candidate solutions, making it amenable to search for the global optimum. The first two parts of this research deal with establishing a unified theory for the finite-size facility placement problem and establishing the theory of dominance for pruning the sub-optimal solutions. Traditionally, the facility location/layout problems are modeled as the Quadratic Assignment Problem (QAP), which is strongly NP-hard. Also, for getting strong lower bounds in the dominance procedure, we may need to solve an instance of the NP-hard Quadratic Semi-Assignment Problem (QSAP). To this end, the third part of this research deals with investigating parallel and High Performance Computing (HPC) methods for solving the Linear Assignment Problem (LAP), which is an important sub-problem of the QAP. The final part of this research deals with investigating parallel and HPC methods for obtaining strong lower bounds and possibly solving large QAPs. Since QAP is known to be a computationally intensive problem, it should be noted that large in this context means problem instances with up to 30 facilities and locations

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

Integrated machine learning and optimization approaches

This dissertation focuses on the integration of machine learning and optimization. Specifically, novel machine learning-based frameworks are proposed to help solve a broad range of well-known operations research problems to reduce the solution times. The first study presents a bidirectional Long Short-Term Memory framework to learn optimal solutions to sequential decision-making problems. Computational results show that the framework significantly reduces the solution time of benchmark capacitated lot-sizing problems without much loss in feasibility and optimality. Also, models trained using shorter planning horizons can successfully predict the optimal solution of the instances with longer planning horizons. For the hardest data set, the predictions at the 25% level reduce the solution time of 70 CPU hours to less than 2 CPU minutes with an optimality gap of 0.8% and without infeasibility. In the second study, an extendable prediction-optimization framework is presented for multi-stage decision-making problems to address the key issues of sequential dependence, infeasibility, and generalization. Specifically, an attention-based encoder-decoder neural network architecture is integrated with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions. The proposed framework is demonstrated to tackle the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing and multi-dimensional knapsack. The results show that models trained on shorter and smaller-dimension instances can be successfully used to predict longer and larger-dimension problems with the presented item-wise expansion algorithm. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. The proposed framework can be advantageous for solving dynamic mixed-integer programming problems that need to be solved instantly and repetitively. In the third study, a deep reinforcement learning-based framework is presented for solving scenario-based two-stage stochastic programming problems, which are computationally challenging to solve. A general two-stage deep reinforcement learning framework is proposed where two learning agents sequentially learn to solve each stage of a general two-stage stochastic multi-dimensional knapsack problem. The results show that solution time can be reduced significantly with a relatively small gap. Additionally, decision-making agents can be trained with a few scenarios and solve problems with a large number of scenarios. In the fourth study, a learning-based prediction-optimization framework is proposed for solving scenario-based multi-stage stochastic programs. The issue of non-anticipativity is addressed with a novel neural network architecture that is based on a neural machine translation system. Furthermore, training the models on deterministic problems is suggested instead of solving hard and time-consuming stochastic programs. In this framework, the level of variables used for the solution is iteratively reduced to eliminate infeasibility, and a heuristic based on a linear relaxation is performed to reduce the solution time. An improved item-wise expansion strategy is introduced to generalize the algorithm to tackle instances with different sizes. The results are presented in solving stochastic multi-item capacitated lot-sizing and stochastic multi-stage multi-dimensional knapsack problems. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. Moreover, results demonstrate that the models can be used to predict similarly structured stochastic programming problems with a varying number of periods, items, and scenarios. The frameworks presented in this dissertation can be utilized to achieve high-quality and fast solutions to repeatedly-solved problems in various industrial and business settings, such as production and inventory management, capacity planning, scheduling, airline logistics, dynamic pricing, and emergency management

Algorithms for Online Advertising Portfolio Optimization and Capacitated Mobile Facility Location

In this dissertation, we apply large-scale optimization techniques including column generation and heuristic approaches to problems in the domains of online advertising and mobile facility location. First, we study the online advertising portfolio optimization problem (OAPOP) of an advertiser. In the OAPOP, the advertiser has a set of targeting items of interest (in the order of tens of millions for large enterprises) and a daily budget. The objective is to determine how much to bid on each targeting item to maximize the return on investment. We show the OAPOP can be represented by the Multiple Choice Knapsack Problem (MCKP). We propose an efficient column generation (CG) algorithm for the linear programming relaxation of the problem. The computations demonstrate that our CG algorithm significantly outperforms the state-of-the-art linear time algorithm used to solve the MCKP relaxation for the OAPOP. Second, we study the problem faced by the advertiser in online advertising in the presence of bid adjustments. In addition to bids, the advertisers are able to submit bid adjustments for ad query features such as geographical location, time of day, device, and audience. We introduce the Bid Adjustments Problem in Online Advertising (BAPOA) where an advertiser determines base bids and bid adjustments to maximize the return on investment. We develop an efficient algorithm to solve the BAPOA. We perform computational experiments and demonstrate, in the presence of high revenue-per-click variation across features, the revenue benefit of using bid adjustments can exceed 20%. Third, we study the capacitated mobile facility location problem (CMFLP), which is a generalization of the well-known capacitated facility location problem that has applications in supply chain and humanitarian logistics. We provide two integer programming formulations for the CMFLP. The first is on a layered graph, while the second is a set partitioning formulation. We develop a branch-and-price algorithm on the set partitioning formulation. We find that the branch-and-price procedure is particularly effective, when the ratio of the number of clients to the number of facilities is small and the facility capacities are tight. We also develop a local search heuristic and a rounding heuristic for the CMFLP

Exact algorithms for pairwise protein structure alignment

Klau, G.W. [Promotor