The Traveling Salesman Problem with Stochastic and Correlated Customers

It is well-known that the cost of parcel delivery can be reduced by designingroutes that take into account the uncertainty surrounding customers’ presences. Thus far, routing problems with stochastic customer presences have relied on the assumption that all customer presences are independent from each other. However, the notion that demographic factors retain predictive power for parcel-delivery efficiency suggests that shared characteristics can be exploited to map dependencies between customer presences. This paper introduces the correlated probabilistic traveling salesman problem (CPTSP). The CPTSP generalizes the traveling salesman problem with stochastic customer presences, also known as the probabilistic traveling salesman problem (PTSP), to account for potentialcorrelations between customer presences. I propose a generic and flexible model formulation for the CPTSP using copulas that maintains computational and mathematical tractability in high-dimensional settings. I also present several adaptations of existing exact and heuristic frameworks to solve the CPTSP effectively. Computational experiments on real-world parcel-delivery data reveal that correlations between stochastic customer presences do not always affect route decisions, but could have a considerable impact on route costestimates

Efficient combinatorial optimization algorithms for logistic problems

The field of logistics and combinatorial optimization features a wealth of NP-hard problems that are of great practical importance. For this reason it is important that we have efficient algorithms to provide optimal or near-optimal solutions. In this work, we study, compare and develop Sampling-Based Metaheuristics and Exact Methods for logistic problems that are important for their applications in vehicle routing and scheduling. More specifically, we study two Stochastic Combinatorial Optimization Problems (SCOPs) and finally a Combinatorial Optimization Problem using methods related to the field of Metaheuristics, Monte Carlo Sampling, Experimental Algorithmics and Exact Algorithms. For the SCOPs studied, we emphasize studying the impact of approximating the objective function to the quality of the final solution found. We begin by examining Solution Methods for the Orienteering Problem with Stochastic Travel and Service Times (OPSTS). We introduce the state-of-the-art before our contributions and proceed to examining our suggested improvements. The core of our improvements stem from the approximation of the objective function using a combination of Monte Carlo sampling and Analytical methods. We present four new Evaluators (approximations) and discuss their advantages and disadvantages. We then demonstrate experimentally the advantages of the Evaluators over the previous state-of-the-art and explore their trade- offs. We continue by generating large reference datasets and embedding our Evaluators in two Metaheuristics that we use to find realistic near-optimal solutions to OPSTS. We demonstrate that our results are statistically significantly better than the previous state-of-the-art. In the next chapter, we present the 2-stage Capacitated Vehicle Routing Problem with Stochastic Demands inspired by an environmental use case. We propose four different solution approaches based on different approximations of the objective function and use the Ant Colony Metaheuristic to find solutions for the problem. We discuss the trade-offs of each proposed solution and finally argue about its potentially important environmental application. Finally, focus on exact methods for the Sequential Ordering Problem (SOP). Firstly, we make an extensive experimental comparison of two exact algorithms existing in the literature from different domains (cargo and transportation and the other compilers). From the experimental comparison and application of the algorithms in new contexts we were able to close nine previously open instances in the literature and improve seventeen more. It also led to insights for the improvement of one of the methods (The Branch-and-Bound Approach - B&B). We proceed with the presentation of the improved version that led to the closing of eight more instances and speeding up the previous version of the B&B algorithm by 4%-98%

An integer L-shaped algorithm for the Dial-a-Ride Problem with stochastic customer delays

AbstractThis paper considers a single-vehicle Dial-a-Ride Problem in which customers may experience stochastic delays at their pickup locations. If a customer is absent when the vehicle serves the pickup location, the request is fulfilled by an alternative service (e.g., a taxi) whose cost is added to the total cost of the tour. In this case, the vehicle skips the corresponding delivery location, which yields a reduction in the total tour cost. The aim of the problem is to determine an a priori Hamiltonian tour minimizing the expected cost of the solution. This problem is solved by means of an integer L-shaped algorithm. Computational experiments show that the algorithm yields optimal solutions on several instances within reasonable CPU times. It is also shown that the actual cost of an optimal solution obtained with this algorithm can be significantly smaller than that of an optimal solution obtained with a deterministic formulation

Towards an IT-based Planning Process Alignment: Integrated Route and Location Planning for Small Package Shippers

To increase the efficiency of delivery operations in small package shipping (SPS), numerous optimization models for routeand location planning decisions have been proposed. This operations research view of defining independent problems hastwo major shortcomings: First, most models from literature neglect crucial real-world characteristics, thus making themuseless for small package shippers. Second, business processes for strategic decision making are not well-structured in mostSPS companies and significant cost savings could be generated by an IT-based support infrastructure integrating decisionmaking and planning across the mutually dependent layers of strategic, tactical and operational planning. We present anintegrated planning framework that combines an intelligent data analysis tool, which identifies delivery patterns and changesin customer demand, with location and route planning tools. Our planning approaches extend standard Location Routing andVehicle Routing models by crucial, practically relevant characteristics like the existence of subcontractors on both decisionlevels and the implicit consideration of driver familiarity in route planning

An Integer L-Shaped Algorithm for the Dial-a-Ride Problem with Stochastic Customer Delays

Abstract This paper considers a single-vehicle Dial-a-Ride problem in which customers may experience stochastic delays at their pickup locations. If a customer is absent when the vehicle serves the pickup location, the request is fulfilled by an alternative service (e.g., a taxi) whose cost is added to the total cost of the tour. In this case, the vehicle skips the corresponding delivery location, which yields a reduction in the total tour cost. The aim of the problem is to determine an a priori Hamiltonian tour minimizing the expected cost of the solution. This problem is solved by means of an integer L-shaped algorithm. Computational experiments show that the algorithm yields optimal solutions for small and medium size instances within reasonable CPU times. It is also shown that the actual cost of an optimal solution obtained with this algorithm can be significantly smaller than that of an optimal solution obtained with a deterministic formulation

Solving Continuous Replenishment Inventory Routing Problems with Route Duration Bounds

In a public health emergency, resupplying points of dispensing (PODs) with the smallest number of vehicles is an important problem in mass dispensing operations. To solve this problem, this paper describes the Continuous Replenishment Inventory Routing Problem (CRIRP) and presents heuristics for finding feasible solutions when the duration of vehicle routes cannot exceed a given bound. This paper describes a special case of the CRIRP that is equivalent to the bin-packing problem. For the general problem, the paper presents an aggregation approach that combines low-demand sites that are close to one another. We discuss the results of computational tests used to assess the quality and computational effort of the heuristics and the aggregation approach

Decentralized algorithm of dynamic task allocation for a swarm of homogeneous robots

The current trends in the robotics field have led to the development of large-scale swarm robot systems, which are deployed for complex missions. The robots in these systems must communicate and interact with each other and with their environment for complex task processing. A major problem for this trend is the poor task planning mechanism, which includes both task decomposition and task allocation. Task allocation means to distribute and schedule a set of tasks to be accomplished by a group of robots to minimize the cost while satisfying operational constraints. Task allocation mechanism must be run by each robot, which integrates the swarm whenever it senses a change in the environment to make sure the robot is assigned to the most appropriate task, if not, the robot should reassign itself to its nearest task. The main contribution in this thesis is to maximize the overall efficiency of the system by minimizing the total time needed to accomplish the dynamic task allocation problem. The near-optimal allocation schemes are found using a novel hybrid decentralized algorithm for a dynamic task allocation in a swarm of homogeneous robots, where the number of the tasks is more than the robots present in the system. This hybrid approach is based on both the Simulated Annealing (SA) optimization technique combined with the Discrete Particle Swarm Optimization (DPSO) technique. Also, another major contribution in this thesis is the formulation of the dynamic task allocation equations for the homogeneous swarm robotics using integer linear programming and the cost function and constraints are introduced for the given problem. Then, the DPSO and SA algorithms are developed to accomplish the task in a minimal time. Simulation is implemented using only two test cases via MATLAB. Simulation results show that PSO exhibits a smaller and more stable convergence characteristics and SA technique owns a better quality solution. Then, after developing the hybrid algorithm, which combines SA with PSO, simulation instances are extended to include fifteen more test cases with different swarm dimensions to ensure the robustness and scalability of the proposed algorithm over the traditional PSO and SA optimization techniques. Based on the simulation results, the hybrid DPSO/SA approach proves to have a higher efficiency in both small and large swarm sizes than the other traditional algorithms such as Particle Swarm Optimization technique and Simulated Annealing technique. The simulation results also demonstrate that the proposed approach can dislodge a state from a local minimum and guide it to the global minimum. Thus, the contributions of the proposed hybrid DPSO/SA algorithm involve possessing both the pros of high quality solution in SA and the fast convergence time capability in PSO. Also, a parameters\u27 selection process for the hybrid algorithm is proposed as a further contribution in an attempt to enhance the algorithm efficiency because the heuristic optimization techniques are very sensitive to any parameter changes. In addition, Verification is performed to ensure the effectiveness of the proposed algorithm by comparing it with results of an exact solver in terms of computational time, number of iterations and quality of solution. The exact solver that is used in this research is the Hungarian algorithm. This comparison shows that the proposed algorithm gives a superior performance in almost all swarm sizes with both stable and small execution time. However, it also shows that the proposed hybrid algorithm\u27s cost values which is the distance traveled by the robots to perform the tasks are larger than the cost values of the Hungarian algorithm but the execution time of the hybrid algorithm is much better. Finally, one last contribution in this thesis is that the proposed algorithm is implemented and extensively tested in a real experiment using a swarm of 4 robots. The robots that are used in the real experiment called Elisa-III robots