Erratum—Exact Algorithms for the Clustered Vehicle Routing Problem

Abstract non present

New methods and results in the optimisation of solar power tower plants

Renewable energy technology has seen great advances in recent decades, combined with an ever increasing interest in the literature. Solar Power Tower (SPT) plants are a form of Concentrating Solar Power (CSP) technology which continue to be developed around the world, and are formed of subsystems that are open to optimisation. This thesis is concerned with the development of new methods and results in the optimisation of SPT plants, with particular focus on operational optimi- sation. Chapter 1 provides background information on the energy sector, before describing the design and modelling of an SPT plant. Here, the optical theory behind the transfer of incident radiation in the system is developed and the relevant equations presented. In Chapter 2, the cleaning operations of the heliostat eld are optimised for a xed schedule length using Binary Integer Linear Programming (BILP). Problem dimensionality is addressed by a clustering algorithm, before an ini- tial solution is found for the allocation problem. Finally, a novel local search heuristic is presented that treats the so-called route \attractiveness" through the use of a sequential pair-wise optimisation procedure that minimises a weighted attractiveness measure whilst penalising for overall energy loss. Chapters 3-6 investigate the aiming strategy utilised by the heliostat eld when considering a desired ux distribution pro le and operational constraints. In Chapter 3, a BILP model was developed, where a pre-de ned set of aim- ing points on the receiver surface was chosen. The linear objective function was constrained with linear equalities that related to distribution smoothing (to pro- tect receiver components from abnormal ux loads) via the use of penalisation. Chapter 4 extended this model by instead considering continuous variables with no xed grid of aiming points. This led to an optimisation problem with a non- linear, non-convex objective function, with non-linear constraints. In this case, a gradient ascent algorithm was developed, utilising a non-standard step-size selection technique. Chapter 5 further extended the aiming point optimisation topic to consider the dynamic case. In this sense, the aiming strategy across a period of time could be optimised, taking into account SPT plant technologi- cal limitations. Two algorithms were considered, Penalisation and Augmented Lagrangian, where theoretical properties for optimality and solution existence were presented. Finally Chapter 6 considered the efects of inclement weather on the optimisation model presented in Chapter 3. Stochastic processes were in- vestigated to determine optimal aiming strategies at a xed point in time when weather data could not be known for certain. All research presented in this thesis is illustrated using real-world data for an SPT plant, and conclusions and recommendations for future work are presented

Three-Dimensional Capacitated Vehicle Routing Problems with Loading Constraints

City logistics planning involves organizing the movement of goods in urban areas carried out by logistics operators. The loading and routing of goods are critical components of these operations. Efficient utilization of vehicle space and limiting number of empty vehicle movements can strongly impact the nuisances created by goods delivery vehicles in urban areas. We consider an integrated problem of routing and loading known as the three-dimensional loading capacitated vehicle routing problem (3L-CVRP). 3L-CVRP consists of finding feasible routes with the minimum total travel cost while satisfying customers’ demands expressed in terms of cuboid and weighted items. Practical constraints related to connectivity, stability, fragility, and LIFO are considered as parts of the problem. We address the problem in two stages. Firstly, we address the three-dimensional (3D) loading problem followed by 3L-CVRP. The main objective of a 3D loading problem without routing aspect is finding the best way of packing 3D items into vehicles or containers to increase the loading factor with the purpose of minimizing empty vehicle movements. We present the general linear programming model to the pure three-dimensional vehicle loading problem and solve it by CPLEX. To deal with large-sized instances, Column Generation (CG) technique is applied. The designed method in this work outperforms the best existing techniques in the literature.   The 3DVLP with allocation and capacity constraints, called 3DVLP-AC, is also considered. For the 3DVLP-AC, CPLEX could handle moderate-sized instances with up to 40 customers. To deal with large-sized instances, a Tabu Search (TS) heuristic algorithm is developed. There are no solution methods or lower bounds (LBs) for the 3DVLP-AC existent in the literature by which to evaluate the TS results. Therefore, we evaluate our TS with the CPLEX results for small instances. 3L-CVRP is addressed by using CG technique. To generate new columns, the pricing problem that is part of CG is solved by using two approaches: 1-by means of shortest path problem with resource constraints (ESPPRC) and loading problem, and 2-a heuristic pricing method (HP). CG using HP with a simple scheme can attain solutions competitive with the efficient TS algorithms described in the literature

Reinforced Lin-Kernighan-Helsgaun Algorithms for the Traveling Salesman Problems

TSP is a classical NP-hard combinatorial optimization problem with many practical variants. LKH is one of the state-of-the-art local search algorithms for the TSP. LKH-3 is a powerful extension of LKH that can solve many TSP variants. Both LKH and LKH-3 associate a candidate set to each city to improve the efficiency, and have two different methods, $\alpha$-measure and POPMUSIC, to decide the candidate sets. In this work, we first propose a Variable Strategy Reinforced LKH (VSR-LKH) algorithm, which incorporates three reinforcement learning methods (Q-learning, Sarsa, Monte Carlo) with LKH, for the TSP. We further propose a new algorithm called VSR-LKH-3 that combines the variable strategy reinforcement learning method with LKH-3 for typical TSP variants, including the TSP with time windows (TSPTW) and Colored TSP (CTSP). The proposed algorithms replace the inflexible traversal operations in LKH and LKH-3 and let the algorithms learn to make a choice at each search step by reinforcement learning. Both LKH and LKH-3, with either $\alpha$-measure or POPMUSIC, can be significantly improved by our methods. Extensive experiments on 236 widely-used TSP benchmarks with up to 85,900 cities demonstrate the excellent performance of VSR-LKH. VSR-LKH-3 also significantly outperforms the state-of-the-art heuristics for TSPTW and CTSP.Comment: arXiv admin note: text overlap with arXiv:2107.0687

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Monte Carlo Method with Heuristic Adjustment for Irregularly Shaped Food Product Volume Measurement

Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another method for measuring volume of objects uses Monte Carlo method. Monte Carlo method performs volume measurements using random points. Monte Carlo method only requires information regarding whether random points fall inside or outside an object and does not require a 3D reconstruction. This paper proposes volume measurement using a computer vision system for irregularly shaped food products without 3D reconstruction based on Monte Carlo method with heuristic adjustment. Five images of food product were captured using five cameras and processed to produce binary images. Monte Carlo integration with heuristic adjustment was performed to measure the volume based on the information extracted from binary images. The experimental results show that the proposed method provided high accuracy and precision compared to the water displacement method. In addition, the proposed method is more accurate and faster than the space carving method

The Catalog Problem:Deep Learning Methods for Transforming Sets into Sequences of Clusters

The titular Catalog Problem refers to predicting a varying number of ordered clusters from sets of any cardinality. This task arises in many diverse areas, ranging from medical triage, through multi-channel signal analysis for petroleum exploration to product catalog structure prediction. This thesis focuses on the latter, which exemplifies a number of challenges inherent to ordered clustering. These include learning variable cluster constraints, exhibiting relational reasoning and managing combinatorial complexity. All of which present unique challenges for neural networks, combining elements of set representation, neural clustering and permutation learning.In order to approach the Catalog Problem, a curated dataset of over ten thousand real-world product catalogs consisting of more than one million product offers is provided. Additionally, a library for generating simpler, synthetic catalog structures is presented. These and other datasets form the foundation of the included work, allowing for a quantitative comparison of the proposed methods’ ability to address the underlying challenge. In particular, synthetic datasets enable the assessment of the models’ capacity to learn higher order compositional and structural rules.Two novel neural methods are proposed to tackle the Catalog Problem, a set encoding module designed to enhance the network’s ability to condition the prediction on the entirety of the input set, and a larger architecture for inferring an input- dependent number of diverse, ordered partitional clusters with an added cardinality prediction module. Both result in an improved performance on the presented datasets, with the latter being the only neural method fulfilling all requirements inherent to addressing the Catalog Problem

Online optimization in routing and scheduling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (leaves 169-176).In this thesis we study online optimization problems in routing and scheduling. An online problem is one where the problem instance is revealed incrementally. Decisions can (and sometimes must) be made before all information is available. We design and analyze (polynomial-time) online algorithms for a variety of problems. We utilize worst-case competitive ratio (and relaxations thereof), asymptotic and Monte Carlo simulation analyses in our study of these algorithms. The focus of this thesis is on online routing problems in arbitrary metric spaces. We begin our study with online versions of the Traveling Salesman Problem (TSP) and the Traveling Repairman Problem (TRP). We then generalize these basic problems to allow for precedence constraints, capacity constraints and multiple vehicles. We give the first competitive ratio results for many new online routing problems. We then consider resource augmentation, where we give the online algorithm additional resources: faster servers, larger capacities, more servers, less restrictive constraints and advanced information. We derive new worst-case bounds that are relaxations of the competitive ratio.(cont.) We also study the (stochastic) asymptotic properties of these algorithms - introducing stochastic structure to the problem data, unknown and unused by the online algorithm. In a variety of situations we show that many online routing algorithms are (quickly) asymptotically optimal, almost surely, and we characterize the rates of convergence. We also study classic machine sequencing problems in an online setting. Specifically, we look at deterministic and randomized algorithms for the problems of scheduling jobs with release dates on single and parallel machines, with and without preemption, to minimize the sum of weighted completion times. We derive improved competitive ratio bounds and we show that many well-known machine scheduling algorithms are almost surely asymptotically optimal under general stochastic assumptions. For both routing and sequencing problems, we complement these theoretical derivations with Monte Carlo simulation results.by Michael Robert Wagner.Ph.D