The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

Stochastic programming for City Logistics: new models and methods

The need for mobility that emerged in the last decades led to an impressive increase in the number of vehicles as well as to a saturation of transportation infrastructures. Consequently, traffic congestion, accidents, transportation delays, and polluting emissions are some of the most recurrent concerns transportation and city managers have to deal with. However, just building new infrastructures might be not sustainable because of their cost, the land usage, which usually lacks in metropolitan regions, and their negative impact on the environment. Therefore, a different way of improving the performance of transportation systems while enhancing travel safety has to be found in order to make people and good transportation operations more efficient and support their key role in the economic development of either a city or a whole country. The concept of City Logistics (CL) is being developed to answer to this need. Indeed, CL focus on reducing the number of vehicles operating in the city, controlling their dimension and characteristics. CL solutions do not only improve the transportation system but the whole logistics system within an urban area, trying to integrate interests of the several. This global view challenges researchers to develop planning models, methods and decision support tools for the optimization of the structures and the activities of the transportation system. In particular, this leads researchers to the definition of strategic and tactical problems belonging to well-known problem classes, including network design problem, vehicle routing problem (VRP), traveling salesman problem (TSP), bin packing problem (BPP), which typically act as sub-problems of the overall CL system optimization. When long planning horizons are involved, these problems become stochastic and, thus, must explicitly take into account the different sources of uncertainty that can affect the transportation system. Due to these reasons and the large-scale of CL systems, the optimization problems arising in the urban context are very challenging. Their solution requires investigations in mathematical and combinatorial optimization methods as well as the implementation of efficient exact and heuristic algorithms. However, contributions answering these challenges are still limited number. This work contributes in filling this gap in the literature in terms of both modeling framework for new planning problems in CL context and developing new and effective heuristic solving methods for the two-stage formulation of these problems. Three stochastic problems are proposed in the context of CL: the stochastic variable cost and size bin packing problem (SVCSBPP), the multi-handler knapsack problem under uncertainty (MHKPu) and the multi-path traveling salesman problem with stochastic travel times (mpTSPs). The SVCSBPP arises in supply-chain management, in which companies outsource the logistics activities to a third-party logistic firm (3PL). The procurement of sufficient capacity, expressed in terms of vehicles, containers or space in a warehouse for varying periods of time to satisfy the demand plays a crucial role. The SVCSBPP focuses on the relation between a company and its logistics capacity provider and the tactical-planning problem of determining the quantity of capacity units to secure for the next period of activity. The SVCSBPP is the first attempt to introduce a stochastic variant of the variable cost and size bin packing problem (VCSBPP) considering not only the uncertainty on the demand to deliver, but also on the renting cost of the different bins and their availability. A large number of real-life situations can be satisfactorily modeled as a MHKPu, in particular in the last mile delivery. Last mile delivery may involve different sequences of consolidation operations, each handled by different workers with different skill levels and reliability. The improper management of consolidation operations can cause delay in the operations reducing the overall profit of the deliveries. Thus, given a set of potential logistics handlers and a set of items to deliver, characterized by volume and random profit, the MHKPu consists in finding a subset of items which maximizes the expected total profit. The profit is given by the sum of a deterministic profit and a stochastic profit oscillation, with unknown probability distribution, due to the random handling costs of the handlers.The mpTSPs arises mainly in City Logistics applications. Cities offer several services, such as garbage collection, periodic delivery of goods in urban grocery distribution and bike sharing services. These services require the planning of fixed and periodic tours that will be used from one to several weeks. However, the enlarged time horizon as well as strong dynamic changes in travel times due to traffic congestion and other nuisances typical of the urban transportation induce the presence of multiple paths with stochastic travel times. Given a graph characterized by a set of nodes connected by arcs, mpTSPs considers that, for every pair of nodes, multiple paths between the two nodes are present. Each path is characterized by a random travel time. Similarly to the standard TSP, the aim of the problem is to define the Hamiltonian cycle minimizing the expected total cost. These planning problems have been formulated as two-stage integer stochastic programs with recourse. Discretization methods are usually applied to approximate the probability distribution of the random parameters. The resulting approximated program becomes a deterministic linear program with integer decision variables of generally very large dimensions, beyond the reach of exact methods. Therefore, heuristics are required. For the MHKPu, we apply the extreme value theory and derive a deterministic approximation, while for the SVCSBPP and the mpTSPs we introduce effective and accurate heuristics based on the progressive hedging (PH) ideas. The PH mitigates the computational difficulty associated with large problem instances by decomposing the stochastic program by scenario. When effective heuristic techniques exist for solving individual scenario, that is the case of the SVCSBPP and the mpTSPs, the PH further reduces the computational effort of solving scenario subproblems by means of a commercial solver. In particular, we propose a series of specific strategies to accelerate the search and efficiently address the symmetry of solutions, including an aggregated consensual solution, heuristic penalty adjustments, and a bundle fixing technique. Yet, although solution methods become more powerful, combinatorial problems in the CL context are very large and difficult to solve. Thus, in order to significantly enhance the computational efficiency, these heuristics implement parallel schemes. With the aim to make a complete analysis of the problems proposed, we perform extensive numerical experiments on a large set of instances of various dimensions, including realistic setting derived by real applications in the urban area, and combinations of different levels of variability and correlations in the stochastic parameters. The campaign includes the assessment of the efficiency of the meta-heuristic, the evaluation of the interest to explicitly consider uncertainty, an analysis of the impact of problem characteristics, the structure of solutions, as well as an evaluation of the robustness of the solutions when used as decision tool. The numerical analysis indicates that the stochastic programs have significant effects in terms of both the economic impact (e.g. cost reduction) and the operations management (e.g. prediction of the capacity needed by the firm). The proposed methodologies outperform the use of commercial solvers, also when small-size instances are considered. In fact, they find good solutions in manageable computing time. This makes these heuristics a strategic tool that can be incorporated in larger decision support systems for CL

Order batching and picking optimization in terms of supply chain management (SCM)

In distribution center (DC), at the time of forming a batch, by considering the order holding time and picking time in the system, an algorithm based on the first-come, first served based (FCFS) rule is presented. In the proposed algorithm, both order picking factor and order holding factor are used in order to reflect the throughput of the system and response of orders.;Furthermore, some simple batching policies for considering the order holding time in the system are presented. They may result in meeting its customers\u27 requirements for larger numbers of smaller orders and rapid turnaround. They reflect the well-known supply chain management (SCM) concept by taking the customer\u27s need into consideration. Their performance measure of order response time that consists of order picking time and order holding time is evaluated and compared.;Finally, this thesis also develops a new optimization-based joint order batching and picking framework for warehousing and distribution systems. The nested partitions (NP) method that integrates global sampling of the feasible region and local search heuristic is applied to this problem. To speed up the computation, the improved NP-algorithm is developed. Also, by taking the special structure of the problem in account, an improved NP method in terms of small computational time is developed

Design Optimization of Photovoltaic System for Domestic Customers

In the present work, a comparison between different population based optimization methods are applied to design optimization of standalone Photovoltaic (SPV) system. The purpose of these methodologies is to obtain optimum values of the design parameters of SPV system, such that the overall economic profit is maximized throughout the PV system lifetime operational period. Out of many design parameters available for SPV system, in the present work only few parameters are taken. The optimal design parameters chosen here are PV modules optimum tilt angle, optimum number of PV module and optimal positioning of PV modules within the provided installation area. The objective function of the proposed evolutionary optimization algorithms implemented for design optimization of the SPV system is the total profit incurred during the lifetime operational period of SPV system, which has to be maximized. Simulation results of design optimization of SPV system by using Genetic Algorithm (GA),qParticle Swarm Optimization (PSO)qand Differential Evolutionq (DE) technique are obtained. Simulation results shows that DE and PSO have similar performance and both of them had performed better compared to GA when all algorithms are computed for equal iterations and population size

The Dynamic Multi-objective Multi-vehicle Covering Tour Problem

This work introduces a new routing problem called the Dynamic Multi-Objective Multi-vehicle Covering Tour Problem (DMOMCTP). The DMOMCTPs is a combinatorial optimization problem that represents the problem of routing multiple vehicles to survey an area in which unpredictable target nodes may appear during execution. The formulation includes multiple objectives that include minimizing the cost of the combined tour cost, minimizing the longest tour cost, minimizing the distance to nodes to be covered and maximizing the distance to hazardous nodes. This study adapts several existing algorithms to the problem with several operator and solution encoding variations. The efficacy of this set of solvers is measured against six problem instances created from existing Traveling Salesman Problem instances which represent several real countries. The results indicate that repair operators, variable length solution encodings and variable-length operators obtain a better approximation of the true Pareto front

Modeling and Solving Large-scale Stochastic Mixed-Integer Problems in Transportation and Power Systems

In this dissertation, various optimization problems from the area of transportation and power systems will be respectively investigated and the uncertainty will be considered in each problem. Specifically, a long-term problem of electricity infrastructure investment is studied to address the planning for capacity expansion in electrical power systems with the integration of short-term operations. The future investment costs and real-time customer demands cannot be perfectly forecasted and thus are considered to be random. Another maintenance scheduling problem is studied for power systems, particularly for natural gas fueled power plants, taking into account gas contracting and the opportunity of purchasing and selling gas in the spot market as well as the maintenance scheduling considering the uncertainty of electricity and gas prices in the spot market. In addition, different vehicle routing problems are researched seeking the route for each vehicle so that the total traveling cost is minimized subject to the constraints and uncertain parameters in corresponding transportation systems. The investigation of each problem in this dissertation mainly consists of two parts, i.e., the formulation of its mathematical model and the development of solution algorithm for solving the model. The stochastic programming is applied as the framework to model each problem and address the uncertainty, while the approach of dealing with the randomness varies in terms of the relationships between the uncertain elements and objective functions or constraints. All the problems will be modeled as stochastic mixed-integer programs, and the huge numbers of involved decision variables and constraints make each problem large-scale and very difficult to manage. In this dissertation, efficient algorithms are developed for these problems in the context of advanced methodologies of optimization and operations research, such as branch and cut, benders decomposition, column generation and Lagrangian method. Computational experiments are implemented for each problem and the results will be present and discussed. The research carried out in this dissertation would be beneficial to both researchers and practitioners seeking to model and solve similar optimization problems in transportation and power systems when uncertainty is involved

Discrete particle swarm optimization for combinatorial problems with innovative applications.

Master of Science in Computer Science. University of KwaZulu-Natal, Durban 2016.Abstract available in PDF file

Tactical design of last mile logistical systems

Tactical Design of Last Mile Logistical Systems Alexander M. Stroh 161 Pages Directed by Dr. Alan Erera and Dr. Alejandro Toriello This dissertation consists of three distinct logistical topics, unified by a focus on the intelligent design of last mile logistical systems at a tactical level. The three design problems all arise within package delivery supply chains, though the mathematical models and solution techniques developed in these studies can be applied to other logistics systems. We propose models that do not attempt to capture granular minute by minute operational decision making, but rather, system behavior on average so that we may approximate the impact of various design choices. In Chapter 2, we study tactical models for the design of same-day delivery (SDD) systems. While previous literature includes operational models to study SDD, they tend to be detailed, complex, and computationally difficult to solve. Thus, such models may not provide any insight into tactical SDD design variables and their impact on the average performance of the system. We propose a simplified vehicle dispatching model that captures the average behavior of an SDD system from a single depot location by utilizing continuous approximation techniques. We analyze the structure of vehicle dispatching policies given by our model for various families of problem instances and develop techniques to find optimal dispatching policies that require only simple computations. Our models can help answer various tactical design questions including how to select a fleet size, determine an order cutoff time, and combine SDD and overnight order delivery operations. In Chapter 3, we study the tactical optimization of SDD systems under the assumption that service regions are allowed to vary over the course of each day. In most existing studies of last mile logistics problems, service regions are assumed to be static. Service regions which are designed too small or cutoff SDD availability too soon may potentially lose SDD market share, while regions which are designed too large or accept orders too late may result in costly operations or failed deliveries, resulting in a loss of customer goodwill. We use a continuous approximation approach to capture average system behavior and derive optimal dynamic service region areas and tactical vehicle dispatching policies which maximize the expected number of SDD orders served per day. Furthermore, we compare such designs to fixed service region designs or capacitated service region designs. In Chapter 4, we introduce the concept of cycle time considering capacitated vehicle routing problems, which are motivated by the desire to decrease the average time packages spent within a delivery network. Traditional vehicle routing models focus on the resource usage of the system whereas our models instead consider the impact of routing policies on the units being served. We explicitly consider pre-routing waiting times at a depot, total demand-weighted accumulated routing times, vehicle capacity constraints, and designing repeatable delivery routes in our models. We present two set partitioning formulations for such problems and derive efficient solution techniques so that the impact of various design parameters can be assessed.Ph.D