Developing an Enhanced Algorithms to Solve Mixed Integer Non-Linear Programming Problems Based on a Feasible Neighborhood Search Strategy

Engineering optimization problems often involve nonlinear objective functions, which can capture complex relationships and dependencies between variables. This study focuses on a unique nonlinear mathematics programming problem characterized by a subset of variables that can only take discrete values and are linearly separable from the continuous variables. The combination of integer variables and non-linearities makes this problem much more complex than traditional nonlinear programming problems with only continuous variables. Furthermore, the presence of integer variables can result in a combinatorial explosion of potential solutions, significantly enlarging the search space and making it challenging to explore effectively. This issue becomes especially challenging for larger problems, leading to long computation times or even infeasibility. To address these challenges, we propose a method that employs the "active constraint" approach in conjunction with the release of nonbasic variables from their boundaries. This technique compels suitable non-integer fundamental variables to migrate to their neighboring integer positions. Additionally, we have researched selection criteria for choosing a nonbasic variable to use in the integerizing technique. Through implementation and testing on various problems, these techniques have proven to be successful

A modified differential evolution based solution technique for economic dispatch problems

Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading effects the objective function becomes nondifferentiable and has many local minima in the solution space. Traditional methods may fail to reach the global solution of ED problems. Most of the existing stochastic methods try to make the solution feasible or penalize an infeasible solution with penalty function method. However, to find the appropriate penalty parameter is not an easy task. Differential evolution is a population-based heuristic approach that has been shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution based solution technique along with a tournament selection that makes pair-wise comparison among feasible and infeasible solutions based on the degree of constraint violation for economic dispatch problems. We reformulate the nonsmooth objective function to a smooth one and add nonlinear inequality constraints to original ED problems. We consider five ED problems and compare the obtained results with existing standard deterministic NLP solvers as well as with other stochastic techniques available in literature.Fundação para a Ciência e a Tecnologia (FCT

Large-scale mixed integer optimization approaches for scheduling airline operations under irregularity

Perhaps no single industry has benefited more from advancements in computation, analytics, and optimization than the airline industry. Operations Research (OR) is now ubiquitous in the way airlines develop their schedules, price their itineraries, manage their fleet, route their aircraft, and schedule their crew. These problems, among others, are well-known to industry practitioners and academics alike and arise within the context of the planning environment which takes place well in advance of the date of departure. One salient feature of the planning environment is that decisions are made in a frictionless environment that do not consider perturbations to an existing schedule. Airline operations are rife with disruptions caused by factors such as convective weather, aircraft failure, air traffic control restrictions, network effects, among other irregularities. Substantially less work in the OR community has been examined within the context of the real-time operational environment. While problems in the planning and operational environments are similar from a mathematical perspective, the complexity of the operational environment is exacerbated by two factors. First, decisions need to be made in as close to real-time as possible. Unlike the planning phase, decision-makers do not have hours of time to return a decision. Secondly, there are a host of operational considerations in which complex rules mandated by regulatory agencies like the Federal Administration Association (FAA), airline requirements, or union rules. Such restrictions often make finding even a feasible set of re-scheduling decisions an arduous task, let alone the global optimum. The goals and objectives of this thesis are found in Chapter 1. Chapter 2 provides an overview airline operations and the current practices of disruption management employed at most airlines. Both the causes and the costs associated with irregular operations are surveyed. The role of airline Operations Control Center (OCC) is discussed in which serves as the real-time decision making environment that is important to understand for the body of this work. Chapter 3 introduces an optimization-based approach to solve the Airline Integrated Recovery (AIR) problem that simultaneously solves re-scheduling decisions for the operating schedule, aircraft routings, crew assignments, and passenger itineraries. The methodology is validated by using real-world industrial data from a U.S. hub-and-spoke regional carrier and we show how the incumbent approach can dominate the incumbent sequential approach in way that is amenable to the operational constraints imposed by a decision-making environment. Computational effort is central to the efficacy of any algorithm present in a real-time decision making environment such as an OCC. The latter two chapters illustrate various methods that are shown to expedite more traditional large-scale optimization methods that are applicable a wide family of optimization problems, including the AIR problem. Chapter 4 shows how delayed constraint generation and column generation may be used simultaneously through use of alternate polyhedra that verify whether or not a given cut that has been generated from a subset of variables remains globally valid. While Benders' decomposition is a well-known algorithm to solve problems exhibiting a block structure, one possible drawback is slow convergence. Expediting Benders' decomposition has been explored in the literature through model reformulation, improving bounds, and cut selection strategies, but little has been studied how to strengthen a standard cut. Chapter 5 examines four methods for the convergence may be accelerated through an affine transformation into the interior of the feasible set, generating a split cut induced by a standard Benders' inequality, sequential lifting, and superadditive lifting over a relaxation of a multi-row system. It is shown that the first two methods yield the most promising results within the context of an AIR model.PhDCommittee Co-Chair: Clarke, John-Paul; Committee Co-Chair: Johnson, Ellis; Committee Member: Ahmed, Shabbir; Committee Member: Clarke, Michael; Committee Member: Nemhauser, Georg

Code Generation in the Columbia Esterel Compiler

The synchronous language Esterel provides deterministic concurrency by adopting a semantics in which threads march in step with a global clock and communicate in a very disciplined way. Its expressive power comes at a cost, however: it is a difficult language to compile into machine code for standard von Neumann processors. The open-source Columbia Esterel Compiler is a research vehicle for experimenting with new code generation techniques for the language. Providing a front-end and a fairly generic concurrent intermediate representation, a variety of back-ends have been developed. We present three of the most mature ones, which are based on program dependence graphs, dynamic lists, and a virtual machine. After describing the very different algorithms used in each of these techniques, we present experimental results that compares twenty-four benchmarks generated by eight different compilation techniques running on seven different processors

Code Generation in the Columbia Esterel Compiler

The synchronous language Esterel provides deterministic concurrency by adopting a semantics in which threads march in step with a global clock and communicate in a very disciplined way. Its expressive power comes at a cost, however: it is a difficult language to compile into machine code for standard von Neumann processors. The open-source Columbia Esterel Compiler is a research vehicle for experimenting with new code generation techniques for the language. Providing a front-end and a fairly generic concurrent intermediate representation, a variety of back-ends have been developed. We present three of the most mature ones, which are based on program dependence graphs, dynamic lists, and a virtual machine. After describing the very different algorithms used in each of these techniques, we present experimental results that compares twenty-four benchmarks generated by eight different compilation techniques running on seven different processors

On the Routing and Location of Mobile Facilities

Mobile facilities play important roles in many applications, including health care, public services, telecommunications, and humanitarian relief logistics. While mobile facilities operate in different manners, it is generally considered important for a decision maker to be capable of efficiently deploying mobile facilities. This dissertation discusses two problems on the use of mathematical models and algorithms for determining efficient deployments of mobile facilities. First we discuss the mobile facility routing problem (MFRP), which effectively models the operations of a wide class of mobile facilities that have significant relocation times and cannot service demand during transit. Chapter 2 discusses the single MFRP (SMFRP), which is to determine a route for a single mobile facility to maximize the demand serviced during a continuous-time planning horizon. We present two exact algorithms, and supporting theoretical results, when the rate demand is generated is modeled using piecewise constant functions. The first is a dynamic program that easily extends to solve cases where the demand functions take on more general forms. The second exact algorithm has a polynomial worst-case runtime. Chapter 3 discusses the MFRP, which addresses the situation when multiple mobile facilities are operating in an area. In such a case, mobile facilities at different locations may provide service to a single event, necessitating the separation of the events generating demand from the locations mobile facilities may visit in our model. We show that the MFRP is NP-hard, present several heuristics for generating effective routes, and extensively test these heuristics on a variety of simulated data sets. Chapter 4 discusses formulations and local search heuristics for the (minisum) mobile facility location problem (MFLP). This problem is to relocate a set of existing facilities and assign clients to these facilities while minimizing the movement costs of facilities and clients. We show that in a certain sense the MFLP generalizes the uncapacitated facility location and p-median problems. We observe that given a set of facility destinations, the MFLP decomposes into two polynomially solvable subproblems. Using this decomposition observation, we propose a new, compact IP formulation and novel local search heuristics. We report results from extensive computational experiments

Integrated service selection, pricing and fullfillment planning for express parcel carriers - Enriching service network design with customer choice and endogenous delivery time restrictions

Express parcel carriers offer a wide range of guaranteed delivery times in order to separate customers who value quick delivery from those that are less time but more price sensitive. Such segmentation, however, adds a whole new layer of complexity to the task of optimizing the logistics operations. While many sophisticated models have been developed to assist network planners in minimizing costs, few approaches account for the interplay between service pricing, customer decisions and the associated restrictions in the distribution process. This paper attempts to fill this research gap by introducing a heuristic solution approach that simultaneously determines the ideal set of services, the associated pricing and the fulfillment plan in order to maximize profit. By integrating revenue management techniques into vehicle routing and eet planning, we derive a new type of formulation called service selection, pricing and fulfillment problem (SSPFP). It combines a multi-product pricing problem with a cycle-based service network design formulation. In order derive good-quality solutions for realistically-sized instances we use an asynchronous parallel genetic algorithm and follow the intuition that small changes to prices and customer assignments cause minor changes in the distribution process. We thus base every new solution on the most similar already evaluated fulfillment plan. This adapted initial solution is then iteratively improved by a newly-developed route-pattern exchange heuristic. The performance of the developed algorithm is demonstrated on a number of randomly created test instances and is compared to the solutions of a commercial MIP-solver.Series: Schriftenreihe des Instituts für Transportwirtschaft und Logistik - Supply Chain Managemen

Optimised decision-making under grade uncertainty in surface mining

Mining schedule optimisation often ignores geological and economic risks in favour of simplistic deterministic methods. In this thesis a scenario optimisation approach is developed which uses MILP optimisation results from multiple conditional simulations of geological data to derive a unique solution. The research also generated an interpretive framework which incorporates the use of the Coefficient of Variation allowing the assessment of various optimisation results in order to find the solution with the most attractive risk-return ratio

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems