Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

A risk-based approach to solving the problem of airline schedule operational management

The paper discusses the problem of optimal regulation of aircraft assignments for airline flights. Due to the fact that the activities of the airline are subject to changes caused by both external and internal environment, the planned schedule needs continuous management and control. In the event when the actual flight schedule deviates from the planned one, it is necessary to promptly make a decision on adjusting (restoring) the schedule and reassigning aircraft. Operational schedule management involves making adjustments to the current schedule from a depth of several hours to several days. The solution to the problem is to determine the unambiguous correspondence of flights and specific aircraft subject to maximizing the likelihood of meeting production targets and observing a number of restrictions. The task of managing airline schedules belongs to the class of scheduling optimization problems for parallel-sequential systems studied within the scheduling theory. It is NP-hard and requires the development of computationally efficient solution algorithms. However, the issue of choosing criteria for the optimization problem deserves special attention, since the correct choice plays an essential role in terms of assessing the effectiveness of decision-making. In the theory of decision-making, no general method for choosing the optimality criteria has been found. The definition of the target criterion depends on the expectations of the production. Within the framework of this paper, an original criterion is proposed for constructing an optimal solution to the discrete problem of managing aircraft assignments, the main idea of which is to find a balance between the duration of the schedule and the number of flights with a negative deviation from the planned schedule by assessing the level of punctuality violation risk. The paper gives a detailed concept of punctuality, describes an approach to assessing the level of risk, and also proposes an original formal formulation of the task of operational management of aircraft assignments based on the criterion of minimizing the risk of violation of flight punctuality.

Solutions and memory effect of fractional-order chaotic system: A review (Interdisciplinary Physics)

Fractional calculus is a 300 years topic, which has been introduced to real physics systems modeling and engineering applications. In the last few decades, fractional-order nonlinear chaotic systems have been widely investigated. Firstly, the most used methods to solve fractional-order chaotic systems are reviewed. Characteristics and memory effect in those method are summarized. Then we discussed the memory effect in the fractional-order chaotic systems through the fractional-order calculus and numerical solution algorithms. It shows that the integer-order derivative has full memory effect, while the fractional-order derivative has nonideal memory effect due to the kernel function. Memory lose and short memory are discussed. Finally, applications of the fractional-order chaotic systems regarding the memory effects are investigated. The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.

Assessment of Voltage Imbalance Improvement and Power Loss Reduction in Residential Distribution Systems in Taiwan

In this study, the non-dominated sorting genetic algorithm II (NSGA-II) is used to optimize the annual phase arrangement of distribution transformers connected to primary feeders to improve three-phase imbalance and reduce power loss. Based on the data of advanced metering infrastructure (AMI), a quasi-real-time ZIP load model and typical sample distribution systems in Taiwan are constructed. The equivalent circuit models and solution algorithms for typical distribution systems in Taiwan are built using the commercial software package MATLAB. A series of simulations, analyses, comparisons, and explorations is executed. Finally, the quantitative evaluation results for improving the voltage imbalance and reducing the power loss are summarized. For the series of studies, the percentage reductions in (1) total power imbalance TSI, (2) total line loss TLL, (3) average voltage drop AVD, (4) total voltage imbalance factors for zero/negative sequences Td0/Td2, and (5) neutral current of the main transformer ILCO are up to 45.48%, 4.06%, 16.61%, 63.99%, 21.33%, and 88.01%, respectively. The results obtained in this study can be applied for energy saving and can aid the authorities to implement sustainable development policies in Taiwan.

Metaheuristics in the Humanitarian Supply Chain

Everyday there are more disasters that require Humanitarian Supply Chain (HSC) attention; generally these problems are difficult to solve in reasonable computational time and metaheuristics (MHs) are the indicated solution algorithms. To our knowledge, there has not been a review article on MHs applied to HSC. In this work, 78 articles were extracted from 2016 publications using systematic literature review methodology and were analyzed to answer two research questions: (1) How are the HSC problems that have been solved from Metaheuristics classified? (2) What is the gap found to accomplish future research in Metaheuristics in HSC? After classifying them into deterministic (52.56%) and non-deterministic (47.44%) problems; post-disaster (51.28%), pre-disaster (14.10%) and integrated (34.62%); facility location (41.03%), distribution (71.79%), inventory (11.54%) and mass evacuation (10.26%); single (46.15%) and multiple objective functions (53.85%), single (76.92%) and multiple (23.07%) period; and the type of Metaheuristic: Metaphor (71.79%) with genetic algorithms and particle swarm optimization as the most used; and non-metaphor based (28.20%), in which search algorithms are mostly used; it is concluded that, to consider the uncertainty of the real context, future research should be done in non-deterministic and multi-period problems that integrate pre- and post-disaster stages, that increasingly include problems such as inventory and mass evacuation and in which new multi-objective MHs are tested.

Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming

We consider the optimal value function of a parametric optimization problem. A large number of publications have been dedicated to the study of continuity and differentiability properties of the function. However, the differentiability aspect of works in the current literature has mostly been limited to first order analysis, with focus on estimates of its directional derivatives and subdifferentials, given that the function is typically nonsmooth. With the progress made in the last two to three decades in major subfields of optimization such as robust, minmax, semi-infinite and bilevel optimization, and their connection to the optimal value function, there is a need for a second order analysis of the generalized differentiability properties of this function. This could enable the development of robust solution algorithms, such as the Newton method. The main goal of this paper is to provide estimates of the generalized Hessian for the optimal value function. Our results are based on two handy tools from parametric optimization, namely the optimal solution and Lagrange multiplier mappings, for which completely detailed estimates of their generalized derivatives are either well-known or can easily be obtained.

Stochastic Last-Mile Delivery with Crowd-Shipping and Mobile Depots

This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.