Interactive optimisation (IO) combines the analytical power of optimisation frameworks with human's contextual expertise. However, prior IO approaches require human users to repeatedly provide the same type of input or directly modify the model to incorporate different information. As a result, IO frameworks elicit a narrow range of human knowledge or require substantial optimisation expertise from users. To address these limitations, an IO framework is proposed that allows human users to respond to multiple types of queries. The framework aims to produce higher-fidelity stochastic multi-objective mixed-integer linear programming models. It employs targeted questions to elicit specific information from users, a Monte Carlo-based framework to transform human responses into input data for a scenario-based optimisation model formulation, and uses a Conditional Value at Risk (CVaR) formulation to balance expected performance with risk tolerances. Computational experiments on a supplier selection problem demonstrate that this framework can narrow the reality gap and converge towards the ground-truth solution. Moreover, it dynamically adapts to user feedback, and when the human expresses insufficient confidence in the solution's performance, it can recommend solutions with narrower performance confidence intervals.

Renewable power generators typically participate as price-takers in current electricity markets, and market clearing prices are determined by cost curves of conventional generators while treating renewable generation as negative load. In this paper, we analyze a new design of electricity markets where renewable power generators are able to bid their expectation-adjusted cost curves into the market, just like the cost curves of conventional generators. We formally define the new market model, and mathematically show how the renewable cost curves should be determined for the new market to be equivalent to the current market in terms of overall system cost. We further establish that on the average, the total revenue of both conventional and renewable generators, as well as the total cost to consumers, under the proposed market is the same as the current practice. While equivalent in terms of aggregate cost and revenue measures, the new market design allows renewables to be direct participants in the bidding process and bid according to their risk-return tolerance. We demonstrate our analytical results numerically using data obtained from the the Texas grid.

This article formulates and solves a stochastic optimization model to investigate the impact of crowdsourced platforms (e.g., ridesharing, on‐demand delivery, volunteer food rescue, and carpooling) offering small, personalized menus of requests and incentive offers for drivers to choose from. To circumvent nonlinear variable relationships, we exploit model structure to formulate the program as a stochastic linear integer program. The proposed solution approach models stochastic responses as a sample of variable and fixed scenarios, and to counterbalance solution overfitting, uses a participation ratio parameter. The problem is also decomposed and iterated among two separate subproblems, one which optimizes menus, and another, which optimizes incentives. Computational experiments, based on a ride sharing application using occasional drivers demonstrate the importance of using multiple scenarios to capture stochastic driver behavior. Our method provides robust performance even when discrepancies between predicted and observed driver behaviors exist. Computational results show that offering menus and personalized incentives can significantly increase match rates and platform profit compared to recommending a single request to each driver. Further, compared to the menu‐only model, the average driver income is increased, and more customer requests are matched. By strategically using personalized incentives to prioritize promising matches and to increase drivers' willingness to accept requests, our approach benefits both drivers and customers. Higher incentives are offered when drivers are more likely to accept, while fewer incentives and menu slots are reserved for driver‐request pairs less likely to be accepted.

This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed-integer semi-infinite bilevel program and show that it can be converted into a mixed-integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst-case possibilities.

We consider a new class of max flow network interdiction problems, where the defender is able to introduce new arcs to the network after the attacker has made their interdiction decisions. We prove properties of when this restructuring will not increase the value of the minimum cut, which has important practical interpretations for problems of disrupting drug trafficking networks. In particular, it demonstrates that disrupting lower levels of these networks will not impact their operations when replacing the disrupted participants is easy. For the bilevel mixed integer linear programming formulation of this problem, we devise a column-and-constraint generation (C&CG) algorithm to solve it. Our approach uses partial information on the feasibility of restructuring plans and is shown to be orders of magnitude faster than previous C&CG methods. We demonstrate that applying decisions from standard max flow network interdiction problems can result in significantly higher flows than interdictions that account for the restructuring.

We consider a new class of multi-period network interdiction problems, where interdiction and restructuring decisions are decided upon before the network is operated and implemented throughout the time horizon. We discuss how we apply this new problem to disrupting domestic sex trafficking networks, and introduce a variant where a second cooperating attacker has the ability to interdict victims and prevent the recruitment of prospective victims. This problem is modeled as a bilevel mixed integer linear program (BMILP), and is solved using column-and-constraint generation with partial information. We also simplify the BMILP when all interdictions are implemented before the network is operated. Modeling-based augmentations are proposed to significantly improve the solution time in a majority of instances tested. We apply our method to synthetic domestic sex trafficking networks, and discuss policy implications from our model. In particular, we show how preventing the recruitment of prospective victims may be as essential to disrupting sex trafficking as interdicting existing participants.

Urban deliveries of goods have become a rising challenge due to the increase of online shopping in addition to the traditional business‐to‐business (B2B) dynamics. To maintain a satisfactory level of service, carriers must conduct delivery operations under restrictive environments, creating undesirable externalities such as congestion and pollution. Urban micro‐consolidation centers (UMCs) are defined as on‐street or off‐street spaces where all the deliveries within a certain radius are dropped and reconsolidated to be delivered by more sustainable last‐leg modes. Their main purpose is to mitigate such negative externalities. This work formulates the last‐mile delivery problem assisted by UMCs as a mixed‐integer quadratically‐constrained program and develops a greedy heuristic solution, inspired by the decomposition algorithms for large‐scale optimization. The simulation results and a case study in Manhattan, New York show how the heuristic provides reasonable results with respect to the exact solution while also shedding light on how its solution can be utilized for freight‐efficient urban design and policy planning.

We consider two new problems regarding the impact of edge addition or removal on the modularity of partitions (or community structures) in a network. The first problem seeks to add edges to enforce that a desired partition is one partition that maximizes modularity. The second problem seeks to find the sparsest representation of a network that has the same partition with maximum modularity as the original network. We present integer programming formulations, a row generation algorithm, and heuristic algorithms to solve these problems. Further, we demonstrate a counter-intuitive behavior of modularity that makes the development of heuristics for general networks difficult. We then present results on a selection of social and illicit networks from the literature.

Peer-to-peer logistics platforms coordinate independent drivers to fulfill requests for last mile delivery and ridesharing. To balance demand-side performance with driver autonomy, a new stochastic methodology provides drivers with a small but personalized menu of requests to choose from. This creates a Stackelberg game, in which the platform leads by deciding what menu of requests to send to drivers, and the drivers follow by selecting which request(s) they are willing to fulfill from their received menus. Determining optimal menus, menu size, and request overlaps in menus is complex as the platform has limited knowledge of drivers' request preferences. Exploiting the problem structure when drivers signal willingness to participate, we reformulate our problem as an equivalent single-level Mixed Integer Linear Program (MILP) and apply the Sample Average Approximation (SAA) method. Computational tests recommend a training sample size for inputted SAA scenarios and a test sample size for completing performance analysis. Our stochastic optimization approach performs better than current approaches, as well as deterministic optimization alternatives. A simplified formulation ignoring 'unhappy drivers' who accept requests but are not matched is shown to produce similar objective values with a fraction of the runtime. A ridesharing case study of the Chicago Regional transportation network provides insights for a platform wanting to provide driver autonomy via menu creation. The proposed methods achieved high demand performance as long as the drivers are well compensated (e.g., even when drivers are allowed to reject requests, on average over 90% of requests are fulfilled when 80% of the fare goes to drivers; this drops to below 60% when only 40% of the fare goes to drivers). Thus, neither the platform nor the drivers benefit from low driver compensation due to its resulting low driver participation and thus low request fulfillment. Finally, for the cases tested, a maximum menu size of 5 is recommended as it produces good quality platform solutions without requiring much driver selection time.

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other nonconvex methods require the rank or sparsity to be known a priori, we use nonconvex regularizers to minimize the rank and $l_0$ norm without the estimator bias from the convex relaxation. We present a novel analysis of the alternating proximal gradient descent algorithm applied to such problems, and bound the error between the iterates and the ground truth sparse and low rank matrices. The algorithm and error bound can be applied to sparse optimization, matrix completion, and robust principal component analysis as special cases of our results.

This paper develops a framework to create resilience indices for multi-echelon assembly supply chain (MEASC) networks. Each supplier within this network assembles a component from a series of sub-components received from other suppliers, thus, disruptions at suppliers can cascade and significantly affect the performance of the whole network. The framework combines the decision rules developed in [32] and Monte Carlo simulation. These indices can evaluate the vulnerability of a MEASC network to different types of disruptive events and to estimate with statistical confidence the impact of such events. As an extension, this approach is applied to individual suppliers to create individual resilience indices and identify the most vulnerable suppliers within the network. The resilience indices can further be used to understand how certain mitigation efforts improve resilience and identify improvements that potentially make the network less vulnerable to a certain type of disruptive event. It can further be applied to understand how certain mitigation efforts improve resilience (e.g., safety stocks at suppliers or requiring key suppliers to have back-up capacities at their other assembly locations), which is important in determining thecorrect requirements of the MEASC network to meet certain post-disruptive event performance criteria. (C) 2020 Elsevier Ltd. All rights reserved.

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective technique to solve the problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than the nuclear norm and can more accurately reduce the effect of noise on the measurements. We develop efficient algorithms based on iteratively reweighted nuclear norm schemes, while also utilizing the low rank factorization for semidefinite programs put forth by Burer and Monteiro. We prove convergence and computationally show the advantages over convex relaxations and alternating minimization methods. Additionally, the computational complexity of each iteration of our algorithm is on par with other state of the art algorithms, allowing us to quickly find solutions to the rank minimization problem for large matrices.

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be lifted to give an equivalent semidefinite program with complementarity constraints. The formulation requires two positive semidefinite matrices to be complementary. This is a continuous and nonconvex reformulation of the rank minimization problem. We develop two relaxations and show that constraint qualification holds at any stationary point of either relaxation of the rank minimization problem, and we explore the structure of the local minimizers.

This work extends the logical benders approach for solving linear programs with complementarity constraints proposed by Hu et al. (SIAM J Optim 19(1):445–471, 2008) and Bai et al. (Comput Optim Appl 54(3):517–554, 2013). We develop a novel interpretation of the logical Benders method as a reversed branch-and-bound search, where the whole exploration procedure starts from the leaf nodes in an enumeration tree. This insight enables us to provide a new framework over which we can combine master problem and cut generation in a single process. It also allows us to diversify the search, leading computationally to stronger cuts. We also present an optimization-based sparsification process which makes the cut generation more efficient. Numerical results are presented to show the effectiveness of this enhanced method. Results are also extended to problems with more complementarity constraints, exceeding those that can be handled by the original method in the cited references.

During the development of a suite of computer-aided decision support tools for the restoration of interdependent infrastructures impacted by an extreme natural hazard event, it became apparent that the release of vulnerability data on actual infrastructure systems could raise security concerns. As a result, an artificial and customizable infrastructure dataset was developed based on experiences with creating real, but not public, data that can be used for modeling, analysis, and decision making. The purpose of this paper is to describe the rationale and methodology for assembling the database for customizable artificial community (CLARC), an artificial coastal community of approximately 500,000 people and 1,065 square miles, that includes five civil infrastructure networks (electricity, water, wastewater, transportation, and communications) and social infrastructures, such as public safety, healthcare, and critical commercial services including fuel and banking that communities rely upon during an emergency as well as population and other socio-economic factors. The interdependencies that exist between the civil infrastructure systems and between civil and social infrastructures are included in the dataset and are attributes to assist with modeling and analysis. This paper discusses the dataset in detail, describes why and how it was assembled, and includes a virtual case study that uses the CLARC dataset to simulate the impacts on the civil and social infrastructure of a hypothetical Category 3 hurricane and the community’s response and recovery from that event. The dataset is openly available for use by the research and practitioner communities.

This work considers the problem of restoration decision making by supply chain managers under uncertainty. Specifically, we consider an oil supply chain network that has suffered a cyber attack. As a result of the attack, critical services to the supply chain are lost, and the manager has uncertain information regarding when these services will be available. We first consider a deterministic model where the supply chain manager has complete information about the restoration of damaged services. We extend this model to a stochastic programming model involving several different recovery scenarios. We present computational results for a realistic case study developed with an extensive literature survey. We compare results of the stochastic model with average deterministic results, and show that the average deterministic results do not produce good solutions for an uncertain setting. We conclude with general remarks on how supply chain managers should consider restoration decisions under uncertainty.

We formally present the problem of scheduling tasks with effectiveness precedence relationships in order to achieve the minimum total weighted completion time. We provide the problem formulation and define the scope of the problem considered. We present computational complexity results for this problem and an approximation algorithm for it. We prove the theoretical performance of our algorithm and demonstrate its efficiency and practical performance through computational testing, which includes a comparison to the optimal results obtained with an integer programming formulation.

Today's deep learning models are primarily trained on CPUs and GPUs. Although these models tend to have low error, they consume high power and utilize large amount of memory owing to double precision floating point learning parameters. Beyond the Moore's law, a significant portion of deep learning tasks would run on edge computing systems, which will form an indispensable part of the entire computation fabric. Subsequently, training deep learning models for such systems will have to be tailored and adopted to generate models that have the following desirable characteristics: low error, low memory, and low power. We believe that deep neural networks (DNNs), where learning parameters are constrained to have a set of finite discrete values, running on neuromorphic computing systems would be instrumental for intelligent edge computing systems having these desirable characteristics. To this extent, we propose the Combinatorial Neural Network Training Algorithm (CoNNTrA), that leverages a coordinate gradient descent-based approach for training deep learning models with finite discrete learning parameters. Next, we elaborate on the theoretical underpinnings and evaluate the computational complexity of CoNNTrA. As a proof of concept, we use CoNNTrA to train deep learning models with ternary learning parameters on the MNIST, Iris and ImageNet data sets and compare their performance to the same models trained using Backpropagation. We use following performance metrics for the comparison: (i) Training error; (ii) Validation error; (iii) Memory usage; and (iv) Training time. Our results indicate that CoNNTrA models use 32x less memory and have errors at par with the Backpropagation models.