Nonlinear Cost Research Articles

Optimal subset selection for causal inference using machine learning ensembles and particle swarm optimization

We suggest and evaluate a method for optimal construction of synthetic treatment and control samples for the purpose of drawing causal inference. The balance optimization subset selection problem, which formulates minimization of aggregate imbalance in covariate distributions to reduce bias in data, is a new area of study in operations research. We investigate a novel metric, cross-validated area under the receiver operating characteristic curve (AUC) as a measure of balance between treatment and control groups. The proposed approach provides direct and automatic balancing of covariate distributions. In addition, the AUC-based approach is able to detect subtler distributional differences than existing measures, such as simple empirical mean/variance and count-based metrics. Thus, optimizing AUCs achieves a greater balance than the existing methods. Using 5 widely used real data sets and 7 synthetic data sets, we show that optimization of samples using existing methods (Chi-square, mean variance differences, Kolmogorov–Smirnov, and Mahalanobis) results in samples containing imbalance that is detectable using machine learning ensembles. We minimize covariate imbalance by minimizing the absolute value of the distance of the maximum cross-validated AUC on M folds from 0.50, using evolutionary optimization. We demonstrate that particle swarm optimization (PSO) outperforms modified cuckoo swarm (MCS) for a gradient-free, non-linear noisy cost function. To compute AUCs, we use supervised binary classification approaches from the machine learning and credit scoring literature. Using superscore ensembles adds to the classifier-based two-sample testing literature. If the mean cross-validated AUC based on machine learning is 0.50, the two groups are indistinguishable and suitable for causal inference.

Distributed Optimization Over Time-Varying Networks With Minimal Connectivity

Many existing distributed optimization algorithms are applicable to time-varying networks, whereas their convergence results are established under the standard $B$ -connectivity condition. In this letter, we establish the convergence of the Fenchel dual gradient methods, proposed in our prior work, under a less restrictive and indeed minimal connectivity condition on undirected networks, which, referred to as joint connectivity, requires the infinitely occurring agent interactions to form a connected graph. Compared to the existing distributed optimization algorithms that are guaranteed to converge under joint connectivity, the Fenchel dual gradient methods are able to handle nonlinear local cost functions and nonidentical local constraints. We also demonstrate the effectiveness of the Fenchel dual gradient methods over time-varying networks satisfying joint connectivity via simulations.

List Group Price Analysis of the Grid Engineering Quantity in Grid International EPC Bidding

In the international EPC bidding, company’s own business objectives are used to determine the expected profit level of the power grid project. Therefore, the composition and calculation on the bidding price and sub-items of the power grid engineering fees, measure project fees, other project fees and regulations fees as well as taxes are introduced in the paper under the grid project quantity list pricing model. Moreover, in terms of the problem on the cost allocation in the bidding price of the grid project quantity list, a nonlinear cost allocation model is established to obtain the optimal solution with the help of Kuhn-Tucker condition. Then the nature of the optimal solution is analyzed, which proves that the optimal solution can be used as the cost sharing standard or reference basis in the grid project quantity list.

Visualizing and Optimizing Portfolio with Nonlinear Transaction Costs and Specific Constraints

In this paper, we consider the portfolio selection problem, with nonlinear transaction costs, basic constraints and probabilistic constraints. Such a problem cannot be handled by the usual quadratic or convex optimization methods.  We develop a heuristic method which yields to computation of efficient (suboptimal) solution of the problem. We describe our heuristic method for finding optimal portfolio based on solving many small optimization problems over large generation number, thus we obtain a good suboptimal solution.  Experimental results are demonstrated and visualized with various widely used indexes: stocks in US market: U.S. three – months treasury bills, U.S. long – term government bonds, S&P 500, Wilshire 5000, NASDAQ, Lehman Brothers corporate bond index, EAFE foreign stock index, and Gold recorded from (Jan 2000 – Jan 2008) with enhanced performance.  Finally, the results suggest that nonlinear transactions costs improve considerably the value of optimal portfolio over investment period, especially for portfolio with smaller among all assets.

Comparison of metaheuristic optimisation methods for grid-edge technology that leverages heat pumps and thermal energy storage

Grid-edge technology can unlock flexibility from consumers to contribute to meeting the growing need for flexibility in European energy systems. Furthermore, power-to-heat technology such as heat pumps and thermal energy storage has been shown to both decarbonise heat and enable the cost-effective integration of more renewable electricity into the grid. The consumer's reaction to price signals in this context presents the opportunity to simultaneously unlock operational cost reductions for consumers and localised implicit demand-side flexibility to benefit grid operators.In this paper, the prediction accuracy, run-time, and reliability of several (metaheuristic) optimisation algorithms to derive optimal operation schedules for heat pump-based grid-edge technology are investigated. To compare effectiveness, an optimisation effectiveness indicator OEI is defined. Particle Swarm Optimisation (PSO) and Genetic Algorithm (GA) were found to be most effective and robust in yielding quasi-optimal minima for the non-linear, multi-modal, and discontinuous cost function. GA optimisation with binary variables is 5–15 times more effective than with continuous variables. Using continuous variables, PSO is more effective than GA due to smaller optimisation error, shorter run-time, and higher reliability (smaller standard deviation). Simulated Annealing and Direct (Pattern) Search were found to be not very effective.

Optimal investment, derivative demand, and arbitrage under price impact

AbstractThis paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.

A Branch-and-Price Algorithm for Facility Location with General Facility Cost Functions

Most existing facility location models assume that the facility cost is either a fixed setup cost or made up of a fixed setup and a problem-specific concave or submodular cost term. This structural property plays a critical role in developing fast branch-and-price, Lagrangian relaxation, constant ratio approximation, and conic integer programming reformulation approaches for these NP-hard problems. Many practical considerations and complicating factors, however, can make the facility cost no longer concave or submodular. By removing this restrictive assumption, we study a new location model that considers general nonlinear costs to operate facilities in the facility location framework. The general model does not even admit any approximation algorithms unless P = NP because it takes the unsplittable hard-capacitated metric facility location problem as a special case. We first reformulate this general model as a set-partitioning model and then propose a branch-and-price approach. Although the corresponding pricing problem is NP-hard, we effectively analyze its structural properties and design an algorithm to solve it efficiently. The numerical results obtained from two implementation examples of the general model demonstrate the effectiveness of the solution approach, reveal the managerial implications, and validate the importance to study the general framework.

On incentives and optimal effort to improve bus transit performance

ABSTRACT This paper studies incentive-based subsidy to transit systems to improve performance. It derives a formula for optimal effort that equalizes marginal cost and marginal benefit and derives some principles from it among which is that the larger the value of a transit system’s performance criterion the larger the effort it will exert to improve it. Next, using a constrained cost minimization approach it derives a nonlinear cost function that includes optimal effort and estimates it using an unbalanced panel data of single mode U.S. bus transit systems. The results show that optimal effort is the equivalent of seven full-time employees (15,243 labor hours) per year and in real terms it results in 0.6% cost saving (US$198,331) and US$836,796 in incentive subsidy per observation. The implications of these findings are examined.

Nonlinear Model Predictive Control of Steam-Assisted-Gravity-Drainage Well Operations for Real-Time Production Optimization

Summary In deep oil-sands deposits using the steam-assisted-gravity-drainage (SAGD) recovery process, real-time optimization (RTO) involves controlling optimum subcool to ensure steam conformance. Contemporary workflows use linear model predictive control (MPC) with oversimplified models that are inadequate to represent highly complex, spatially distributed, and nonlinear reservoir dynamics. In this research, two novel workflows using nonlinear MPC (NMPC) are proposed. The first workflow reduces an NMPC problem to linear MPC by estimating an equivalent linear model of a nonlinear black-box model in a mean-square-error sense. Another approach is to use nonlinear dynamic models explicitly for accurate prediction of the plant states and/or outputs. The resulting nonconvex, nonlinear cost optimization problem is solved using an interior-point algorithm at each control interval. Proposed workflows are tested using the history-matched, field-scale model of a SAGD reservoir located in northern Alberta, Canada. Qualitative and quantitative analysis of the results reveals that nonlinear black-box models based on system identification theory can successfully capture the nonlinearity of the SAGD process. Also, both workflows can control the subcool above the desired set-point while ensuring stable well operations. More than a 24% increment is achieved in net present value (NPV) using proposed NMPC workflows compared with the field operations with no closed-loop control. Overall, NMPC can successfully be used for improved RTO, energy efficiency, and greenhouse gas emissions while considering available surface facilities and well configurations.

Stochastic and distributed scheduling of shipboard power systems using MθFOA-ADMM

This article introduces an effective stochastic operation framework for optimal energy management of the shipboard power systems including large, nonlinear and dynamic loads. The proposed framework divides the ship power system into several agents, which coordinate with each other based on their demands/supplies until. The alternating direction method of multipliers (ADMM) is deployed as the multi-agent framework to solve the reformulated distributed energy management problem in the ship. Two types of turbo-generators are considered in the proposed system model, including single-shaft and twin-shaft models, to increase the part-load efficiency in certain times when facing variable speed operation. The proposed distributed framework is equipped with a recursive mechanism, which helps the ship system for running optimal load scheduling when facing insufficient power generation. In order to model the uncertainty effects associated with the forecast error in the interval-ahead load demand, a stochastic framework based on unscented transform is devised which can work in the nonlinear and correlated environments of shipboard power systems. Due to the nonlinear cost function in each agent, a powerful optimization algorithm based on modified θ-firefly algorithm (Mθ-FOA) is proposed. This is a phasor algorithm, which helps for escaping from premature convergence and getting trapped in local optima. The appropriate performance of the proposed stochastic model is examined on the real dataset of a ship power system. The simulation results show the high robustness, guarantied consensus, economic operation and feasible solution when power generation shortage based on load shedding in the system.

Fast distributed control design for DC linked microgrids

A centralized controller for a DC linked hybrid microgrid requires costly communication infrastructure. To minimize the costs, in this paper, a sparse distributed controller is formulized by introducing an l1 penalty term to the cost function to enforce at most not more than neighbor-to neighbor links. This makes the design nonlinear which exhausts large amount of computation times. Therefore, by some transformations, the nonlinear cost function is converted to an approximate quadratic one; which has better optimization characteristics, i.e. fast convergence rate and unimodal. The proposed fast distributed controller Design (FDCD) algorithm is employed for a 3-bus and a 69-bus (consist of 7 hybrid microgrid) distribution systems controller design. The results indicate that the obtained sparse distributed controller performs well as if a centralized controller is in operation. It can successfully suppress various types of faults injected to the AC, DC, and DC link sides of the network. The algorithm convergence rate is substantially lower than some other contestant algorithms. A problem that is solved by FDCD in 5 min, it takes 10 min for the others to be completed.

The Properties of Conjectural Variations in the Nonlinear Stackelberg Oligopoly Model

The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. The conjectural variations of each agent, i.e., the expected responses (changes in actions) of his counteragents that optimize their utility functions, are studied. Formulas for calculating the conjectural variations of each agent and also the sum of the conjectural variations of all agents in the environment of each agent are derived. The signs of conjectural variations under an arbitrary level of Stackelberg leadership are analyzed. The following properties of conjectural variations are established: 1) the variations are negative if the cost functions of all environmental agents are either convex or concave; 2) the variations are positive if the agents with concave cost functions (the ones with the positive scale effect) prevail in the environment over the agents with convex cost functions (the ones with the negative scale effect). The sum of the agent’s conjectural variations is: 1) negative and its magnitude is bounded above by 1 if the environmental agents mainly have convex cost functions; 2) positive and unlimited if the agents with concave cost functions prevail in the environment.

Coordinating biomass supply chains for remote communities: a comparative analysis of non-cooperative and cooperative scenarios

The absence of economies of scale is a major barrier in use of renewable energy sources in small and dispersed off-grid remote communities. For example, in northern Canada, diesel is currently the main source of electricity and heat generation. Coordination of biomass supply chains could play a key role in improving the cost efficiency and reliability of bioenergy generation through bundled ordering and creation of storage hubs. In this study, a supply chain management model with multiple suppliers and multiple end-user communities is formulated. The proposed model enables us to analyse and compare the outcomes of adopting a cooperative coordination strategy (with a joint pay-off for communities) versus a non-cooperative coordination strategy (with individual payoffs for communities). Other peculiar attributes of the proposed model rest in the addressing of restricted ordering schedules and quantities (due to unavailability of pathways) by advocating nonlinear ordering and distribution costs (to incorporate quantity discounts) achieved through coordinated and/or collective inventories. A real biomass supply chain case study of three northernmost Nunavik communities in Quebec is considered to show the applicability of the model and provide insights for uptake of bioenergy sources in remote off-grid communities.

Geo-registration and Geo-location Using Two Airborne Video Sensors

Geo-registration and geo-location of data collected by video sensors such as electro-optical and infrared cameras are two fundamental steps in the airborne surveillance of ground targets. With the availability of high-resolution imaging sensors and detailed mapping or terrain data sources, video data plays an increasingly important role in modern surveillance platforms like unmanned aerial vehicles and airborne, ground, or maritime surveillance systems. Surveillance systems without any compensation for the inevitable sensor registration errors, i.e., biases, may make geo-location erroneous and render the surveillance platform less effective for precision targeting. This article deals with the modeling of sensor biases in geo-location and proposes a method to estimate them. The proposed method leads to a minimization problem with a nonlinear cost function. Detailed derivation of the bias model is given along with an algorithm to find the bias parameters. The achievable lower bounds for debiased geo-location are provided and simulations are used to demonstrate the validity of the proposed method.

Chaotic triopoly game: a congestion case

In this paper, we propose a simple network consisting of only two nodes and two paths. The first node, which is called the source, has three competing firms that send their quantities of load via the two paths to the second node, called the destination node. The static game that describes the reaction among the three firms is constructed. The Nash equilibrium point of the static game is discussed. Assuming a gradient firm based rule we investigate the dynamic game which has the same Nash equilibrium as in the static game. The local stability conditions of the Nash equilibrium are obtained in terms of the reactivity parameters among the firms and the nonlinear costs functions adopted by those firms. The obtained results are supported by a numerical simulation that in turn gives routes where Nash equilibrium may lose its stability. The simulation shows that Nash equilibrium loses its stability via flip and fold bifurcations and then chaos exists.

Robust online video super-resolution using an efficient alternating projections scheme

Video super-resolution reconstruction (SRR) algorithms attempt to reconstruct high-resolution (HR) video sequences from low-resolution observations. Although recent progress in video SRR has significantly improved the quality of the reconstructed HR sequences, it remains challenging to design SRR algorithms that achieve good quality and robustness at a small computational complexity, being thus suitable for online applications. In this paper, we propose a new adaptive video SRR algorithm that achieves state-of-the-art performance at a very small computational cost. Using a nonlinear cost function constructed considering characteristics of typical innovation outliers in natural image sequences and an edge-preserving regularization strategy, we achieve state-of-the-art reconstructed image quality and robustness. This cost function is optimized using a specific alternating projections strategy over non-convex sets that is able to converge in a very few iterations. An accurate and very efficient approximation for the projection operations is also obtained using tools from multidimensional multirate signal processing. This solves the slow convergence issue of stochastic gradient-based methods while keeping a small computational complexity. Simulation results with both synthetic and real image sequences show that the performance of the proposed algorithm is similar or better than state-of-the-art SRR algorithms, while requiring only a small fraction of their computational cost.

Complex Workpiece Positioning System With Nonrigid Registration Method for 6-DoFs Automatic Spray Painting Robot

To reduce the labor effort in hazardous environments like spray painting, an automatic car part spray painting machine has been set up. This article presents an intelligent location procedure for this machine. The location procedure assumes that the car part is placed with a tiny arbitrary pose, furthermore some kinds of parts under inspection undergoes through the deformation and thus it contains a nonrigid model. To tackle this problem, a workpiece positioning system works though multicamera is established first. Subsequently, a novel modified iterative closest point (ICP) algorithm is proposed which registers the nonrigid shape to the undeformed source shape in the training library. The modified ICP combines the ideas from traditional ICP and deformation estimation from bounded biharmonic weights. It solves a nonlinear cost function by using Levenberg–Marquardt algorithm. As a result, it estimates the transformation of the target point cloud with regards to the source point cloud. Additionally, it improves the accuracy of traditional ICP and increases its scope to nonrigid shapes. By employing these results in our location procedure, it can estimate the 6-DOF pose of the car part to be painted in addition to that it also estimates the deformation compared to the source cloud in the training library. This information is subsequently used to modify the guidance trajectory of the spray gun. In this article, a test case of front bumper is given, as it is commonly made of soft plastic materials and undergoes deformation under the influence of the external force. All the stated results support the efficacy of our algorithm.

Optimal deployment of charging stations considering path deviation and nonlinear elastic demand

This study aims to determine the optimal deployment of charging stations for battery electric vehicles (BEVs) by maximizing the covered path flows taking into account the path deviation and nonlinear elastic demand, referred to as DCSDE for short. Under the assumption that the travel demand between OD pairs follows a nonlinear inverse cost function with respect to the generalized travel cost, a BCAP-based (battery charging action-based path) model will be first formulated for DCSDE problem. A tailored branch-and-price (B&P) approach is proposed to solve the model. The pricing problem to determine an optimal path of BEV is not easily solvable by available algorithms due to the path-based nonlinear cost term in the objective function. We thus propose a customized two-phase method for the pricing problem. The model framework and solution method can easily be extended to incorporate other practical requirements in the context of e-mobility, such as the maximal allowable number of stops for charging and the asymmetric round trip. The numerical experiments in a benchmark 25-node network and a real-world California State road network are conducted to assess the efficiency of the proposed model and solution approach.

Trading with small nonlinear price impact

We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.

Canadian Regional Agriculture Model: PMP Applied to the Beef Sector in Canada

This paper describes the Positive Mathematical Programming (PMP), the method for calibrating models of agricultural livestock production and resource use by a nonlinear total cost function. The PMP method is applied to agricultural sectoral models to study changes in policy and market signals. The Canadian Regional Agriculture Model (CRAM) is a regional, multi-sectoral, comparative static, partial equilibrium, mathematical programming model developed and maintained by Agriculture and Agri-Food Canada (AAFC) since mid-eighties. The PMP process converts a linear model using flexibility constraints into a nonlinear model in the absence of the flexibility constraints. A component of CRAM is the beef sector. The elements of the set of total cost curves are defined as quadratic function in terms of the number of cows and calves in the beef production activities. The marginal cost curves were then approximated using the shadow values from linear programming solution with linear curves. Once the flexibility constraints were removed, the model automatically calibrates to the base year production levels. The results from four scenarios indicated the beef sector of CRAM could predict the impact of the scenarios on the size of beef herd. In Scenario 1 where cash costs were increased by 10 percent, the breeding herd size decreased from 3.73 percent in New Brunswick to 0.0 percent in Ontario and Quebec. In Scenario 2 where barley costs were decreased by 10 percent, the breeding herd size increased from 0 percent for British Columbia, Alberta, Ontario, Quebec, Prince Edward Island and Nova Scotia to 1.93 percent for New Brunswick. In Scenario 3 where carcass weight per beef cow could be increased by 10 percent, the increase in beef herd size ranged from 0 percent for Ontario and Quebec to 2.56 percent for New Brunswick. In Scenario 4 where world beef prices were increased by 10 percent increase in beef herd size ranged from 4.48 percent for Manitoba to 25.78 percent for New Brunswick.