Nonlinear Cost Function Research Articles

An individual evolutionary learning model meets Cournot

We extend the individual evolutionary learning model by incorporating other-regarding considerations and apply the model to some Cournot games. Using a model fitted to the experimental data of a repeated three-player Cournot game (with non-linear cost and demand functions), we provide out-of-sample predictions regarding the “feedback effects” and “number effects” and test them using the data gathered via newly conducted experiments. The prediction regarding the feedback effect is partially confirmed. Namely, it is observed for the three- and four-player games, but not the two-player game. The prediction regarding the number effect is also partially confirmed in that while the model predicts the number effect to be observed with detailed feedback, and not under aggregate feedback, the effect is observed with both types of feedback.

Estimating Asymmetric Fuel Price Responses in Croatia

Abstract Background According to many studies, the transmission of oil prices to retail fuel prices is asymmetric. Fuel prices react faster if oil prices rise and more slowly if oil prices fall. Different standard econometric procedures lead to different results. The Linex approach, which is based on formulating the non-linear adjustment cost function, reflects the theory. It uses the generalised method of moments to estimate the reaction functions, which demands many observations. Objectives The paper investigates the price asymmetry in the Croatian retail fuel market using standard approaches and the Linex approach. Methods/Approach The simple and dynamic asymmetry models, error correction models, threshold autoregressive co-integration, and the Linex approach are used to verify the hypothesis of asymmetric reactions of gasoline and diesel prices in Croatia. Results The results using the standard methods are mixed, while the Linex approach indicates price asymmetry, the size of which is measured with the average price bias. The results correspond to other studies worldwide. Conclusions The authors' preferred Linex approach detects price asymmetries, even with large data samples with frequent changes in trends and volatilities. According to the approach, the question is not whether prices are formed asymmetrically but the size of the asymmetry.

Improved memory-type ratio estimator for population mean in stratified random sampling under linear and non-linear cost functions

This paper offers an improved memory-type ratio estimator in stratified random sampling under linear and non-linear cost functions. The issue is given as all integer non-linear programming problems (AINLPPs). The sampling properties mainly the bias and the mean squared error of the introduced estimator are derived up to the first order of approximation. The optimum value of the characterizing scalar is obtained by the Lagrange method of maxima–minima. The least value of the MSE of the suggested estimator is also obtained for this optimum value of the charactering constant. The suggested estimator is compared both theoretically and empirically with the competing estimators. Under this setup, the optimum allocation with mean square error of the suggested estimator is attained, and the estimator is compared to other comparable estimators. The AINLPP is solved using the genetic programming approach, which is applied to both actual and simulated data sets from a bivariate normal distribution.

Dynamics of a Cournot game with bounded rational firms and various scale effects.

In this paper, we focus on a dynamic Cournot game in the market with a nonlinear (isoelastic) demand function. In our model, there are N competing firms featured by nonlinear cost functions, which enhances our model's resemblance to real-world scenarios. Firstly, we focus on the homogeneous case where firms' marginal costs change at equal rates. We establish analytical expressions of the market supply at equilibrium and perform comparative static analysis. In addition, we investigate the local stability under different economies of scale and show that there could be multiple stable equilibria if firms face economies of scale. The heterogeneous case where firms' marginal costs change at distinct rates is much more complex, thus we investigate the duopoly game with only two firms involved. Methods of symbolic computations such as triangular decomposition and partial cylindrical algebraic decomposition are employed in the analytical investigations of the equilibrium, which is nearly impossible by using the pencil-and-paper approach since the closed-form equilibrium is quite complicated. According to the computational results, we derive that two stable positive equilibria may coexist if both firms face economies of scale. Additionally, we conduct preliminary numerical simulations and find two different types of complex dynamics of the model considered in this paper: complex trajectories such as periodic and chaotic orbits may appear; the topological structure of the basins of attraction may be complex.

State Parameter Fusion Estimation for Intelligent Vehicles Based on IMM-MCCKF

The prerequisite for intelligent vehicles to achieve autonomous driving and active safety functions is acquiring accurate vehicle state parameters. Traditional Kalman filters often underperform in non-Gaussian noise environments due to their reliance on Gaussian assumptions. This paper presents the IMM-MCCKF filter, which integrates the interacting multiple model theory (IMM) and the maximum correntropy cubature Kalman filter method (MCCKF), for estimating the state parameters of intelligent vehicles. The IMM-MCCKF successfully suppresses non-Gaussian noise by optimizing a nonlinear cost function using the maximum correntropy criteria, allowing it to capture and analyze signal data outliers accurately. The filter designs various state and measurement noise submodels to adapt to the environment dynamically, thus reducing the impact of unknown noise statistical properties. Accurately measuring the velocity of a vehicle and the angle at which its center of mass drifts sideways is of utmost importance for its ability to maneuver, maintain stability, and ensure safety. These parameters are critical for implementing advanced control systems in intelligent vehicles. The study begins by constructing a nonlinear Dugoff tire model and a three-degrees-of-freedom (3DOF) vehicle model. Subsequently, utilizing low-cost vehicle sensor signals, joint simulations are conducted on the CarSim-Simulink platform to estimate vehicle state parameters. The results demonstrate that in terms of estimation accuracy and robustness in non-Gaussian noise scenarios, the proposed IMM-MCCKF filter consistently outperforms the MCCKF and CKF algorithms.

TV-based phase retrieval for speckle coded diffraction imaging

Speckle coded diffraction imaging (SCDI) has emerged as a new and developing lensless imaging method, which provides an effective imaging method for dense and connected objects. The conventional alternating-projection-based phase retrieval algorithm for SCDI relies on phase constraints between multiple diffraction images, and its disadvantage is that it often necessitates a large number of measurements to ensure high-quality reconstruction. In order to reduce the measurements, we propose to regularize the non-convex phase retrieval with total variation (TV)–based prior, and thus construct the TV-based cost function for SCDI. The alternating direction method is used to solve the nonlinear cost function, and recover the object and unknown speckle illumination. As both simulations and experiments demonstrate, the proposed TV-based reconstruction algorithm can recover the complex object and the unknown speckle pattern with high fidelity using 16 measurements, compared with hundreds of measurements used for AP-based algorithm.

A heuristic-based benders decomposition for the hybrid relief distribution network minimizing deprivation cost of vulnerable areas

PurposeThe study aims to optimize truck routes by minimizing social and economic costs. It introduces a strategy involving diverse drones and their potential for reusing at DNs based on flight range. In HTDRP-DC, trucks can select and transport various drones to LDs to reduce deprivation time. This study estimates the nonlinear deprivation cost function using a linear two-piece-wise function, leading to MILP formulations. A heuristic-based Benders Decomposition approach is implemented to address medium and large instances. Valid inequalities and a heuristic method enhance convergence boundaries, ensuring an efficient solution methodology.Design/methodology/approachResearch has yet to address critical factors in disaster logistics: minimizing the social and economic costs simultaneously and using drones in relief distribution; deprivation as a social cost measures the human suffering from a shortage of relief supplies. The proposed hybrid truck-drone routing problem minimizing deprivation cost (HTDRP-DC) involves distributing relief supplies to dispersed demand nodes with undamaged (LDs) or damaged (DNs) access roads, utilizing multiple trucks and diverse drones. A Benders Decomposition approach is enhanced by accelerating techniques.FindingsIncorporating deprivation and economic costs results in selecting optimal routes, effectively reducing the time required to assist affected areas. Additionally, employing various drone types and their reuse in damaged nodes reduces deprivation time and associated deprivation costs. The study employs valid inequalities and the heuristic method to solve the master problem, substantially reducing computational time and iterations compared to GAMS and classical Benders Decomposition Algorithm. The proposed heuristic-based Benders Decomposition approach is applied to a disaster in Tehran, demonstrating efficient solutions for the HTDRP-DC regarding computational time and convergence rate.Originality/valueCurrent research introduces an HTDRP-DC problem that addresses minimizing deprivation costs considering the vehicle’s arrival time as the deprivation time, offering a unique solution to optimize route selection in relief distribution. Furthermore, integrating heuristic methods and valid inequalities into the Benders Decomposition approach enhances its effectiveness in solving complex routing challenges in disaster scenarios.

New exact and heuristic algorithms for general production and delivery integration

This study considers a general production and delivery integration problem, commonly faced by a manufacturer that adopts make-to-order and commit-to-delivery business strategies. In the problem, the manufacturer determines acceptance or rejection of customers, produces products for accepted customers, and cooperates with third-party logistics providers who offer multiple shipping modes chosen by the manufacturer to deliver the finished products to customers. To better reflect the practical needs, this problem takes into account nonlinear production cost functions, nonlinear earliness and tardiness penalty functions, and nonlinear shipping cost functions of both shipping time and shipping quantity. The problem is to determine an integrated customer acceptance, production, and delivery plan by minimizing the total cost of production, shipping and inventory holding, and the total penalty of rejection, earliness, and tardiness. We investigate two variants of the problem where splittable delivery for the orders from customers is allowed and where splittable delivery is not allowed. For both the variants, we develop exact algorithms which achieve pseudo-polynomial running time in some practical situations, and design column generation-based heuristic algorithms to find near-optimal solutions efficiently. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions for the instances generated randomly, with average optimality gap less than 4% in a reasonable running time.

Wind Power Bidding Based on an Ensemble Differential Evolution Algorithm with a Problem-Specific Constraint-Handling Technique

The intermittent nature of wind power generation induces great challenges for power bidding in the electricity market. The deployment of battery energy storage can improve flexibility for power bidding. This paper investigates an optimal power bidding strategy for a wind–storage hybrid power plant in the day-ahead electricity market. To handle the challenges of the uncertainties of wind power generation and electricity prices, the optimal bidding problem is formulated as a risk-aware scenario-based stochastic programming, in which a number of scenarios are generated using a copula-based approach to represent the uncertainties. These scenarios consider the temporal correlation of wind power generation and electricity prices between consecutive time intervals. In the stochastic programming, a more practical but nonlinear battery operation cost function is considered, which leads to a nonlinear constrained optimization problem. To solve the nonlinear constrained optimization problem, an ensemble differential evolution (EDE) algorithm is proposed, which makes use of the merits of an ensemble of mutant operators to generate mutant vectors. Moreover, a problem-specific constraint-handling technique is developed. To validate the effectiveness of the proposed EDE algorithm, it is compared with state-of-the-art DE-based algorithms for constrained optimization problems, including a constrained composite DE (C2oDE) algorithm and a novel DE (NDE) algorithm. The experimental results demonstrate that the EDE algorithm is much more reliable and much faster in finding a better bidding strategy against benchmarking algorithms. More precisely, the average values of the success rate are 0.893, 0.667, and 0.96 for C2oDE, NDE, and EDE, respectively. Compared to C2oDE and NDE, the average value of the mean number of function evaluations to succeed with EDE is reduced by 76% and 59%, respectively.

Two efficient logarithmic formulations to solve nonconvex economic dispatch

To solve economic dispatch (ED) with nonconvex nonlinear generation cost functions, this paper adopts a global optimization technique where piecewise linear approximation (PLA) functions replace the nonlinear functions. However, a problem with this technique is that the PLA model requires incorporating many discrete variables into the optimization model, which may render the model computationally expensive. This paper presents two efficient representation techniques of the PLAs, which scale logarithmically, including binary zig-zag (ZZB) and general integer zig-zag (ZZI). We replace the nonconvex cost functions in the ED with their PLAs and obtain an alternative ED formulation where two logarithmic techniques model the PLAs. Then, one can efficiently solve the alternative ED model with the standard branch-and-cut/bound-based algorithms to the desired optimality gap. To verify the techniques’ efficacy, we consider test systems having 13, 38, 40, 80, and 160 units. The numerical evaluations show that the logarithmic techniques presented can yield high-quality optimal solutions in less than 2 seconds in the considered cases, illustrating the techniques’ efficiency.

Leaf properties estimation enhancement over heterogeneous vegetation by correcting for terrestrial laser scanning beam divergence effect

The need for an accurate description of forest structure is increased as it is a key for monitoring carbon storage, energy, and mass exchange, and different ecosystem functions. The leaf area index (LAI), the leaf area density (ul), and the leaf inclination distribution function (LIDF) are regarded as important and critical keys allowing the characterization of the forest structure. The dependency between these properties and the heterogeneity of the forest makes their estimation challenging and delicate. In this context, despite the expanding body of works reporting forest structure properties retrieval using infinitesimal footprint size terrestrial LiDAR system (TLS) data, there seem to be few works evaluating the influence of the TLS beam divergence effect (i.e. its size increase with distance from the sensor), on the estimation accuracy, even though the influence is not negligible. In this study, we aim to jointly estimate LAI/ul and LIDF using non-infinitesimal footprint size TLS data based on forward/inverse radiative transfer (RT) modeling. Our approach assumes a uniform distribution of azimuth angles enabling us to attain valuable insights into inclination angles and leaf area density while simplifying our computational efforts. The forward modeling allows an understanding of the interaction between vegetation structure properties and TLS light beams, while the inversion allows retrieving the properties given the TLS data. The inversion technique is based on the maximum likelihood estimator (MLE). Our problem turns out to be a non-linear and high-dimensional cost function to be optimized. To tackle this complexity, the global optimization technique, the shuffled complex evolution (SCE-UA), is adapted to find the globally optimal solution. Our developed approach is validated with simulated and actual forest TLS point clouds acquired from Estonian Pine, Birch, and Spruce stands. Our findings using simulated data prove that our estimates are in agreement with the actual ul and LIDF values with (MAEul∈0.00120.0043) and (RMSEul∈0.01370.0224). In the actual case, RMSELAI for Pine, Birch and Spruce stands are 0.1066, 0.014, and 0.070, respectively. In all cases, our approach outperforms state-of-the-art techniques.

Blind CFO estimation based on weighted subspace fitting criterion with fuzzy adaptive gravitational search algorithm

AbstractThis paper deals with the blind carrier frequency offset (CFO) estimation based on weighted subspace fitting (WSF) criterion with fuzzy adaptive gravitational search algorithm (GSA) for the interleaved orthogonal frequency-division multiplexing access (OFDMA) uplink system. For the CFO estimation problem, it is well known that the WSF has superior statistical characteristics and better estimation performance. However, the type of CFO estimation must pass through the high-dimensional space problem. Optimizing complex nonlinear multimodal functions requires a large computational load, which is difficult and not easy to maximize or minimize nonlinear cost functions in large parameter spaces. This paper firstly presents swarm intelligence (SI) optimization algorithms such as GSA, particle swarm optimization (PSO), and hybrid PSO and GSA (PSOGSA) to improve estimation accuracy and reduce the computational load of search. At the same time, this paper also integrates a fuzzy inference system to WSF-GSA to dynamically adjust the gravitational constant, which can not only reduce the searching computational load, but also improve the performance of GSA in the global optimization and solution accuracy. Finally, several simulation results are provided for illustrating the effectiveness of the proposed estimator.

Nonlinear-cost random walk: Exact statistics of the distance covered for fixed budget.

We consider the nonlinear-cost random-walk model in discrete time introduced in Phys. Rev. Lett. 130, 237102 (2023)10.1103/PhysRevLett.130.237102, where a fee is charged for each jump of the walker. The nonlinear cost function is such that slow or short jumps incur a flat fee, while for fast or long jumps the cost is proportional to the distance covered. In this paper we compute analytically the average and variance of the distance covered in n steps when the total budget C is fixed, as well as the statistics of the number of long or short jumps in a trajectory of length n, for the exponential jump distribution. These observables exhibit a very rich and nonmonotonic scaling behavior as a function of the variable C/n, which is traced back to the makeup of a typical trajectory in terms of long or short jumps, and the resulting entropy thereof. As a by-product, we compute the asymptotic behavior of ratios of Kummer hypergeometric functions when both the first and last arguments are large. All our analytical results are corroborated by numerical simulations.

Nonlinear metaheuristic cost optimization and ANFIS computing of feedback retrial queue with two dependent phases of service under Bernoulli working vacation

Today, with real-life problems, modeling is a primary step in organizing, analyzing and optimizing them. Queueing theory is a particular approach used to model this category of issues. Space constraints, feedback, service dependency, etc. are often inseparable from the issues they create. In light of this objective, this research presents a model and analysis of the steady-state behavior of an [Formula: see text] feedback retrial queue with two dependent phases of service under a Bernoulli vacation policy. The service times for the two stages are often independent in normal queueing frameworks. We presume that they are dependent random variables in this case. Indeed, this dependence is one-way (i.e., the service time of the second phase has no effect on the service time of the first phase). Yet, the first phase service time has an impact on the second phase service time. In order to determine the steady-state probabilities and probability-generating functions (PGF) for the different states, the supplementary variable technique (SVT) was utilized. Furthermore, a broad range of performance metrics had been established. The generated metrics are then envisioned and validated with the aid of graphs and tables. Additionally, a nonlinear cost function is constructed, which is subsequently minimized by distinct approaches like particle swarm optimization (PSO), artificial bee colony (ABC) and genetic algorithm (GA). Furthermore, we used certain figures to examine the convergence of these optimization methods. Finally, validation outcomes are compared with neuro-fuzzy results generated with the “adaptive neuro-fuzzy inference system” (ANFIS).

Levenberg-Marquardt Algorithm Applied for Foggy Image Enhancement

In this paper, we introduce a novel Model Based Foggy Image Enhancement using Levenberg-Marquardt non-linear estimation (MBFIELM). It presents a solution for enhancing image quality that has been compromised by homogeneous fog. Given an observation set represented by a foggy image, it is desired to estimate an analytical function dependent on adjustable variables that best cross the data in order to approximate them. A cost function is used to measure how the estimated function fits the observation set. Here, we use the Levenberg-Marquardt algorithm, a combination of the Gradient descent and the Gauss-Newton method, to optimize the non-linear cost function. An inverse transformation will result in an enhanced image. Both visual assessments and quantitative assessments, the latter utilizing a quality defogged image measure introduced by Liu et al. (2020), are highlighted in the experimental results section. The efficacy of MBFIELM is substantiated by metrics comparable to those of recognized algorithms like Artificial Multiple Exposure Fusion (AMEF), DehazeNet (a trainable end-to-end system), and Dark Channel Prior (DCP). There exist instances where the performance indices of AMEF exceed those of our model, yet there are situations where MBFIELM asserts superiority, outperforming these standard-bearers in algorithmic efficacy.

Economic dispatch optimization considering operation cost and environmental constraints using the HBMO method

Increasing electrical energy use has led to the development of power systems so nowadays some power systems have been expanded into geographical regions whose total size is equal to a continent. In line with this development, which has several benefits, like other fields, it has been discussed new issues in the power system field such as economic distribution. Over several decades and with the growing consumption of electrical energy, its supply systems have increased so that today the load distribution among energy production units with the lowest cost has become one of the most widely and complicated issues of power system utilization. In this paper, a mutant version of the honey bee mating optimization (HBMO) algorithm based on collective intelligence is proposed for power system economic-emission dispatch (E-ED). The proposed algorithm has been used to solve the E-ED problem with nonlinear cost functions including plant-induced limitations such as steam inlet valves, balancing the production and consumption in the system, restricted zones, production limits, and increasing and decreasing rates. Moreover, considering production cost functions, environmental pollution, and losses, the load distribution issue, which is one of the most important issues in today’s system, has been investigated. In this paper, we attempt to increase the efficiency and balance of the standard algorithm for local and final searches using the adaptive nonlinear system. In the proposed algorithm, the final optimized answer is considered a criterion to be stopped the program optimization. In addition, to improve the search for the final answer, improvements have been made in the local and final search structure. The simulation results show that the efficiency of this algorithm in solving the problem of economic load distribution is better than other algorithms.

Integrated production and transportation scheduling problem under nonlinear cost structures

We consider an integrated production and transportation scheduling problem arising in several make-to-order settings, where customer orders have release times and pre-specified delivery time windows. These orders are first processed in a plant and, thereafter, delivered to their customer sites by transporters (e.g., freight trains, ships, or air flights) with fixed departure times and nonlinear transportation cost functions. If the processing of an order is completed but not immediately delivered, it will be stored temporarily, incurring inventory holding costs. The objective is finding an integrated schedule for production and transportation such that the total cost of inventory holding and transportation is minimized. In this study, we consider the following two cases: one where partial delivery is not allowed, and the other where partial delivery is allowed. For each case, we propose an exact algorithm to find optimal solutions for small-scale instances, and a heuristic algorithm to find near-optimal solutions for large-scale instances. For the randomly generated test instances, the computational results reveal that the exact algorithms significantly outperform a commercial optimization solver in terms of the computational times and the number of instances solved within a specified time limit, and the heuristic algorithms are capable of generating near-optimal solutions within a reasonable computational time. Finally, we incorporate considerations of sequence-dependent setup time into the problem and apply the approaches for designing the algorithms to address the more general problem.

Cost of Diffusion: Nonlinearity and Giant Fluctuations.

We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model-inspired by the way taxi meters work-exhibits a very rich behavior. The cost for trajectories of equal length and equal duration exhibits giant fluctuations at a critical value of the scaled distance traveled. Furthermore, the full distribution of the cost until the target is reached exhibits an interesting "freezing" transition in the large-deviation regime. All the analytical results are corroborated by numerical simulations. Our results also apply to elastic systems near the depinning transition, when driven by a random force.

Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut

Prepositioning of relief supplies has been widely addressed to cover the demands of humanitarian emergencies. However, cost inefficiency, item type limitation, and damage risk make solely relying on prepositioning unrealistic. We develop two-stage stochastic models that incorporate prepositioning, physical capacity reservation, and production capacity reservation for reactive procurement. As an alternative to the traditional physical capacity reservation, the production capacity reservation is inspired by the practice of the automotive industry, garment industry, etc. for manufacturing personal protective equipment during the pandemic. Our models minimize the supply-side monetary costs and the demand-side social impacts, i.e., deprivation costs. The discretized deprivation cost function is introduced to handle the nonlinear deprivation cost function. The hierarchical nature of our stochastic models motivates us to utilize the logic-based Benders decomposition (LBBD). Our Benders master problem contains one set of nonbinary integer variables for prepositioning inventory and another set of continuous variables for estimating the second-stage costs, which differs from the existing LBBD works that typically contain binary and continuous variables in the master problem. Hence, a new type of logic-based Benders optimality cut, namely logic-based subgradient cut, is first introduced. To compute the cutting coefficients efficiently, heuristics that can lead to almost optimal solutions is developed. We also develop warm-start cutting planes, namely wait-and-see cuts and expected-value cuts, to help with better upper bounds and lower bounds. Extensive numerical results followed by a case study validate the efficiency of the solution method, the value of incorporating stochasticity, and the superiority of the capacity reservation.

A simplified economic model predictive control for a gas lifted oil production network based on modifier adaptation

We propose a novel simplified economic model predictive controller (EMPC) for supervisory control of an offshore petroleum production network composed of two wells, a riser, and a separator. The proposed controller uses a gradient-and-modifier-based methodology to mimic a nonlinear EMPC (it considers a nonlinear process model and cost function), while only solving quadratic programming. We alter the modifier adaptation to depend on an estimator and employ slack variables to improve feasibility. Tips for appropriate design, to improve stability and robustness, are presented. Since the tested facility is subject to multiple disturbances, we also use a regulatory controller to stabilize the system. Finally, we compare our method to a linear EMPC and self-optimizing control in various scenarios considering disturbances, noise, and model inconsistencies. The proposed controller always tends towards the economic optimal point, presenting similar nominal performance as the others advanced controllers and better robustness.