Additive Cost Function Research Articles

Minimum dose walking path planning in a nuclear radiation environment based on a modified A* algorithm

An additional cost function for the case with turning points is introduced to the A* algorithm, which can reduce unnecessary turning points. Therefore, the modified A* algorithm consists of three parts: the actual cost function, the estimated cost function, and the turning point cost function. The three functions are normalized so that they can be compared without dimensionality to obtain the optimal path planning in radiation environments. Based on the Geant4 Monte Carlo program, the radiation field model is established and the dose distribution data is obtained. We assign weights to the functions to smooth out the three different cost functions and avoid scenarios in which one function is much greater than the other two. In a small-scale simulation experiment, the path generated by the modified algorithm is consistent with that calculated by the traditional A* method, but the number of turning points is significantly reduced. The modified algorithm takes less time and the cumulative dose on the path is slightly lower. Modified A*, traditional A* and PRM algorithms are used for path planning and comparison in the complex radiation environment of multiple γ sources. The PRM algorithm takes the least computation time to search the path, but the cumulative exposure dose is random. For the path planning of multi-task operation in a radiation field, the cumulative radiation dose of the path planned by the modified A* algorithm is equivalent to that of the traditional A* algorithm, but the modified A* algorithm significantly reduces the number of turning points, the calculation time is significantly shortened, and the execution efficiency is improved. The modified A* algorithm can be used as a reference for path planning for workers in radiation workplaces.

Almost Envy-Free Allocations of Indivisible Goods or Chores with Entitlements

We here address the problem of fairly allocating indivisible goods or chores to n agents with weights that define their entitlement to the set of indivisible resources. Stemming from well-studied fairness concepts such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) for agents with equal entitlements, we present, in this study, the first set of impossibility results alongside algorithmic guarantees for fairness among agents with unequal entitlements. Within this paper, we expand the concept of envy-freeness up to any good or chore to the weighted context (WEFX and XWEF respectively), demonstrating that these allocations are not guaranteed to exist for two or three agents. Despite these negative results, we develop a WEFX procedure for two agents with integer weights, and furthermore, we devise an approximate WEFX procedure for two agents with normalized weights. We further present a polynomial-time algorithm that guarantees a weighted envy-free allocation up to one chore (1WEF) for any number of agents with additive cost functions. Our work underscores the heightened complexity of the weighted fair division problem when compared to its unweighted counterpart.

Robust Approximate Dynamic Programming for Nonlinear Systems With Both Model Error and External Disturbance.

Model error and external disturbance have been separately addressed by optimizing the definite H∞ performance in standard linear H∞ control problems. However, the concurrent handling of both introduces uncertainty and nonconvexity into the H∞ performance, posing a huge challenge for solving nonlinear problems. This article introduces an additional cost function in the augmented Hamilton-Jacobi-Isaacs (HJI) equation of zero-sum games to simultaneously manage the model error and external disturbance in nonlinear robust performance problems. For satisfying the Hamilton-Jacobi inequality in nonlinear robust control theory under all considered model errors, the relationship between the additional cost function and model uncertainty is revealed. A critic online learning algorithm, applying Lyapunov stabilizing terms and historical states to reinforce training stability and achieve persistent learning, is proposed to approximate the solution of the augmented HJI equation. By constructing a joint Lyapunov candidate about the critic weight and system state, both stability and convergence are proved by the second method of Lyapunov. Theoretical results also show that introducing historical data reduces the ultimate bounds of system state and critic error. Three numerical examples are conducted to demonstrate the effectiveness of the proposed method.

Individual subject evaluated difficulty of adjustable mazes generated using quantum annealing

In this study, the maze generation using quantum annealing is proposed. We reformulate a standard algorithm to generate a maze into a specific form of a quadratic unconstrained binary optimization problem suitable for the input of the quantum annealer. To generate more difficulty mazes, we introduce an additional cost function Qupdate to increase the difficulty. The difficulty of the mazes was evaluated by the time to solve the maze of 12 human subjects. To check the efficiency of our scheme to create the maze, we investigated the time-to-solution of a quantum processing unit, classical computer, and hybrid solver. The results show that Qupdate generates difficult mazes tailored to the individual. Furthermore, it show that the quantum processing unit is more efficient at generating mazes than other solvers. Finally, we also present applications how our results could be used in the future.

Approximately EFX allocations for indivisible chores

In this paper, we study how to fairly allocate a set of m indivisible chores to a group of n agents, each of which has a general additive cost function on the items. Since envy-free (EF) allocations are not guaranteed to exist, we consider the notion of envy-freeness up to any item (EFX). In contrast to the fruitful results regarding the (approximation of) EFX allocations for goods, very little is known for the allocation of chores. Prior to our work, for the allocation of chores, it is known that EFX allocations always exist for two agents or general number of agents with identical ordering cost functions. For general instances, no non-trivial approximation result regarding EFX allocation is known. In this paper, we make progress in this direction by providing several polynomial time algorithms for the computation of EFX and approximately EFX allocations. We show that for three agents we can always compute a (2+6)-approximation of EFX allocation. For n≥4 agents, our algorithm always computes a (3n2−n)-approximation. We also study the bi-valued instances, in which agents have at most two cost values on the chores. For three agents, we provide an algorithm for the computation of EFX allocations. For n≥4 agents, we present algorithms for the computation of partial EFX allocations with at most (n−1) unallocated items; and (n−1)-approximation of EFX allocations.

Constrained stochastic differential games with Markovian switchings and additive structure: The total expected payoff

The main objective of this work is to give conditions for the existence of Nash equilibria for a nonzero-sum constrained stochastic differential game with additive structure and Markovian switchings. In this type of game, each player is interested only in maximizing their finite-horizon total payoff when an additional cost function of the same type is required to be dominated above by another function (in particular, by a constant). The dynamic system for this game is controlled by two players and evolves according to a Markov-modulated diffusion (also known as switching diffusions or piecewise diffusion or diffusion with Markovian switchings). Given that, each player has to solve an optimization problem with constraints. The existence of a Nash equilibrium is thus proved using the Lagrange multipliers approach combined with standard dynamic programming arguments. The Lagrange approach allows the transformation of a constrained game into an unconstrained game. Therefore, this work gives conditions under which a Nash equilibrium for the unconstrained stochastic differential game is also a Nash equilibrium for the corresponding nonzero-sum constrained stochastic differential game. The theory developed here is illustrated by a pollution accumulation problem with two players. Therein, the evolution is governed by a linear stochastic differential equation with Markovian switching, and the decay pollution rate depends on a Markov chain.

Fairness criteria for allocating indivisible chores: connections and efficiencies

We study several fairness notions in allocating indivisible chores (i.e., items with disutilities) to agents who have additive and submodular cost functions. The fairness criteria we are concerned with are envy-free up to any item, envy-free up to one item, maximin share (MMS), and pairwise maximin share (PMMS), which are proposed as relaxations of envy-freeness in the setting of additive cost functions. For allocations under each fairness criterion, we establish their approximation guarantee for other fairness criteria. Under the additive setting, our results show strong connections between these fairness criteria and, at the same time, reveal intrinsic differences between goods allocation and chores allocation. However, such strong relationships cannot be inherited by the submodular setting, under which PMMS and MMS are no longer relaxations of envy-freeness and, even worse, few non-trivial guarantees exist. We also investigate efficiency loss under these fairness constraints and establish their prices of fairness.

Real-world implementation and evaluation of a Model Predictive Control framework in an office space

In this work, Model Predictive Control (MPC) is experimentally implemented on a Heating, Ventilation and Air Conditioning (HVAC) system of a large-scale office space. As controller model, a physics-based Modelica building model is calibrated based on historic data pursuing an iterative, nonlinear optimization approach. For the calibration period with a horizon of seven weeks, the calibrated model exhibits a high model accuracy with a Root Mean Square Error (RMSE) of 0.49 °C between the measured and estimated room temperature. The MPC toolchain includes modules for state estimation and forecasts of disturbances quantities (such as outdoor temperature, solar radiation including calculation of the direct and diffuse fraction, supply temperatures and occupancy). The MPC execution comprises the operation of heating based on radiators and floor heating (via regulation of valve openings) as well as shading of three Venetian blind systems (via regulation of vertical position and slat inclination angle). The experiment is conducted during a heating period with a duration of three weeks from October 21 to November 11, 2022. The heating actuators are controlled considering their typical dynamics and take into account the night setback during unoccupied office periods. User acceptance of the automated shading control is included through additional cost function terms for the shading operation. The field test reveals the predictive control capabilities of the proposed MPC toolchain in a real-life scenario, demonstrating energy-efficient building operation and total average discomfort of 0.53 Kh/d. The MPC formulation provides flexibility regarding adjustability of the control towards energy efficiency, thermal comfort, daylight transmission and non-oscillating shading control. Finally, the disturbance forecast accuracies for outdoor temperature and the solar radiation quantities are evaluated and the MPC control performance is compared against a conventional control approach.

Double voltage vector model predictive control for grid-connected cascade H-bridge multilevel inverter with fixed switching frequency

Model predictive control (MPC) is an outstanding control method which can achieve superior dynamic response, nonlinear control and multi-objective collaborative control. However, because of unfixed switching frequency, the harmonic spectrum of the output current is dispersed, which would make it difficult to design the output filter. In this work, a double voltage vector model predictive control (DVV-MPC) algorithm for grid-connected cascade H-bridge (CHB) multilevel inverter is presented. The algorithm not only has the advantages of MPC but also produces fixed the switching frequency of the inverter. It is realized by a modulation stage with two adjacent voltage vectors in one switching cycle. And the duty cycle of the associated voltage level is obtained by minimizing an additional cost function. This method is suitable for the cascades of n cells inverter. For reducing the computation burden and eliminating the computation delay, adjacent regions prediction method and time-delay compensation method are applied to the inverter. Finally, in this paper, the proposed strategy is applied to a single-phase grid-connected 7-level CHB inverter. Simulation and experiment are executed to show the advantages of the proposed control algorithm in dynamic state and steady state.

Extended Ising Machine with Additional Non-quadratic Cost Functions

We have developed a method to extend the functionality of the Ising machine, which currently has an energy function limited to a binary-quadratic form. The proposed method utilizes auxiliary variables dependent on the decision variables of the problem to be solved so that it can be accelerated by hardware parallel processing. Auxiliary variables add third-order or higher terms or rectified linear unit-type nonlinear functions to the binary-quadratic energy function of the Ising machine, modifying the value of the energy difference resulting from the reversal of the decision variable. To enable parallel computation, the computation of the energy change uses information that can be accessed locally by the decision neurons. We confirmed that the proposed method works for the 0/1 linear knapsack problem, the quadratic knapsack problem, the 3-SAT problem, and the random 3-XORST problem.

Fair and Efficient Allocations of Chores under Bivalued Preferences

We study the problem of fair and efficient allocation of a set of indivisible chores to agents with additive cost functions. We consider the popular fairness notion of envy-freeness up to one good (EF1) with the efficiency notion of Pareto-optimality (PO). While it is known that EF1+PO allocations exists and can be computed in pseudo-polynomial time in the case of goods, the same problem is open for chores. Our first result is a strongly polynomial-time algorithm for computing an EF1+PO allocation for bivalued instances, where agents have (at most) two disutility values for the chores. To the best of our knowledge, this is the first non-trivial class of chores to admit an EF1+PO allocation and an efficient algorithm for its computation. We also study the problem of computing an envy-free (EF) and PO allocation for the case of divisible chores. While the existence of EF+PO allocation is known via competitive equilibrium with equal incomes, its efficient computation is open. Our second result shows that for bivalued instances, an EF+PO allocation can be computed in strongly polynomial-time.

Fine scale reconstruction (VIC#) by implementing additional constraints and coarse-grid approximation into VIC+\u2009

This study proposes a method that complements Vortex-In-Cell plus (VIC+) (Schneiders and Scarano, Exp Fluids 57:139, 2016), a data assimilation technique that reconstructs a dense flow field from sparse particle tracks. Here, the focus is on the treatment of boundary conditions. In the VIC+ method, the choice of boundary conditions significantly affects a large part of the inner domain through their role as Dirichlet boundary conditions of the Poisson equations. By nature, there are particle tracks on one side of the boundaries, and often, due to experimental limitations, the track density is low, just close to the boundaries. This lack of data near the boundaries leads to a poor iterative update of the boundary condition for VIC+. Overall, the VIC+ method tends to be sensitive about the specific choice of the initial conditions, including the inner domain and the boundaries. Without prior flow information, a large padded volume has been proposed to achieve stable and reliable convergence, at the cost of a large number of additional unknowns that need to be optimized. The present method pursues the following concepts to resolve the above issues: use of the smallest possible padding size, reconstruction starting with “all zero” initial conditions, and progressive correction of the boundary conditions by considering the continuity law and the Navier–Stokes equation. These physical laws are incorporated as additional terms in the cost function, which so far only contained the disparity between PTV measurements and the VIC+ reconstruction. Here, the Navier–Stokes equation allows an instantaneous pressure field to be optimized simultaneously with the velocity and acceleration fields. Moreover, the scale parameters in VIC+ are redefined to be directly computed from PTV measurement instead of using the initial condition, and new scaling factors for the additional cost function terms are introduced. A coarse-grid approximation is employed in order to both improve reconstruction stability and save computation time. It provides a subsequent finer-grid with its low-resolution result as an initial condition while the interrogation volume slightly shrinks. A numerical assessment is conducted using synthetic PTV data generated from the direct numerical simulation data of forced isotropic turbulence from the Johns Hopkins Turbulence Database. Improved reconstructions, especially near the volume boundary, are achieved while the virtues of VIC+ are preserved. As an experimental assessment, the existing data from a time-resolved water jet is processed. Two reconstruction domains with different sizes are considered to compare the boundary of the smaller domain with the inside of the larger one. Visible enhancements near the boundary of the smaller domain are observed for this new approach in time-varying flow fields despite the limited input from PTV data.Graphical abstract

Dynamic Optimization Approach to Estimate Kinetic Parameters of Monod-Based Microalgae Growth Models.

The biomass concentration of microalgae growth in photobioreactor was predicted using the Monod-based growth models. Kinetic parameters such as maximum specific growth rate and saturation constant of light intensity were evaluated by nonlinear least squares methods that focused on minimizing the sum of squares error (SSE). The importance of good initial guess for the nonlinear least squares method was also discussed. The optimal control problem of the microalgae growth model was determined based on parameter sensitivity. Therefore, a dynamic optimization approach was used where an optimal input design method was formulated to obtain a control function of a problem. The dynamic state equations, additional state equations, cost function, and Hamiltonian function were used to establish a control function of microalgae growth in a photobioreactor. Hence, the biomass production of microalgae can be predicted using numerical methods such as the Taylor series method.

Data-Selective Least Squares Methods for Elliptic Localization With NLOS Mitigation

In this letter, we consider the problem of 2-D elliptic localization, where multiple spatially separated sensors, including the transmitters and receivers, are exploited to locate the signal reflecting/relaying target in the mixed line-of-sight/nonline-of-sight (NLOS) environments. We begin by revisiting a plain closed-form linear least squares (LS) solution. As it is vulnerable to the existence of erroneous time-sum-of-arrival (TSOA) measurements under the NLOS conditions, we then devise two new data-selective LS methods, by which the outliers can be identified and mitigated and a higher level of resistance to the NLOS bias errors can be provided. To conduct data selection, the first algorithm combines the use of the traditional linear LS estimator and an additional cost function, whereas the second relies on the parameterization of the TSOA-defined ellipses and follows a nonlinear LS estimation criterion. Based on the simulations, we demonstrate the effectiveness of the proposed methods in NLOS error mitigation at acceptable computational costs.

An Improved Finite-Control-Set Model Predictive Flux Control for Asymmetrical Six-Phase PMSMs With a Novel Duty-Cycle Regulation Strategy

This work presents an improved finite-control-set model predictive flux control (FCS-MPFC) for asymmetrical six-phase permanent magnet synchronous machine (ASPMSM) with a novel duty-cycle regulation strategy. Firstly, virtual vector concept is adopted to suppress harmonic currents without additional cost function and the corresponding weighting factor. Then, 12 virtual vectors with higher voltage utilization are developed. Meanwhile, for the sake of strengthening steady-state performance, a novel duty-cycle regulation strategy incorporating the well-known Lagrange multiplier method is proposed. In this strategy, the reconfigurable set of voltage vectors (SVV), which consists of an active and a null virtual vector, can be determined without second modification, hence highly mitigating additional computation burden. Furthermore, in order to realize the purpose of unified switching frequency, the SVVs are implemented in terms of regular rather than irregular PWM signal pattern. Finally, experimental results prove the effectiveness of the proposed method.

Slide-Drilling Guidance System Optimizes Directional Drilling Path

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 194096, “Slide-Drilling Guidance System for Directional-Drilling Path Optimization,” by Can Pehlivanturk and John D’Angelo, The University of Texas at Austin, and Dingzhou Cao, Anadarko, et al., prepared for the 2019 SPE/IADC International Drilling Conference and Exhibition, The Hague, 5–7 March. The paper has not been peer approved. The amount of uncertainty related to directional drilling makes accurate drilling challenging, leaving much to human know-how and interpretation. Additionally, few path-planning methods in the literature consider the directional steering tool being used. The formulation of the problem of optimization varies greatly between rotary steerable systems (RSS) and mud-motor configurations. Additional cost functions and constraints exist for mud-motor use, which significantly increases the complexity of the problem. A slide-drilling-guidance system is proposed to combat this issue and to help automate directional drilling. Introduction Despite the numerous technological advancements that made directional drilling a reality, directional drilling is still viewed more as an art than as a science. The drillstring and penetrated rock formations are complex systems whose interaction makes prediction and planning highly uncertain. Analytical, geometric approaches have sought to formulate the curvature of the well path in a way that eases the planning process and ensures smooth trajectories. The literature on directional drilling is rich in well-path-optimization methodologies based on operating constraints and well-path geometry. However, few of these methods seem to consider the tool used to generate the well path, and those that do typically use RSS because these yield better results from a technical perspective. Mud motors, however, are still used extensively because of cost effectiveness. The complete paper proposes a directional-drilling guidance system targeted at downhole motors and slide drilling to generate optimal well paths and associated slide-drilling instructions. Instead of a simplistic shortest-path approach, various cost functions aimed at maximizing the value of the well are considered. For wellbore-propagation prediction, a computationally efficient and accurate model is used. The proposed methodology is built into a software package and is being developed and implemented currently for use in the real-time drilling (RTD) system of an operator. The three main modules of the software are discussed in detail in the complete paper. The wellbore-propagation model predicts the evolution of the borehole and returns the predicted 3D path given the initial condition and a slide sheet. The fitness-evaluation module calculates the fitness of the 3D path using a cost function and returns a scalar value representing the overall value of the path. The genetic-algorithm solver generates candidate slide sheets and approaches an optimal slide sheet by iterating over generations. Software Implementation Graphical User Interface (GUI). The GUI serves as a tool to visualize the well under consideration and to study the optimization results and the effectiveness of the approach. The GUI is written in MATLAB and uses the Runtime environment. Here, the data for the planned path and the actual survey data are loaded. The planned path and the surveyed path (up to the time for which such data are available) are displayed.

Improved Deadbeat FC-MPC Based on the Discrete Space Vector Modulation Method with Efficient Computation for a Grid-Connected Three-Level Inverter System

The utilization of three-level T-type (3L T-type) inverters in finite set-model predictive control (FS-MPC) of grid-connected systems yielded good performance in terms of current ripples and total harmonic distortions. To further improve the system’s performance, discrete space vector modulation (DSVM) was utilized to synthesize a higher number of virtual voltage vectors. A deadbeat control (DBC) method was used to alleviate the computational burden and provide the optimum voltage vector selection. However, 3L inverters are known to suffer from voltage deviation, owing to the imbalance of the neutral-point voltage. We have proposed a simplified control strategy for balancing the neutral point in the FS-MPC with DSVM and DBC of grid-connected systems, not requiring a weighting factor or additional cost function calculation. The effectiveness of the proposed method was validated using simulation and experiment results. Our experimental results show that the execution time of the proposed algorithm was significantly reduced, while its current quality performance was not affected.

Flight Phase Control Strategies for Airborne Wind Energy Systems

Traditional Danish concept wind turbines face many constraints when upscaling in order to access higher wind speeds, such as size, mechanical loading and weight. It is possible that some of these constraints could be circumvented through use of airborne wind energy systems (AWES).With research into AWES becoming more prominent, the topic of launching and landing the system must be analysed in detail. Currently several concepts are being pursued with differing launch and land technologies. For all systems it is likely that minimising launch and land cycles will be a key objective due to increased energy costs and hardware risk in these phases.This research focuses on a cross-wind ground-based generation system and discusses the problem of the launch and land policy with regards to the wind speed at operational height. The paper also discusses the use of an airborne powered loiter phase and a grounded waiting phase. A key consideration when analysing this problem is wind speed measurement uncertainty (including the degree of temporal averaging) and how to integrate this uncertainty into any launch & land policy.The present research concerns cost-benefit analysis with respect to generated and consumed energy cost functions for each flight phase. It is found that for any given AWES there will be an optimum airborne loiter time after which a system should be landed. This avoids landings due to short-duration low wind periods.This research will be followed up by further analysis of additional cost functions such as reliability and failure aspects associated with each of the above phases. Further research will also consider the impact of short term forecasting of various accuracy levels on the optimal control policy and performance of AWES.

Creation of Numerical Constants in Robust Gene Expression Programming

The problem of the creation of numerical constants has haunted the Genetic Programming (GP) community for a long time and is still considered one of the principal open research issues. Many problems tackled by GP include finding mathematical formulas, which often contain numerical constants. It is, however, a great challenge for GP to create highly accurate constants as their values are normally continuous, while GP is intrinsically suited for combinatorial optimization. The prevailing attempts to resolve this issue either employ separate real-valued local optimizers or special numeric mutations. While the former yield better accuracy than the latter, they add to implementation complexity and significantly increase computational cost. In this paper, we propose a special numeric crossover operator for use with Robust Gene Expression Programming (RGEP). RGEP is a type of genotype/phenotype evolutionary algorithm closely related to GP, but employing linear chromosomes. Using normalized least squares error as a fitness measure, we show that the proposed operator is significantly better in finding highly accurate solutions than the existing numeric mutation operators on several symbolic regression problems. Another two important advantages of the proposed operator are that it is extremely simple to implement, and it comes at no additional computational cost. The latter is true because the operator is integrated into an existing crossover operator and does not call for an additional cost function evaluation.

Similarity Domains Machine for Scale-Invariant and Sparse Shape Modeling.

We present an approach to extend the functionality and the use of kernel machines in image processing applications. We introduce a novel way to design spatial kernel machines with spatial properties and demonstrate how those newly introduced spatial properties enhance the possibilities of the use of kernel machines in image processing applications as a proof of concept. In this paper, we demonstrate four particular extensions: 1) how to model shapes efficiently with spatially computed kernel parameters in a geometrically scalable way; 2) how to visualize the kernel parameters precisely and intuitively on binary 2D shapes; 3) how to construct a one-class classifier from the binary classifier in a straightforward manner without re-training; and 4) how to use the computed kernel parameters for filtering. The existing literature on kernel machines mostly focuses on estimating the optimal kernel parameters via additional cost function(s). In this paper, instead of employing an additional cost function to estimate the kernel-related parameters, we investigate on an analytical solution to predict the actual kernel parameters locally and show how to build a spatial kernel machine with our analytical approach. Classical kernel machines do not perform well on precise shape modeling with a low number of support vectors as demonstrated in this paper. However, we demonstrate and visualize that our analytical approach provides a natural means to relate the kernel parameters to the 2D shapes for sparse shape modeling, where the shape boundary represents the decision boundary. For that, we incorporate the selected kernel function's geometric properties as an additional constraint into the classifier's optimization problem by defining an easy-to-explain and intuitive concept: similarity domains. In our experiments, we study and demonstrate how the resulting new kernel machine enhances the capabilities of the classical kernel machines with applications on shape modeling, (geometrically) scaling the non-linear decision boundary at various scales and precise visualization of the kernel parameters in 2D images.