General Cost Functions Research Articles

Cognitive dissonance and introversion effects on opinion dynamics and echo chamber formation

Bounded confidence models (BCM) are extensively used to model continuous opinion dynamics in social networks. Typically, these models are analysed on static networks where edges do not vary over time. Following in the footsteps of adaptive voter models, further research has considered BCMs in the setting where agents are able to dynamically adjust their edges, which subsequently feedback into the opinion dynamics of the network. Several methods of updating connections have been proposed ranging from random rewiring to more sophisticated approaches based on concordant edges, homophily and cognitive dissonance. We present a modified form of the bounded confidence model, termed the selfish agent opinion (SAO) model, where connection updates are evaluated using a general cost function. Agents in the SAO model maintain two classes of relationships, friends and acquaintances, based on which they update their opinions and edges to optimise a payoff function that may include multiple social factors. This paper explores the effects, which we describe as “cognitive dissonance” and “introversion” that attempt to mimic postulated behaviours associated with the social concepts of the same name, on social network and opinion dynamics. We find that the SAO model naturally produces echo chambers for social networks with increased sensitivity to cognitive dissonance, whilst introversion produces high levels of fragmentation and low opinion mobility. Additionally, the effect of tolerant agents and inquisitive social encounters is investigated. It is found that both the presence of very small numbers of tolerant agents and inquisitive encounters are able to strongly promote consensus formation.

Optimal Salesforce Compensation with General Demand and Operational Considerations

Problem definition: We investigate the optimal salesforce compensation scheme in the context of private information and unobservable actions, considering common operational factors encountered in practice, including inventory costs, contractible versus censored demand information, and controlled versus delegated ordering. Methodology/results: Based on an agency model with general demand and cost functions, we derive optimality conditions for implementable contracts that can achieve the second-best outcome in all scenarios. The contracts are in the forms of a menu with linear compensation for demand or sales, incorporating inventory costs. Moreover, the contracts feature adjustments in compensation corresponding to the ordering level if it is delegated. Managerial implications: Our study reveals that, under reasonably mild conditions, optimal salesforce contracts can still maintain relatively simple forms, even when confronted with common operational factors and generalized demand and cost functions. However, the contracts must be tailored to suit the operational settings. Intriguingly, neither the loss of demand information nor the delegation of inventory decisions would compromise system efficiency at optimum. Funding: H. Song is partially supported by the Key International Cooperation and Exchange Projects of the NSFC [Grant W2411062] and the Foundation for Innovative Research Groups of the NSFC [Grant 71821002]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0400 .

The cost of climate change: A generalized cost function approach for incorporating extreme weather exposure into public transit accessibility

Public transit offers urban populations physical accessibility to resources and opportunities. However, at the same time, transit trips often expose users to extreme environmental conditions, such as extreme heat and cold since transit journeys usually include out-of-vehicle trip segments including walking and waiting. Such exposure can be considered as environmental health costs because exposure to weather extremes can lead to adverse health outcomes. Even worse, climate change is increasing the intensity and frequency of extreme weather events. In this context, how can we make public transit accessibility measures ready for climate change? This paper attempts to answer this question by developing a generalized cost function approach combining travel time and environmental health costs into an integrated measure of dual accessibility: a measure of the travel costs of accessing a fixed number of destinations. We synthesize transport science, environmental health, remote sensing, and urban climatology to empower the proposed framework. To demonstrate the utility of the proposed method, we carry out an example study that incorporates transit passengers' extreme cold exposure into accessibility measures in the city of Winnipeg, Manitoba, Canada. Further, we perform a social equity analysis to investigate whether the increase in total integrated costs (i.e., decrease in accessibility) due to the inclusion of environmental health costs disproportionately affects socially disadvantaged population groups. The proposed method enables a more realistic and practical measurement of public transit accessibility under climate change; thereby, improving the readiness and resilience of our society and transport systems for future challenges.

Quantity Conjectural Variations in Oligopoly Games under Different Demand and Cost Functions and Multilevel Leadership

This paper considers a noncooperative game of quantity competition among firms in an oligopoly market under general demand and cost functions. Each firm’s optimal response to the strategies of other firms is assessed by the magnitude and sign of its conjectural variation, expressing the firm’s expectation regarding the counterparty’s supply quantity change in response to the firm’s unit change in its supply quantity. A game of n firms with the sum of conjectural variations (SCV) regarding all counterparties as the generalized response characteristic is studied. The existence of a bifurcation of the players’ response is revealed; a bifurcation is a strategy profile of the game in which both positive and negative responses are possible with an infinite-magnitude SCV value. Methods are developed for calculating the SCV value under different types of inverse demand functions (linear and power) and cost functions (linear, power, and quadratic), and the impact of these characteristics of firms on the bifurcation state is comparatively analyzed.

The five gradients inequality on differentiable manifolds

The goal of this paper is to derive the so-called five gradients inequality for optimal transport theory for general cost functions on two class of differentiable manifolds: locally compact Lie groups and compact Riemannian manifolds.

Data-driven economic MPC with asymptotic stability and strong duality verification using Hankel matrix

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system.

Safe Reinforcement Learning with Instantaneous Constraints: The Role of Aggressive Exploration

This paper studies safe Reinforcement Learning (safe RL) with linear function approximation and under hard instantaneous constraints where unsafe actions must be avoided at each step. Existing studies have considered safe RL with hard instantaneous constraints, but their approaches rely on several key assumptions: (i) the RL agent knows a safe action set for every state or knows a safe graph in which all the state-action-state triples are safe, and (ii) the constraint/cost functions are linear. In this paper, we consider safe RL with instantaneous hard constraints without assumption (i) and generalize (ii) to Reproducing Kernel Hilbert Space (RKHS). Our proposed algorithm, LSVI-AE, achieves O(√{d³H⁴K}) regret and O(H √{dK}) hard constraint violation when the cost function is linear and O(H?ₖ √{K}) hard constraint violation when the cost function belongs to RKHS. Here K is the learning horizon, H is the length of each episode, and ?ₖ is the information gain w.r.t the kernel used to approximate cost functions. Our results achieve the optimal dependency on the learning horizon K, matching the lower bound we provide in this paper and demonstrating the efficiency of LSVI-AE. Notably, the design of our approach encourages aggressive policy exploration, providing a unique perspective on safe RL with general cost functions and no prior knowledge of safe actions, which may be of independent interest.

Energy Transition and the role of new natural gas turbines for power production: The case of GT11N2 M generators

We study General Electric’s new combined-cycle natural gas generator called GT11N2 M upgrade and quantify its economic benefits and the environmental implications in Ontario. We propose a structural power supply chain model involving upstream supplier General Electric and downstream power firm TransAlta at Sarnia, construct generation, service and maintenance cost functions, and calibrate different customer demand curves using actual market and firm data in the Ontario market. We solve for Stackelberg equilibrium outcomes, and quantify prices, outputs, and emissions based on efficiency rates of GT11N2 M. We consider two types of cost efficiencies implied by GT11N2 M: upstream service and maintenance cost efficiency experienced by General Electric and downstream fuel cost efficiency experienced by TransAlta. We provide new insights in the realm of technology adoption. We find in equilibrium that there exists a large variation in electricity generation over operational modes of GT11N2 M: the total generation can increase in the range of 5% (under “Lifetime” mode) to 18% (under ”Maximum Continuous Load” mode). The output variation is nonlinear and the amount of carbon emissions is largely impacted by operating modes. In particular, the total greenhouse gas emission is expected to increase by 12% in the mixed-mode. Consequently, a policy implication of this research is that clean energy adoption facilitated by GT11N2 M is expected to increase carbon emission due to the “rebound effect”.

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.

Stochastic Optimal Linear Control for Generalized Cost Functions With Time-Invariant Stochastic Parameters.

This study presents the design of feedback controllers for generalized cost functions to deal with stochastic optimal control problems. Target linear systems contain time-invariant stochastic parameters that describe system uncertainty. The cost functions involve nonlinear mappings and polynomial forms of the system states and inputs to express various performance metrics. Unfortunately, these properties cause difficulties in solving the problems. Conventional methods, such as the principle of optimality, are not employed to solve such problems owing to the time-invariant parameters. As opposed to the well-known quadratic functions, handling the generalized cost functions is a complicated task. This study overcomes these challenges by deriving an explicit relation between the cost function and the linear feedback gain of a controller. The derived relation enables the feedback gain to be optimized via a gradient method. A theoretical analysis ensures the convergence of the proposed gradient method. A suboptimal feedback controller is obtained to solve the problem, even for the generalized cost. Furthermore, the controller guarantees robust stability of the feedback system even with the stochastic parameters. It is demonstrated that the proposed cost function can express an expectation of a quadratic cost, risk-sensitive cost, polynomial cost, and input-to-state gain. A numerical simulation shows the effectiveness of the proposed method.

New product introductions with selection of unique and common features in monopoly markets

Firms have to determine the right features and prices for their new products as they introduce new product generations to the market. We consider the problem of determining the features of a new product that a monopolist will introduce into a market that contains an existing product as well as setting the prices of the existing and the new products. The firm also decides on offering only the new product or both the existing and the new products. We explicitly capture the effects of unique features, which are specific to one of the two products, and common features which are shared between the new and the existing product on these decisions. The problem is formulated as a nonlinear-mixed-integer program with general cost, demand, and price functions. For the case of linear cost, demand, and price, the nonlinear-mixed-integer program is converted to a nonlinear program and solved analytically. Based on this solution, the optimal prices for both products and the optimal unique features for the new product are derived in closed form, a linear-time algorithm is presented to determine the optimal common features, and the optimality conditions of keeping the existing product in the market are characterized. We show that the selection of the unique features, but not the common ones, is based on the difference between a feature’s contribution to the product’s demand and its cost adjusted by the price sensitivity in the linear case. Moreover, we find that the firm, if it wants to avoid demand cannibalization, should remove the existing product from the market rather than offer two products with mainly unique features. Capturing the effects of unique and common features directly allows firms to decide on the best rollover strategy and determine the right features and prices.

An E-scooter route assignment framework to improve user safety, comfort and compliance with city rules and regulations

The rapid expansion of dockless shared micromobility systems, particularly dockless e-scooters, presents major opportunities along with challenges that have led some cities to ban these services within their jurisdiction. The safe reintroduction of dockless shared micromobility services requires support through enhancement of e-scooter service implementation, improvement of rider behavior, and enforcement of rules and regulations. This paper develops the micromobility guidance tool (MGT) that guides a shared micromobility user going from a defined origin to a defined destination to a route that meets multiple criteria, including safety, comfort, and compliance. Thus, this tool emphasizes two network features, the type of infrastructure and the condition of infrastructure. Moreover, the tool locates shared micromobility parking that is closest to a user’s destination and sends alerts to avoid prohibited infrastructure types. For each trip, the proposed tool uses a shortest path routing algorithm to assign its route and the Euclidean distance to assign closest parking. A generalized cost function was developed to estimate the time needed to cross a link while considering e-scooter accessibility, user routing preferences, and ordinance restrictions. The effectiveness of MGT was tested through a case study of tens of thousands of dockless shared e-scooter trips within the City of Dallas, TX. As a validation step, several experiments were carried out to examine the developed tool under various scenarios. Routes generated by MGT were compared to actual routes taken by users and to scenarios corresponding to models previously published in the literature. When compared to actual routes taken by riders, case-study findings showed a notable increase in the use of preferred types of infrastructure (bike lanes, sidewalks, one-way roads, etc.), the use of bike infrastructure (bike lanes and bike trails), and the use of better conditions (i.e., less deficient infrastructure). Additionally, a marked reduction in regulatory violations was exhibited. The methodological approach presented here could be generalized to any city network or shared micromobility system. The proposed tool could be required by cities and adopted by shared micromobility providers seeking to improve rider safety, comfort, and compliance. This tool could be integrated into the provider application guiding the user to micromobility-friendly routes and designated parking, a feature not yet available to micromobility users. Finally, this paper has offered policy recommendations and guidance for practice, where the reintroduction of shared e-scooters is being considered by cities and expansion considered in new markets.

Algorithms for Right-sizing Heterogeneous Data Centers

Power consumption is a dominant and still growing cost factor in data centers. In time periods with low load, the energy consumption can be reduced by powering down unused servers. We resort to a model introduced by Lin, Wierman, Andrew, and Thereska [ 23 , 24 ] that considers data centers with identical machines and generalize it to heterogeneous data centers with d different server types. The operating cost of a server depends on its load and is modeled by an increasing, convex function for each server type. In contrast to earlier work, we consider the discrete setting, where the number of active servers must be integral. Thereby, we seek truly feasible solutions. For homogeneous data centers ( d =1), both the offline and the online problem were solved optimally in References [ 3 , 4 ]. In this article, we study heterogeneous data centers with general time-dependent operating cost functions. We develop an online algorithm based on a work function approach that achieves a competitive ratio of 2 d + 1 + ε for any ε > 0. For time-independent operating cost functions, the competitive ratio can be reduced to 2 d + 1. There is a lower bound of 2d shown in Reference [ 5 ], so our algorithm is nearly optimal. For the offline version, we give a graph-based (1+ε)-approximation algorithm. Additionally, our offline algorithm is able to handle time-variable data-center sizes.

Novel methods to determine the slowness and ray-velocity vectors in viscoelastic anisotropic media

SUMMARY Determination of the slowness vector and the homogeneous ray-velocity vector is critical for seismic ray tracing in a viscoelastic anisotropic medium. Three formulae, the traditional g-Hamiltonian, newly developed conjugate real ray tracing (C-RRT) and innovative g*-Hamiltonian, are employed to calculate the ray-velocity vectors with the determined slowness vectors in a viscoelastic anisotropic medium. We demonstrate the forward and reverse searching procedures to determine the ray-velocity vectors' slowness vectors. The former implements either a linear search or an optimization method to find the slowness vectors that lead to homogeneous complex ray-velocity vectors (its real and imaginary parts are parallel). The latter is based on a new generalized cost function and applies an optimization method to find the slowness vector for a known ray direction. Using sandstone as an example material, we compare the accuracies and efficiencies of the three formulae and the two searching procedures. Our examples show that the forward searching procedure with the traditional g-Hamiltonian formula and the linearly searching method may generate unphysical solutions for qSV wave due to its cusps or triplication, but using the optimization method may not only mitigate the influence of the cusps and triplication but also significantly improve the accuracies and efficiencies almost two orders higher. For the reverse searching procedure, we propose a general form of the cost function valid for all the formulae of the ray-velocity vector and easily solved by an optimization method. The examples demonstrate that the solutions yielded by the forward and reverse searching procedures coincide well for all three body waves (qP, qSV and qSH), except for the triplication of the qSV wave. In particular, the optimization method combined with the novel g*-Hamiltonian formula may completely overcome the issues of spurious solutions and the qSV-wave cusp and triplication.

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.

Distributed continuous-time proximal algorithm for nonsmooth resource allocation problem with coupled constraints

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm.

Optimizing the Power System Operation Problem towards minimizing Generation and Damage Costs due to Load Shedding

Optimizing the operational parameters and control of the power system in steady-state conditions is a crucial issue in reducing the costs of power generation and operation. In the case of long-term operation of a power system, besides aiming to minimize power generation costs, the cost of damage caused by load shedding also needs to be considered. This paper presents the optimization of the total cost of a power system including minimizing the generation cost function of power plants or power companies and minimizing the damage cost function caused to customers due to load shedding or power outages. At the same time, the objective function must also ensure the constraints on the operating conditions of the power system. This contributes to maintaining the continuity of the power supply to critical loads and minimizing damage. Base loads, priority loads, or loads that are not allowed to be shed are considered as constraints. The optimization problem is addressed by using the Particle Swarm Optimization (PSO) algorithm and the Cuckoo Search Algorithm (CSA). The IEEE 30-bus test system is applied to validate the reduction in total cost. The result comparison shows that when applying the CSA, the total cost is significantly reduced by 3.75% in comparison with the PSO algorithm. The algorithms are implemented in Matlab to demonstrate the efficiency and accuracy of the proposed method.

Stability and Performance Analysis of NMPC: Detectable Stage Costs and General Terminal Costs

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated with numerical examples.

Methodology for energy management strategies design based on predictive control techniques for smart grids

This article focuses on the development of a general energy management system (EMS) design methodology using on model-based predictive control (MPC) for the control and management of microgrids. Different MPC-based EMS for microgrids have been defined in the literature; however, there is a lack of generality in the proposed that would facilitate adapting to new architectures, energy storage system technology, nature of the bus, application, or purpose. To fill this gap, a novel general formulation that is parameterizable, simple, easily interpretable, and reproducible in different microgrid architectures is presented. This is the result of the development of a novel methodology, which is also presented. It considers the state space formulation of the controller from the initial modelling phase, from the dynamics of the energy storage systems represented by their models to the subsequent definition of the optimisation problem. This is developed through the design of the general cost function and the formulation of constrains, by means of general guidelines and reference values. To evaluate the performance of the developed methodology, simulation tests were carried out for four different microgrid architectures, with different applications and objectives, also considering different generation conditions, demand profiles, and initial conditions. The results showed that, with some simple guidelines and regardless of the case study, the developed MPC controller design methodology can address the technical-economic optimisation problem associated with energy management in microgrids in an easy and intuitive way.

Stability analysis of optimal control problems with time-dependent costs

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general attractors are established. This work covers and generalizes the related results on discounted optimal control problems to more general systems and cost functions.