Utility Function Subject Research Articles

Group Equality in Adaptive Submodular Maximization

In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both nonadaptive and adaptive settings. It is shown that the utility function of many machine learning applications, including data summarization, influence maximization in social networks, and personalized recommendation, satisfies the property of submodularity. Hence, maximizing a submodular function subject to various constraints can be found at the heart of many of those applications. On a high level, submodular maximization aims to select a group of most representative items (e.g., data points). However, the design of most existing algorithms does not incorporate the fairness constraint, leading to underrepresentation or overrepresentation of some particular groups. This motivates us to study the submodular maximization problem with group equality, in which we aim to select a group of items to maximize a (possibly nonmonotone) submodular utility function subject to a group equality constraint. To this end, we develop the first constant-factor approximation algorithm for this problem. The design of our algorithm is robust enough to be extended to solving the submodular maximization problem under a more complicated adaptive setting. Moreover, we further extend our study to incorporating a global cardinality constraint and other fairness notations. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0384 .

Proportionally fair load balancing with statistical quality of service provisioning for aerial base stations

AbstractAerial base stations (ABSs) seem promising to enhance the coverage and capacity of fifth‐generation and upcoming networks. With the flexible mobility of ABSs, they can be positioned in air to maximize the number of users served with a guaranteed quality of service (QoS). However, ABSs may be overloaded or underutilized given inefficient placement, and user association has not been well addressed. Hence, we propose a three‐dimensional ABS placement scheme with a delay‐QoS‐driven user association to balance loading among ABSs. First, a load balancing utility function is designed based on proportional fairness. Then, an optimization problem for joint ABS placement and user association is formulated to maximize the utility function subject to statistical delay QoS requirements and ABS collision avoidance constraints. To solve this problem, we introduce an efficient modified gray wolf optimizer for ABS placement with a greedy user association strategy. Simulation results demonstrate that the proposed scheme outperforms baselines in terms of load balancing and delay QoS provisioning.

The Application of Lagrange Multipliers in Consumer Choice Theory

This article deals with the consumer choice theory developed by Irving Fisher, Francis Edgeworth, Vilfredo Pareto, and John Hicks. A three-dimensional utility function is presented as an alternative to indifference curves. In mainstream textbooks, the indifference curves together with the budget constraint are used to find the optimum of a consumer graphically at a point where the budget line is a tangent line to an indifference curve. In this article, a vertical cross-section of the three-dimensional utility function and the Lagrange multipliers are applied to find the optimum of a consumer directly from the three-dimensional utility function subject to the budget constraint.

Uncertain Optimization of Discrete Supply Networks with Order Delivery Disruption and Risk Preference in the Postepidemic Era

Epidemic blockade leads to increased uncertainty and dynamic supply network disruption. This study considers an uncertain optimization of dynamic supply networks with risk preference and order delivery disruption. Taking the subjective utility of downstream enterprises as a reference point for the utility measurement of order delivery disruption and risk preference, this study constructs a biobjective optimization model with the goal of maximizing the downstream firm’s subjective utility and minimizing the manufacturer’s cost. The influence of each parameter in the downstream firm’s subjective utility function on the integrated optimization was analysed. The research found that the uncertain optimization model with the risk preference of downstream firms for order delivery disruption better controls the actual manufacturer’s order allocation and distribution problems when considering the downstream firms’ behaviour preference characteristics under bounded rationality. When allocating orders, manufacturers should consider that changes in order delivery disruption will cause changes in the subjective utility of downstream enterprises. In the process of multiperiod cooperation between manufacturers and downstream firms, they can obtain downstream firm risk preferences through repeated investigations.

A Sensitivity Analysis of a Certain Mathematical Model of Expert Evaluation of Investment Projects

The paper presents a sensitivity analysis of the developed mathematical model of expert evaluation of investment projects. Processes of investment projects implementations are analyzed as decision-making processes under uncertainty. The mathematical model under study evaluates the effectiveness of an investment project using the NPV index. This index is considered a random variable and can be estimated by an investor as a segment [NPV1; NPV2J. The proposed mathematical model utilizes the probability density function of NPV in the form of Pearson curves of the first type. Another peculiar feature of the mathematical model is utilization of the subjective utility function in decision making of whether to invest or not to invest in some project. The subjective utility function considers individual characteristics of investors and their decision making under risks and uncertainty. Perception of additional information by investors changes depending on their attitude toward risk and missed opportunities and thus reduces uncertainty in decision making. The paper studies this step in detail and provides some conclusions proving the correctness of the developed mathematical model.

The evolutionary stability of in-group altruism in productive and destructive group contests

This article examines the evolutionary stability of other-regarding preferences in a group contest for a prize, which is endogenously determined. In a destructive contest, such as war, contest efforts of all groups decrease the value of the prize. In contrast, in a productive contest, such as a patent race, contest efforts of all groups increase the value of the prize. The indirect evolutionary approach allows to endogenize players’ preferences, that is, the utility weights given by a group member, in her subjective utility function, to the material payoffs of in-group and out-group members. After characterizing the set of evolutionarily stable preference types, I show that the evolutionarily stable degree of in-group altruism is always stronger when the group contest is destructive than when it is productive. Moreover, when the group contest is strongly productive, preference evolution leads to in-group spite. However, a smaller group size and a larger number of competing groups makes this outcome less likely.

Interference Management in NOMA-Based Fog-Radio Access Networks via Scheduling and Power Allocation

This paper analyzes the integration of Non-Orthogonal Multiple Access (NOMA) in a Fog Radio Access Network (FRAN) architecture with limited fronthaul capacity. More precisely, it proposes methods for optimizing the resource allocation for the downlink of a NOMA-based FRAN with multiple resource blocks (RB). The resource allocation problem is formulated as a mixed-integer optimization problem, which determines the user-to-RB assignment, the power allocated to each RB, and the power split levels of the NOMA users served by each RB. The optimization problem maximizes a network-wide rate-based utility function subject to fronthaul-capacity constraints. The paper proposes a feasible decoupled solution for such a non-convex optimization problem using a three-step hybrid centralized/distributed approach, which in part relies on the edge-devices computation capabilities. The paper proposes and compares two distinct methods for solving the assignment problem, namely a Hungarian-based method, and a Multiple Choice Knapsack-based method. The power allocation to RBs and the NOMA power split optimization are solved using the alternating direction method of multipliers (ADMM). Simulations results illustrate the advantages of the proposed methods compared to different baseline schemes, including the conventional Orthogonal Multiple Access (OMA), for different utility functions and different network environments.

Computational Methods in Problems of Subjective Assessment of Investment Decisions Effectiveness

The paper describes the implementation of investment projects under conditions of uncertainty. In the developed mathematical model, the effectiveness of an investment project is evaluated by the NPV index. This index is considered a random variable that can be estimated by an investor to within a segment [NPV1;NPV2]. The main difficulties of the decision-making process arise when the segment [NPV1;NPV2] includes zero value. In the developed model, we use the probability density function of NPV value in the form of Pearson curves of the first type. This paper discusses in detail some particular moments, which are to be taken into consideration while choosing a specific type of probability density function of NPV.
 The main element of the proposed model is the subjective utility function. Many questions regarding the usage of this function in practice are also extensively reviewed in this article. The main requirement for successful usage of the subjective utility function in real life is a well-calculated chapter of scenario analysis of an investment project. This chapter is present in almost all modern business plans. The practical application of the developed mathematical model improves the quality of decisions concerning the investment of funds into projects.

Comparison of different land distribution mechanisms for a land-hungry region

This paper proposes an approach to the development an efficient land distribution mechanism for a particular land-hungry region. We separate budgetary and allocative efficiency and use general utility approach during evaluation of particular distribution mechanisms. We propose a model of potential land users, which allows quantifying the efficiency of a number of mechanisms of land distribution for land-hungry regions. Land users are represented as economic agents with bounded rationality and subjective utility functions. The model calculates allocation efficiency and budgetary efficiency as independent values and thus is more precise. It also has considerable flexibility and can be adjusted to specific agricultural technology and soil types. An analysis of the efficiency of various mechanisms for the test region showed that lottery mechanisms leads to losses of allocative efficiency compared with auction mechanisms. As for the budget revenues, the use of lottery mechanisms leads to much smaller losses of budgetary efficiency in comparison with simultaneous closed auctions of the first and second prices. But of all the mechanisms considered in the paper, the repetitive Vickrey auction leads to the smallest losses of budget efficiency in the model.

Prospect Theoretic Utility Based Human Decision Making in Multi-Agent Systems

This paper studies human decision making via a utility based approach in a binary hypothesis testing framework that includes the consideration of individual behavioral disparity. Unlike rational decision makers who make decisions so as to maximize their expected utility, humans tend to maximize their subjective utilities, which are usually distorted due to cognitive biases. We use the value function and the probability weighting function from prospect theory to model human cognitive biases and obtain their subjective utility function in decision making. First, we show that the decision rule which maximizes the subjective utility function reduces to a likelihood ratio test (LRT). Second, to capture the unreliable nature of human decision making behavior, we model the decision threshold of a human as a Gaussian random variable, whose mean is determined by his/her cognitive bias, and the variance represents the uncertainty of the agent while making a decision. This human decision making framework under behavioral biases incorporates both cognitive biases and uncertainties. We consider several decision fusion scenarios that include humans. Extensive numerical results are provided throughout the paper to illustrate the impact of human behavioral biases on the performance of the decision making systems.

A behavioral microeconomic foundation for car-following models

The objective of this paper is to develop a micro-economic modeling approach for car-following behaviors that may capture different risk-taking tendencies when dealing with different traffic conditions. The proposed framework allows for the consideration of perception subjectivity and judgement errors that may lead to unsafe acceleration driving maneuvers with the possibility of real-end collisions. The modeling approach relies on a generalized utility-based formulation with three specific types of subjective utility functions (SUFs): Prospect Utility (PT) subjective utility function, Constant Relative Risk Aversion (CRRA) subjective utility function, and an Exponential Constant Relative Risk Aversion (ECRA) subjective utility function. The formulation is assessed in terms of its homogeneous macroscopic properties (thus leading to a triangular fundamental diagram) and its non-homogeneous microscopic properties (thus leading to realistic following behavior facing different traffic scenarios).Once tested in terms of feasibility, the modeling approach is calibrated against real-life trajectory data. A Genetic Algorithm (GA) method is adopted to minimize a spacing-mixed-error term while considering inter-driving heterogeneity. The three models (i.e. PT, CRRA and ECRA) produce acceptable error values with the PT model showing the best fit, followed by the ECRA model, followed by the CRRA model. Even though the CRRA and the PT models show similar intensity in the acceleration response to the behavior of a lead vehicle with more disturbance (stochasticity/randomness) seen with the CRRA SUF, the PT and the ECRA models show more realistic wave formation despite their difference in terms of individual acceleration distribution functions. The ECRA model results in an amplified sensitivity to the behavior of the lead vehicle with the acceleration probability distribution function skewed to the left (i.e. towards decelerating rather than accelerating).The calibration exercise is followed by a simulation exercise. The three suggested models produce a homogeneous congestion phase, but a clear transient single/multiple wave formation is seen with the PT and the ECRA models. These latter models are able to reproduce all the congestion regimes observed on real-world surface transportation networks. The ECRA is characterized by a decreased capacity and increased traffic disturbances with additional shockwave formation. Finally, the different models allow the possibility of perception or judgement errors with the explicit incorporation of a collision probability and a collision weight in the suggested formulation approach.

Coevolution of deception and preferences: Darwin and Nash meet Machiavelli

We develop a framework in which individuals' preferences coevolve with their abilities to deceive others about their preferences and intentions. Specifically, individuals are characterised by (i) a level of cognitive sophistication and (ii) a subjective utility function. Increased cognition is costly, but higher-level individuals have the advantage of being able to deceive lower-level opponents about their preferences and intentions in some of the matches. In the remaining matches, the individuals observe each other's preferences. Our main result shows that, essentially, only efficient outcomes can be stable. Moreover, under additional mild assumptions, we show that an efficient outcome is stable if and only if the gain from unilateral deviation is smaller than the effective cost of deception in the environment.

How to Cope With (New) Uncertainties—A Bounded Rationality Approach

Whenever certain axioms are fulfilled decision-making under uncertainty can be modeled as if maximizing the expected utility of results of risky choices over a known state space with non-ambiguous probability weights. As opposed to this, practically coping with ever new uncertainties—new in that statistical, empirical evidence is lacking—requires a purely procedural bounded rationality approach as paradigmatically proposed here. The procedures can be evaluated and improved in view of evidence of their “objective” success or failure whereas the prescription to behave as if maximizing a subjective utility function is of no direct technological use for a boundedly rational actor.

TSRA: An Adaptive Mechanism for Switching between Communication Modes in Full-Duplex Opportunistic Spectrum Access Systems

Full-duplex (FD) communications and self-interference suppression (SIS) techniques can be exploited in opportunistic spectrum access (OSA) systems for simultaneous transmission-sensing (TS) or simultaneous transmission-reception (TR). Motivated by the competing goals of primary user (PU) protection (in the TS mode) and secondary user (SU) performance (in the TR mode), we present an optimal adaptive switching strategy and an associated communication protocol for FD OSA systems. Specifically, we optimize the spectrum-awareness/efficiency tradeoff by allowing the SU link to adaptively switch between various modes, depending on the forecasted PU dynamics. The proposed three-stage adaptive mode-selection strategy maximizes an SU utility function subject to a constraint on the PU collision probability. We also propose a protocol that executes the switching mechanism in a distributed fashion. In practice, SIS is imperfect, resulting in residual self-interference that degrades the sensing performance in the TS mode. Accordingly, we study different spectrum sensing techniques in the TS mode, while illustrating their accuracy-complexity tradeoff. We evaluate the performance of the proposed switching scheme against the listen-before-talk (LBT) scheme using numerical results, simulations, and hardware USRP experiments.

Supplementary Appendix to Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli

Abstract In Heller and Mohlin (2017) we develop a framework in which individuals' preferences coevolve with their abilities to deceive others about their preferences and intentions. Specifically, individuals are characterised by (i) a level of cognitive sophistication and (ii) a subjective utility function. Increased cognition is costly, but higher-level individuals have the advantage of being able to deceive lower-level opponents about their preferences and intentions in some of the matches. In the remaining matches, the individuals perfectly observe each other's preferences. Our main result shows that, essentially, only efficient outcomes can be stable. Moreover, under additional mild assumptions, we show that an efficient outcome is stable if and only if the gain from unilateral deviation is smaller than the effective cost of deception in the environment. In this supplementary analysis we relax the assumption of perfect observability in matches without deception, and study the robustness of our main results to the introduction of partial observability.

Interference Management in Full-Duplex Cellular Networks With Partial Spectrum Overlap

Full-duplex (FD) communication is promoted to double the spectral efficiency when compared with the half-duplex counterpart. In the context of cellular networks, however, FD communication exacerbates the aggregate uplink (UL) and downlink (DL) interference, which diminishes the foreseen FD gains. This paper considers a flexible duplex system, denoted by $\alpha $ -duplex system, wherein a fine-grained bandwidth control for each UL/DL channel pair in each base station (BS) is allowed, which also leads to partial spectrum overlap between the UL and DL channels. This paper addresses the resulting interference management problem by maximizing a network-wide rate-based utility function subject to UL/DL power constraints, so as to determine user-to-BS association, user-to-channel scheduling, the UL and DL transmit powers, and the fraction of spectrum overlap between UL and DL for every user, under the assumption that the number of available channels and users is equal. This paper solves such a non-convex mixed-integer optimization problem in an iterative way by decoupling the problem into several sub-problems. Particularly, the user-to-BS association problem is solved using a matching algorithm that is a generalization of the stable marriage problem. The scheduling problem is solved by an iterative Hungarian algorithm. The power and spectrum overlap problem is solved by successive convex approximation. The proposed iterative strategy guarantees an efficient one-to-one user to BS and channel assignment. It further provides optimized flexible duplexing and power allocation schemes for all transceivers. Simulations results show appreciable gains when comparing the proposed solution with different schemes from the literature.

Two Timescale Joint Beamforming and Routing for Multi-Antenna D2D Networks via Stochastic Cutting Plane

This paper proposes a dynamic resource allocation scheme to exploit the mixed timescale channel state information (CSI) knowledge structure in a multi-antenna base station-assisted device-to-device (D2D) network. The short-term multi-antenna beamforming control at each transmit device is adaptive to the local real-time CSI. The long-term routing and flow control is adaptive to the global topology and the long-term global CSI statistics of the D2D network. The design objective is to maximize a network utility function subject to the average transmit power constraint, the flow balance constraints and the instantaneous physical layer capacity constraints. The mixed timescale problem can be decomposed into a short-term beamforming control problem and a long-term flow and routing control problem. Using the stochastic cutting plane, we propose a low complexity, self-learning algorithm, which converges to the global optimal solution without explicit knowledge of the channel statistics. Simulation illustrates performance gains with several baselines.

Optimization of consumer preferences – an example

In the article we discuss a standard example of an optimization problem. In our problem we are optimizing the objective function, i.e. a consumer utility function with two variables representing quantities of two commodities denoted by x1 and x2. We consider the standard optimization problem in which we maximize the defined utility function subject to a budget constraint. More precisely, the problem is to choose quantities of two commodities 1st and 2nd, in order to maximize u(x1, x2) function subject to the budget constraint. The aim of the article is to present how we can exemplify and solve this kind of problems in a classroom. In the paper we suggest four methods of finding the solution. The first one is based on the graphical interpretation of the problem. Based on this we can get the approximate solution of the defined optimization problem. Then, we present an algebraic approach to find the optimum solution of the given problem. In the first method we use the budget constraint to transform the utility function of two variables into the function of one variable. The second algebraic method of achieving the solution is based on the second Goosen’s law, which is known as the law of marginal utility theory. In the third algebraic method applied to find the maximum of the utility function, we use the Lagrange multipliers. The text emphasizes the educational aspect of the theory of consumer choice.

Complexity Analysis of Joint Subcarrier and Power Allocation for the Cellular Downlink OFDMA System

Consider the cellular downlink Orthogonal Frequency Division Multiple Access (OFDMA) system where a single transmitter transmits signals to multiple receivers on multiple discrete subcarriers. To adapt fast channel fluctuations, the transmitter should be able to dynamically allocate subcarrier and power resources. Assuming perfect channel knowledge, we formulate the joint subcarrier and power allocation problem as two optimization problems: the first is the one of minimizing the total transmission power subject to quality of service constraints, and the second is the one of maximizing a system utility function subject to power budget constraints. In this letter, we show that both the aforementioned formulations of the joint subcarrier and power allocation problem are generally NP-hard. We also identify several subclasses of the problem which are polynomial time solvable.

Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli

We develop a framework in which individuals' preferences coevolve with their abilities to deceive others about their preferences and intentions. Specifically, individuals are characterized by (i) a level of cognitive sophistication and (ii) a subjective utility function. Increased cognition is costly, but higher-level individuals have the advantage of being able to completely deceive lower-level opponents about their preferences and intentions. Only individuals who are of the same cognitive level can observe each other's preferences. Our main result shows that, despite the limited possibility to observe preferences, and despite the strong form of deception, essentially only efficient population states can be stable. Moreover, if the marginal cognitive costs are not too high, then only efficient Nash equilibria are stable. We extend our model to study preferences that depend also on the opponent's type.