Maximization Problem Research Articles

The Application of Derivatives in Enhancing Economic Decision-Making

This paper explores the specific application of derivatives in economic analysis, aiming to provide an effective mathematical tool for economic analysis to improve decision-making efficiency and accuracy. Through two specific cases - the profit maximization problem of fast-moving consumer goods companies and the profit maximization problem of retail enterprises, it can be demonstrated how to use derivatives to solve and analyze economic models, and then propose corresponding optimization suggestions. In addition, through detailed mathematical derivation and data analysis, how derivatives can help enterprises optimize decision-making and improve economic efficiency was analyzed. Research has shown that derivatives, as an important tool in economic analysis, can effectively enhance the scientifically and accuracy of decision-making.

An adaptive differential evolution algorithm driven by multiple probabilistic mutation strategies for influence maximization in social networks

Influence maximization is a critical research topic of social network analysis, particularly with the increasing involvement of individuals in the global networked society. The purpose of the problem is to identify k influential nodes from the social network and activate them initially to maximize the expected number of influenced nodes at the end of the spreading process. Although some meta-heuristics based on swarm intelligence or biological evolution have been proposed to tackle this intractable problem, further investigation is required to refine the exploration and exploitation operations based on the iterative information from the evolutionary process. In this paper, an adaptive differential evolution algorithm driven by multiple probabilistic mutation strategies is proposed for the influence maximization problem. In order to enhance the evolutionary capability of the later stages of the discrete differential evolution, the mutation in the framework, consisting of three policies, namely comprehensive learning particle swarm mutation strategy, differential mutation strategy, and perturbation strategy, is implied based on different probabilistic models. An adaptive local search strategy is presented to improve the local optimum results based on a potential alternative library consisting of structural hole nodes, which guides the differential evolution to find a more optimal solution. Experimental results on six real-world social networks demonstrate the competitive performance of the proposed algorithm in terms of both efficacy and efficiency compared to state-of-the-art algorithms.

Maximizing Influence in Social Networks Using Combined Local Features and Deep Learning-Based Node Embedding.

The influence maximization problem has several issues, including low infection rates and high time complexity. Many proposed methods are not suitable for large-scale networks due to their time complexity or free parameter usage. To address these challenges, this article proposes a local heuristic called Embedding Technique for Influence Maximization (ETIM) that uses shell decomposition, graph embedding, and reduction, as well as combined local structural features. The algorithm selects candidate nodes based on their connections among network shells and topological features, reducing the search space and computational overhead. It uses a deep learning-based node embedding technique to create a multidimensional vector of candidate nodes and calculates the dependency on spreading for each node based on local topological features. Finally, influential nodes are identified using the results of the previous phases and newly defined local features. The proposed algorithm is evaluated using the independent cascade model, showing its competitiveness and ability to achieve the best performance in terms of solution quality. Compared with the collective influence global algorithm, ETIM is significantly faster and improves the infection rate by an average of 12%.

Utility optimization for computation offloading and splitting in time-varying HAP and LEO satellite integrated MEC networks

To provide ubiquitous and low-latency communication and computation services for remote and disaster areas, high altitude platform (HAP) and low earth orbit (LEO) satellite integrated multi-access edge computing (HLS-MEC) networks have emerged as a promising solution. However, most current studies directly assume that the number of connected satellites is fixed and neglect the modeling of the time-varying multi-satellite computing process. Motivated by this, we establish an M/G/K(t) queuing model to illustrate task computation on satellites. To evaluate the efficiency and quality of computation offloading and splitting, we develop a utility model. This model is defined as a difference between a value function that assesses the trade-offs of task offloading, considering latency reductions and energy savings, and a cost function that quantifies expenses related to latency and energy consumption. After formulating the utility maximization problem, we propose the deep reinforcement learning-based offloading and splitting (DBOS) scheme that can overcome the time-varying uncertainties and high dynamics in the HLS-MEC network. Specifically, the DBOS scheme can learn the best computation offloading and splitting policy to maximize the utility by sensing the number of connected satellites, the distance between the HAP and satellites, the available computing resources, and the task arrival rate. Finally, we evaluate and validate the computational complexity and convergence property of the DBOS scheme. Numerical results show that the DBOS scheme outperforms the other three benchmarks and maximizes the utility under time-varying dynamics.

Joint passive beamforming and deployment design for active intelligent reflecting surface-assisted energy harvesting-cognitive radio sensor networks.

To prolong the network lifetime of energy harvesting-cognitive radio sensor networks (EH-CRSNs), this paper integrates active intelligent reflecting surface (IRS) to support both downlink EH and uplink data transmissions and formulates a constrained non-convex optimization problem that maximizes the net energy gain. To solve this problem, a joint passive beamforming and IRS deployment mechanism is proposed to determine the optimal deployment location of the active IRS and optimally configure the IRS reflection coefficient matrices. Specifically, the net energy gain maximization problem at a specified location is divided into two sub-problems according to its characteristics: maximizing the cumulative energy harvested by all CRSNs nodes in the downlink and minimizing the energy consumption of cluster heads in uplink data transmissions, with each sub-problem being solved independently. Furthermore, this paper explores how factors such as the number of active reflecting elements and the amplification power budget influence the optimal deployment location of the active IRS. The findings from this investigation can guide the design of active IRS-assisted EH-CRSNs under specified parameters. Simulation results confirm the aforementioned conclusions and highlight the benefits of the proposed joint mechanism in enhancing net energy gain over various benchmark mechanisms.

Joint channel allocation and transmit power control for underlay EH‐CRNs: A clustering‐based multi‐agent DDPG approach

AbstractTo address the concerns of energy supply and spectrum scarcity for wireless devices, energy harvesting cognitive radio networks have been proposed. To improve spectrum utilization, secondary users (SUs) access the licensed spectrum in underlay mode, which may cause severe interference to primary users and SUs. The focus is on the underlay energy harvesting cognitive radio networks with multiple pairs of SUs, and formulate the long‐term secondary throughput maximization problem as a mixed‐integer non‐linear programming problem. As traditional approaches could hardly solve the mixed‐integer non‐linear programming problem well, a centralized deep deterministic policy gradient (C‐DDPG) approach is proposed that achieves satisfactory throughput performance. To reduce the computational complexity of C‐DDPG, we further propose a clustering‐based multi‐agent DDPG (CMA‐DDPG) approach that combines the advantages of the centralized deep reinforcement learning approach and the distributed deep reinforcement learning approach. In the CMA‐DDPG, a novel interference‐based clustering algorithm is proposed, which partitions the SUs that cause severe mutual interference into one cluster, and the sizes of state space and action space are smaller than those in C‐DDPG. Numerical results validate the superiority of the proposed approaches in terms of the throughput and outage probability, and validate the clustering performance of the interference‐based clustering algorithm in terms of the outage probability of the secondary network.

Using reinforcement learning to autonomously identify sources of error for agents in group missions

When deploying agents to execute a mission with collective behavior, it is common for accidental malfunctions to occur in some agents. It is challenging to distinguish whether these malfunctions are due to actuator failures or sensor issues based solely on interactions with the affected agent. However, we humans know that if we cause a group behavior where other agents collide with a suspected malfunctioning agent, we can monitor the presence or absence of a positional change and identify whether it is the actuator (position changed) or the sensor (position unchanged) that is broken. We have developed artificial intelligence that can autonomously deploy such “information acquisition strategies through collective behavior” using machine learning. In such problems, the goal is to plan collective actions that result in differences between the hypotheses for the state [e.g., actuator or sensor]. Only a few of the possible collective behavior patterns will lead to distinguishing between hypotheses. The evaluation function to maximize the difference between hypotheses is therefore sparse, with mostly flat values across most of the domain. Gradient-based optimization methods are ineffective for this, and reinforcement learning becomes a viable alternative. By handling this maximization problem, our reinforcement learning surprisingly gets the optimal solution, resulting in collective actions that involve collisions to differentiate the causes. Subsequent collective behaviors, reflecting this situation awareness, seemed to involve other agents assisting the malfunctioning agent.

DETERMINING THE OPTIMAL TEMPORARY WASTE DISPOSAL SITES IN THE ALANG-ALANG LEBAR SUB-DISTRICT PALEMBANG USING THE P-CENTRE LOCATION PROBLEM AND P-MEDIAN PROBLEM MODELS

The rapid development of Palembang City comes with an increase in population and a proportionate increase in waste. Providing Temporary Waste Disposal Sites (TWDS) with ideal locations is one way to address the waste problem in Palembang City. The location of the existing TWDS could be more regular and optimal. The problem of determining the optimal TWDS location can be solved by optimization science, as classified in the Set Covering Problem (SCP) model. The SCP model is divided into the -Center Location Problem and -Median Problem models. This study aims to determine the optimal locations for TWDS in the Alang-Alang Lebar Sub-District, Palembang City, by comparing the results of the p-Center Location Problem and p-Median Problem models. Initially, the Alang-Alang Lebar Sub-District had 33 TWDS. After formulating the Set Covering Location Problem and Maximal Covering Location Problem models, we obtain the optimal solution, which we then solve using the -Center Location Problem and -Median Problem models. Based on the results and discussion, the optimal TWDS can meet the demand of each village in the Alang-Alang Lebar Sub-District. The -Center Location Problem and -Median Problem models produce the same optimal TWDS, namely TWDS Pramuka 2 Street and around, TWDS Colonel Sulaiman Amin Street, TWDS Talang Kelapa Ujung, and TWDS Beside Soekarno Hatta Street. This study recommends using both models to determine the optimal TWDS.

IMUNE: A novel evolutionary algorithm for influence maximization in UAV networks

In a network, influence maximization addresses identifying an optimal set of nodes to initiate influence propagation, thereby maximizing the influence spread. Current approaches for influence maximization encounter limitations in accuracy and efficiency. Furthermore, most existing methods are aimed at the IC (Independent Cascade) diffusion model, and few solutions concern dynamic networks. In this study, we focus on dynamic networks consisting of UAV (Unmanned Aerial Vehicle) clusters that perform coverage tasks and introduce IMUNE, an evolutionary algorithm for influence maximization in UAV networks. We first generate dynamic networks that simulate UAV coverage tasks and give the representation of dynamic networks. Novel fitness functions in the evolutionary algorithm are designed to estimate the influence ability of a set of seed nodes in a dynamic process. On this basis, an integrated fitness function is proposed to fit both the IC and SI (Susceptible–Infected) models. IMUNE can find seed nodes for maximizing influence spread in dynamic UAV networks with different diffusion models through the improvements in fitness functions and search strategies. Experimental results on UAV network datasets show the effectiveness and efficiency of the IMUNE algorithm in solving influence maximization problems.

Influence maximization based on discrete particle swarm optimization on multilayer network

Influence maximization (IM) aims to strategically select influential users to maximize information propagation in social networks. Most of the existing studies focus on IM in single-layer networks. However, we have observed that individuals often engage in multiple social platforms to fulfill various social needs. To make better use of this observation, we consider an extended problem of how to maximize influence spread in multilayer networks. The Multilayer Influence Maximization (MLIM) problem is different from the IM problem because information propagation behaves differently in multilayer networks compared to single-layer networks: users influenced on one layer may trigger the propagation of information on another layer. Our work successfully models the information propagation process as a Multilayer Independent Cascade model in multilayer networks. Based on the characteristics of this model, we introduce an approximation function called Multilayer Expected Diffusion Value (MLEDV) for it. However, the NP-hardness of the MLIM problem has posed significant challenges to our work. To tackle the issue, we devise a novel algorithm based on Discrete Particle Swarm Optimization. Our algorithm consists of two stages: 1) the candidate node selection, where we devise a novel centrality metric called Random connectivity Centrality to select candidate nodes, which assesses the importance of nodes from a connectivity perspective. 2)the seed selection, where we employ a discrete particle swarm algorithm to find seed nodes from the candidate nodes. We use MLEDV as a fitness function to measure the spreading power of candidate solutions in our algorithm. Additionally, we introduce a Neighborhood Optimization strategy to increase the convergence of the algorithm. We conduct experiments on four real-world networks and two self-built networks and demonstrate that our algorithms are effective for the MLIM problem.

UAV-mounted IRS assisted wireless powered mobile edge computing systems: Joint beamforming design, resource allocation and position optimization

Intelligent reflecting surface (IRS) and unmanned aerial vehicle (UAV) have been recently used in wireless-powered mobile edge computing (MEC) systems to enhance the computation bits and energy harvesting performance. However, in the conventional IRS- and UAV-aided MEC systems, the IRS is installed at fixed locations on a building, which restricts the computation performance. UAV-mounted IRS (UAV-IRS), as a promising technology, combines the advantages of UAV and IRS. Hence, in this work, we study a UAV-IRS wireless-powered MEC system, where multiple UAV-IRSs are considered between Internet of Things (IoT) devices and the base station to improve the computation bits and energy harvesting. The multi-antenna base station first charges the IoT devices via radio frequency signals, and then IoT devices offload their computation tasks to the base station via UAV-IRSs. We formulate a computation bits maximization problem for all IoT devices by jointly determining detection beamforming at IoT devices, active energy beamforming at the base station, power allocation, time slot assignment, CPU frequency, the phase shifts design in the wireless energy transfer (WET) and task offloading, and UAV-IRSs positions. A block coordinate descent (BCD) algorithm by decomposing the introduced problem into four blocks is proposed, while the detection beamforming, active energy beamforming, transmit power, time slot assignment, CPU frequency, and the phase shifts design in the task offloading are derived in closed-form results. Also, the successive convex approximation and semidefinite relaxation (SDR) are adopted to obtain the UAV-IRS positions and the phase shifts in the WET, respectively. The simulation results verify the effectiveness of the presented BCD method compared with the different benchmark schemes.

A Data-Driven Approach for Optimizing Early-Stage Electric Vehicle Charging Station Placement

This paper presents a novel and practical data-driven approach to sub-optimally allocate charging stations for electric vehicles (EVs) in an early-stage setting. Specifically, we investigate the following problem: For a city with a limited budget for public EV charging infrastructure construction, where should the charging stations be deployed in order to promote the transition of EVs from traditional cars? We develop a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -nearest model and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -nearest model that can capture people's satisfaction towards a certain design and formulate the early-stage EV charging station placement problem as a monotone submodular maximization problem utilizing fine-grained population, trip, transportation network and POI data. A greedy-based algorithm is proposed to solve the problem efficiently with a provable approximation ratio. A case study of Haikou is provided to demonstrate the effectiveness of our approach.

A co-operative game theoretic approach for the budgeted influence maximization problem

A co-operative game theoretic approach for the budgeted influence maximization problem

Theoretical study on demand-side management to reduce imbalance between electricity supply and demand

The gap between electricity supply and demand, which is the electricity imbalance, can have negative economic impacts on retail electricity suppliers. This paper presents a methodology for designing demand response (DR) programs while mitigating the negative impacts. The DR programs require the retailers to set target electricity consumption and prices of economic incentives for customers who cooperate with the DR programs. First, the target electricity consumption is determined by solving a problem of social welfare maximization in which the objective function is the sum of economic surplus of the retailers and their customers and impacts of electricity imbalance. The optimal electricity prices or the optimal rebate levels are then calculated under the principle that rational customers act to maximize their economic surplus. Through numerical simulations, the authors confirmed that the proposed methodology mitigated the impacts of electricity imbalance. Meanwhile, results of the numerical simulations showed that in practical situations, there were cases where the retailers unable to reduce the electricity imbalance profitably. Therefore, the authors additionally discuss ways to assess the electricity imbalance, which motivates the retailers to reduce the imbalance, in such cases.

Escape of an active ring from an attractive surface: Behaving like a self-propelled Brownian particle.

Escape of active agents from metastable states is of great interest in statistical and biological physics. In this paper, we investigate the escape of a flexible active ring, composed of active Brownian particles, from a flat attractive surface using Brownian dynamics simulations. To systematically explore the effects of activity, persistence time, and the shape of attractive potentials, we calculate escape time τ_{e} and effective temperature T_{eff}. We observe two distinct escape mechanisms: Kramers-like thermal activation at small persistence times, where ln(τ_{e})∼1/(k_{B}T_{eff}), and the maximal force problem at large persistence time, where τ_{e} is determined by persistence time. The escape time explicitly depends on the shape of the potential barrier at high activity and large persistence time. Moreover, when the propulsion force is biased along the ring's contour, escape becomes more difficult and is primarily driven by thermal noise. Our findings highlight that, despite its intricate configuration, the active ring can be effectively modeled as a self-propelled Brownian particle when studying its escape from a smooth surface.

Research on Pricing and Dynamic Replenishment Planning Strategies for Perishable Vegetables Based on the RF-GWO Model

This paper addresses the challenges of automated pricing and replenishment strategies for perishable products with time-varying deterioration rates, aiming to assist wholesalers and retailers in optimizing their production, transportation, and sales processes to meet market demand while minimizing inventory backlog and losses. The study utilizes an improved convolutional neural network–long short-term memory (CNN-LSTM) hybrid model, autoregressive moving average (ARIMA) model, and random forest–grey wolf optimization (RF-GWO) algorithm. Using fresh vegetables as an example, the cost relationship is analyzed through linear regression, sales volume is predicted using the LSTM recurrent neural network, and pricing is forecasted with a time series analysis. The RF-GWO algorithm is then employed to solve the profit maximization problem, identifying the optimal replenishment quantity, type, and most effective pricing strategy, which involves dynamically adjusting prices based on predicted sales and market conditions. The experimental results indicate a 5.4% reduction in inventory losses and a 6.15% increase in sales profits, confirming the model’s effectiveness. The proposed mathematical model offers a novel approach to automated pricing and replenishment in managing perishable goods, providing valuable insights for dynamic inventory control and profit optimization.

Inequality as determinant of donation: A theoretical modeling and empirical analysis of Korea.

Recipient financial need is a crucial factor in donation decisions. This study proposes a novel model for determining financial donations, incorporating consumption levels of both donor and recipient within a societal context. Solving our model's utility maximization problem reveals how consumption, donation, and savings are interlinked. Empirical evidence reinforces these findings, aligning with prior research and showing that larger consumption gaps between donors and recipients lead to increased donations. Our findings point towards an inherent altruistic motivation in donation, where elevating the recipient's well-being ultimately enhances the donor's own utility. This reinforces the notion that consideration of the recipient's financial hardship, as reflected by their consumption patterns, is crucial when making donation decisions. Shifting beyond traditional models, this study introduces a groundbreaking approach to financial donations. Our novel model factors in consumption levels of both the donor and recipient, along with the broader societal context, using utility maximization to unravel the intertwined decisions of consumption, donation, and savings. Real-world data validates our model, confirming known donation factors and revealing a key finding: larger disparities in consumption lead to increased giving, suggesting an altruistic drive where helping others boosts personal satisfaction.

Edge-Intelligence-Powered Joint Computation Offloading and Unmanned Aerial Vehicle Trajectory Optimization Strategy

UAV-based air-ground integrated networks offer a significant benefit in terms of providing ubiquitous communications and computing services for Internet of Things (IoT) devices. With the empowerment of edge intelligence (EI) technology, they can efficiently deploy various intelligent IoT applications. However, the trajectory of UAVs can significantly affect the quality of service (QoS) and resource optimization decisions. Joint computation offloading and UAV trajectory optimization bring many challenges, including coupled decision variables, information uncertainty, and long-term queue delay constraints. Therefore, this paper introduces an air-ground integrated architecture with EI and proposes a TD3-based joint computation offloading and UAV trajectory optimization (TCOTO) algorithm. Specifically, we use the principle of the TD3 algorithm to transform the original problem into a cumulative reward maximization problem in deep reinforcement learning (DRL) to obtain the UAV trajectory and offloading strategy. Additionally, the Lyapunov framework is used to convert the original long-term optimization problem into a deterministic short-term time-slot problem to ensure the long-term stability of the UAV queue. Based on the simulation results, it can be concluded that our novel TD3-based algorithm effectively solves the joint computation offloading and UAV trajectory optimization problems. The proposed algorithm improves the performance of the system energy efficiency by 3.77%, 22.90%, and 67.62%, respectively, compared to the other three benchmark schemes.

Different strategies of crop diversification between poor and non-poor farmers: Concepts and evidence from Tanzania

Crop diversification, or growing multiple crops in farmland, has received attention as a risk-reducing strategy for smallholders. This study attempts to show that poor and non-poor farmers adopt different strategies of crop diversification. We first conceptualize farmers’ heterogeneous motivations for crop diversification by introducing a subsistence constraint into a utility maximization problem under uncertainty. Using the Tanzanian National Panel Survey, we then examine whether past experiences of shocks affect the adoption of crop diversification differently between poor and non-poor farmers. We rely on a threshold model to estimate heterogeneous impacts between poor and non-poor farmers. We find that poor farmers adopt crop diversification for robust food securities in response to drought/flood and large increases in food prices for purchase. In contrast, non-poor farmers adopt crop diversification to stabilize market income in response to large increases in input prices and large declines in crop prices for sale.

Order-sensitive competitive revenue maximization for viral marketing in social networks

The Competitive Influence Maximization (CIM) problem is a critical issue in viral marketing, focusing on selecting a set of influential individuals, known as seed users, for competitors to maximize their revenue. These seed users have significant sway in social networks and serve as valuable marketing resources provided by the platform. They are often displayed in a certain order launched by the platform and the potential information hidden in the order can profoundly affect the final marketing outcomes. However, current CIM research predominantly emphasizes designing effective algorithms for seed selection while ignoring the impact of the seed order launched by the platform. Therefore, this paper focuses on identifying the optimal seed order to maximize platform revenue in a competitive market environment. Specifically, we introduce a new problem called Order-Sensitive Competitive Revenue Maximization (OSCRM) to investigate the CIM problem from a new practical perspective. We prove the problem to be NP-hard and present a simple greedy algorithm with a 1/3-approximate ratio. To address it more efficiently, we further propose an enhanced greedy algorithm called GMST. This algorithm leverages the maximum spanning tree (MST) and achieves a 1/2-approximate ratio. Extensive experiments on four real-world datasets demonstrate the effectiveness of our proposed GMST algorithm.