Pareto Optimal Strategy Research Articles

Policy iteration based cooperative linear quadratic differential games with unknown dynamics

This article investigates the Pareto optimality of infinite horizon cooperative linear quadratic (LQ) differential games by policy iteration technique where the system dynamics are partially or completely unknown. Firstly, the policy iteration algorithm for the approximate solutions of the corresponding algebraic Riccati equation (ARE) without any prior knowledge of the matrix parameters of the dynamic system is derived by collecting the input and state information of each player. Secondly, when the presented specific rank condition is satisfied, the convergence of the proposed algorithm is rigorously demonstrated by recursion. Moreover, the weighting approach is employed to obtain the Pareto optimal strategy and the Pareto optimal solutions on the basis of the convex optimization theory. Finally, simulation results are reported to verify the feasibility and correctness of the proposed theoretical results.

Adaptive (re)operations facilitate environmental flow maintenance downstream of multi-purpose reservoirs

Multi-purpose reservoirs support socioeconomic development by providing irrigation, domestic water supply, hydropower, and other services. However, impoundment of water impacts instream aquatic ecosystems. Thus, the concept of minimum environmental flows (MEFs) was established to restore the benefits of naturally flowing rivers by specifying minimum flow rates to be maintained downstream of dams. But varying legislative contexts under which multi-purpose reservoirs operate may not always necessitate MEF releases. To what extent the release of MEF affects other sectoral benefits remains an open-ended and possibly a site-specific inquiry. A related issue is − how does the order in which releases are prioritized influences sectoral performances? We analyse these issues for the Nagarjuna Sagar reservoir, one of the largest multipurpose reservoirs in southern India. We formulate two versions of a multi-objective decision problem. PF_MEF formulation prioritizes MEF releases over releases for water demand satisfaction, followed by hydropower releases. PF_nMEF formulation follows the regional legislative rule releasing first for demand satisfaction, followed by hydropower and MEF releases. The objectives include: annual demand deficits (minimize), hydropower production (maximize), reliability of maintaining MEF (maximize), and reliability of non-exceedance of high flows downstream (maximize). A dynamic rule using radial basis functions (RBFs) specifies releases as a function of reservoir storage and the Borg multi-objective evolutionary algorithm is used to identify the Pareto approximate solutions. The reliability of MEF satisfaction, annual demand deficits, and hydropower production attained across the Pareto-optimal strategies obtained for PF_MEF (PF_nMEF) formulation is 86–99 % (63–80%), 47–1063 (17.6–340) Mm3, and 3452–3703 (3408–3650) GWh, respectively. Results thus indicate that prioritizing MEF releases improves can meet MEF requirements without significant compromises in other objectives. We hypothesize that similar investigations may reveal how simple modification of release order may improve ability of other reservoirs to meet environmental goals.

Dynamic Event-Triggered Safe Control for Nonlinear Game Systems With Asymmetric Input Saturation.

This article focuses on the Pareto optimal issues of nonlinear game systems with asymmetric input saturation under dynamic event-triggered mechanism (DETM). First, the safe control is guaranteed by transforming the system with safety constraints into the one without state constraints utilizing barrier function. The united cost function integrating nonquadratic utility function is constructed to provide the foundation to achieve the Pareto optimal solutions. Then, the adaptive dynamic programming method with concurrent learning is proposed to approximate the Pareto optimal strategies wherein both current and historical data are utilized. To further lessen the consumptions of computation/communication resources, the DETM is integrated into the adaptive algorithm framework which can avoid Zeno phenomena. All the signals of the closed-loop system are proved to be uniformly ultimately bounded. Finally, the simulation results are given to validate the effectiveness of the proposed method from several aspects.

Pareto optimality in cooperative differential game of nonlinear mean-field backward stochastic system

This paper is concerned with a necessary condition and a sufficient condition for the existence of Pareto optimal strategy in a cooperative game driven by a nonlinear mean-field backward stochastic system. First, the game problem is equivalently converted into a set of constrained single objective optimal control problems. Next, we utilise Ekeland's variational principle to dispose constraints, and propose a necessary condition in the form of stochastic maximum principle. Meanwhile, we point out that under certain convex assumptions, the necessary condition we proposed is also sufficient. Finally, we give an example to explain the above theoretical results.

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

Impacts of supply chain leadership on dynamic pricing under consumer patience information asymmetry

AbstractAs the online market rapidly develops, firms will face strategic consumers who differ in buying times. Given that the leadership structure in supply chains affects the chain members' decision‐making and performance, we study this impact in a two‐period dynamic pricing setting with an upstream manufacturer and a downstream retailer, where the patience degree of consumers is the retailer's private information. We examine two leadership scenarios: retailer dominance and manufacturer dominance. The two members play a signaling game under retailer dominance, whereas the manufacturer can only set its wholesale price based on its prior belief under manufacturer dominance. Our analysis indicates that when consumers are more patient, the retailer tends to share its private information with the manufacturer under retailer dominance to avoid the reduction of its retail margin and enhance its profitability. However, the retailer may keep the consumers' patience information private when the manufacturer dominates the supply chain because the manufacturer will set a compromised wholesale price and passively cede profits to the retailer. Finally, we examine consumer surplus and social welfare. We demonstrate that retailer dominance is the Pareto optimal strategy.

Exploring the Power & Loads Paradigm: Tocha Farm Case Study

Wind energy plays a vital role in the European Union’s decarbonization and electrification efforts. The present study addresses wind farm control strategies exploring the design space of optimal solutions and understanding how these solutions vary when different objectives and meteorological scenarios are considered. The goal is to bridge the gap in existing literature by avoiding the simplification of the multi-objective optimization problem into single-objective using the weights method. This method was not chosen due to its various limitations, particularly its inability to deal with non-convex Pareto fronts. Instead, in this work, a multiobjective optimization method is adopted that overcomes these constraints and offers a set of solutions (the Pareto front) where the decision maker selects the most suitable solution. The methodology involves four main steps: flow calculation using FLORIS, aerodynamic load calculation with CCBlade, conversion of loads into damage equivalent moments (DEM), and multi-objective optimization using a direct multi-search (DMS) algorithm. By exploring various objectives, such as power and fatigue loads at different components, and different wind turbines, this study aims to explore the design space and quantify the potential improvement in terms of the defined cost-functions. The study utilizes data from Tocha Wind Farm in Portugal, that comprises five VESTAS wind turbines. Strain gauges, accelerometers, and meteorological measurements are used for data collection. Simulations under ‘greedy control’, where a turbine is affected by a wake, are compared with campaign data, considering a fixed wind speed and varying turbulence intensity. The optimization reveals Pareto-optimal strategies and the respective optimal yaw angles. Considering a wind velocity of 8 m.s −1 and a wind direction of 308°, power may improve up to 4.6%, and the blade root DEM and tower base DEM up to 5.7% and 84%, respectively. The study highlights the impact of considering multiple objectives and supports the selection of wind farm control strategies to effectively manage critical structural components, thereby extending the lifespan of the wind farm.

Achieving optimal trade-off for student dropout prediction with multi-objective reinforcement learning

Student dropout prediction (SDP) in educational research has gained prominence for its role in analyzing student learning behaviors through time series models. Traditional methods often focus singularly on either prediction accuracy or earliness, leading to sub-optimal interventions for at-risk students. This issue underlines the necessity for methods that effectively manage the trade-off between accuracy and earliness. Recognizing the limitations of existing methods, this study introduces a novel approach leveraging multi-objective reinforcement learning (MORL) to optimize the trade-off between prediction accuracy and earliness in SDP tasks. By framing SDP as a partial sequence classification problem, we model it through a multiple-objective Markov decision process (MOMDP), incorporating a vectorized reward function that maintains the distinctiveness of each objective, thereby preventing information loss and enabling more nuanced optimization strategies. Furthermore, we introduce an advanced envelope Q-learning technique to foster a comprehensive exploration of the solution space, aiming to identify Pareto-optimal strategies that accommodate a broader spectrum of preferences. The efficacy of our model has been rigorously validated through comprehensive evaluations on real-world MOOC datasets. These evaluations have demonstrated our model’s superiority, outperforming existing methods in achieving optimal trade-off between accuracy and earliness, thus marking a significant advancement in the field of SDP.

Pareto Optimal Strategy Under H∞ Constraint for the Mean-Field Stochastic Systems in Infinite Horizon.

This article focuses on the mean-field linear-quadratic Pareto (MF-LQP) optimal strategy design for stochastic systems in infinite horizon, which is with the H∞ constraint when the system is disturbed by external interferences. The stochastic bounded real lemma (SBRL) with any initial state in infinite horizon is first investigated based on the stabilizing solution of the generalized algebraic Riccati equation (GARE). Then, by discussing the convexity of the cost functional, the stochastic indefinite MF-LQP control problem is defined and solved based on the MF-LQ theory and Pareto theory. When the worst case disturbance is considered in the collaborative multiplayer system, we show that the Pareto optimal strategy design with H∞ constraint [or robust Pareto optimal strategy, (RPOS)] can be given via solving two coupled GAREs. When the worst case disturbance and the Pareto efficient strategy work, all Pareto solutions are obtained by a generalized Lyapunov equation. Finally, a practical example shows that the obtained results are effective.

Necessary and Sufficient Conditions for Pareto Optimal Solution of Backward Stochastic System With Application

This paper is interested in studying a new kind of Pareto cooperative differential game of backward stochastic differential equation. Based on characterizations of Pareto optimal solution, the game problem is transformed into a set of single objective optimal control problems with constraints of backward stochastic differential equations. In the first place, a necessary condition for Pareto optimal strategy is established by virtue of Ekeland's variational principle, and then it is proved that the necessary condition is also sufficient under certain convex assumption. To shed light on the application of the above theoretical results, a linear-quadratic game and a kind of optimal portfolio and consumption selection problem are also solved explicitly.

Cluster head selection strategy of WSN based on binary multi-objective adaptive fish migration optimization algorithm

In deployed wireless sensor networks (WSNs), how to efficiently transmit information collected by sensor nodes with limited energy is a challenging problem. An appropriate cluster head selection strategy can efficiently solve this problem, but there are many factors to be considered, such as energy consumption, the coverage of cluster head nodes, and the number of cluster head nodes. Each factor has a profound impact on the performance of wireless sensor networks, and there are conflicts among them. In order to solve the conflict of multiple factors and obtain the optimal selection strategy of the cluster head node, this paper proposes a Binary Multi-Objective Adaptive Fish Migration Optimization (BMAFMO) algorithm. The algorithm introduces the Pareto optimal solution storage strategy to improve the global search ability of the optimization algorithm and transform the continuous solution into a binary solution according to the sigmoid transformation function to solve the problem of cluster head node selection. The new algorithm was comprehensively tested using eight test problems and four test metrics. At the same time, the reliability of the algorithm is tested by rank sum test. The test results show that the BMAFMO algorithm obtained the best results in 78.13% test problems compared with other algorithms. Finally, the BAMFMO algorithm is applied to solve the cluster head selection problem of WSN and the simulation results show the novel algorithm has better optimization ability than other heuristic algorithms.

Two-Layered Hierarchical Optimization Strategy With Distributed Potential Game for Interconnected Hybrid Energy Systems.

Due to the existence of different stakeholders, it makes competitive game characteristic in hybrid energy systems (HESs). Combined with the high-dimensional complexity and output uncertainty of distributed energy resources, the optimal operation of HESs can be a more challenging problem. Here, this article proposes a potential game-based two-layered hierarchical optimization strategy to deal with this problem. With consideration of its high-dimensional complexity, a two-layered hierarchical HES model is created, consisting of an upper-level and a lower-level model. For properly solving competitive relationships among different stakeholders in the upper-level model, a multiagent system for stakeholders is created and a potential game is employed with a distributed primal-dual perturbed algorithm, and its convergence and optimality have been both proved. Moreover, an uncertainty and robustness analysis is done with coordination between lower and upper models, which deduces a feasible robust uncertainty interval in the lower-level model. For better dealing with the lower-level model, a gradient descent-based multiobjective differential evolution (GD-MODE) algorithm is utilized to optimize the economic cost and emission issue simultaneously, producing a set of Pareto-optimal schemes. Combined with simulation results, it is proven that the proposed method can reduce computational complexity as well as properly deal with uncertainty problems for the optimal operation of HESs.

Pareto optimal solution set strategy based on multiobjective optimization for the clinching tools

Pareto optimal solution set strategy based on multiobjective optimization for the clinching tools

Eco-CCUS: A cost-effective pathway towards carbon neutrality in China

Carbon capture, utilization and storage (CCUS) technologies have attracted great expectations to meet carbon neutrality targets by reducing atmospheric CO2 concentrations. However, most of the existing CCUS technologies are based on an industrial approach with disproportionate economic cost and environmental side effects and remain at an early stage of technological development. This study proposed an ecosystem-based CCUS strategy (Eco-CCUS) to exploit the enormous carbon sequestration potential of ecosystems with low economic cost and mature technology. With undeveloped crop residues as feedstock, it was estimated that Eco-CCUS could bring 0.38 Gt CO2 sequestration capacity every year in China (accounting for 36.89% of the CO2 fixation rates of a terrestrial ecosystem) and has a lower economic cost (100.93 ± 9.38 Yuan/tCO2) compared to that of traditional CCUS technologies. Further analysis showed that the low economic cost of Eco-CCUS was closely related to high crop density, low gross domestic product, and medium transportation distance. A Pareto-optimal strategy was employed to help minimize national aggregate economic costs and identify the priority regions during nationwide deployment of Eco-CCUS. Moreover, Eco-CCUS can bring considerable economic benefit for farmers (223.08 ± 19.60 Yuan per capita) with the future highly developed carbon trade market. This study offers a promising and cost-effective technology to help achieve the carbon neutrality goal, contributing to the sustainable economic and ecological development of contemporary rural China.

Towards Robust Task Assignment in Mobile Crowdsensing Systems

Mobile Crowdsensing (MCS), which assigns outsourced sensing tasks to volunteer workers, has become an appealing paradigm to collaboratively collect data from surrounding environments. However, during actual task implementation, various unpredictable disruptions are usually inevitable, which might cause a task execution failure and thus impair the benefit of MCS systems. Practically, via reactively shifting the pre-determined assignment scheme in real time, it is usually impossible to develop reassignment schemes without a sacrifice of the system performance. Against this background, we turn to an alternative solution, i.e., proactively creating a robust task assignment scheme offline. In this work, we provide the first attempt to investigate an important and realistic RoBust Task Assignment (RBTA) problem in MCS systems, and try to strengthen the assignment scheme's robustness while minimizing the workers' traveling detour cost simultaneously. By leveraging the workers' spatiotemporal mobility, we propose an assignment-graph-based approach. Firstly, an assignment graph is constructed to locally model the assignment relationship between the released MCS tasks and available workers. And then, under the framework of evolutionary multi-tasking, we devise a population-based optimization algorithm, namely EMTRA, to effectively achieve adequate Pareto-optimal schemes. Comprehensive experiments on two real-world datasets clearly validate the effectiveness and applicability of our proposed approach.

Modeling desirable futures at local scale by combining the nature futures framework and multi-objective optimization

AbstractEnvisioning positive scenarios that recognize the multiple values of nature is fundamental for designing transformative changes in local socio-ecological systems. This study developed a protocol with three specifications for operationalizing the Nature Futures Framework (NFF) in a landscape scenario analysis using a multi-objective optimization framework composed of: (1) exploring nature-positive futures, (2) seeking alternative pathways for targets satisfying visions of plural values, and (3) screening key direct drivers to achieve the targets. This research conducted a case study of a rural landscape in northeastern Japan. First, 110 strategies of landscape management options were simulated from 2015 to 2100 using a forest landscape model, LANDIS-II. The simulation developed a data frame of four integrated indicators of the NFF values for each year and strategy. Second, nature-positive strategies were screened using the common values. Pareto optimal strategies were then identified to obtain equally good solutions. Finally, the key response options to achieve good nature-positive futures were identified using decision tree analysis. Our protocol identified (1) multiple, but few nature-positive and Pareto optimal strategies that satisfied NFF visions, (2) nature-positive, but not Pareto optimal strategies, and (3) non-nature-positive strategies. In most Pareto optimal strategies, the maximized value perspectives changed over time. Our protocol also identified key response options to achieve three different NFF value perspectives in the case study area: (1) clear or selective cutting in forestry and (2) solar PV installation on abandoned pastureland in agriculture and energy sectors. We discussed the implication for local landscape management, localizing NFF narratives to develop future scenarios and modeling practice of NFF. The protocol does not depend on a specific model and indicator. Thus, our scalable protocol can be applied to scenarios and model practices in any region to support envisioning plausible, feasible, and positive futures, and designing future stakeholder collaboration.

Mean-Field Control for Stochastic Delay Systems via Static Output Feedback Strategy

In this paper, we consider mean-field control based on the static output feedback (SOF) strategy for stochastic delay systems. First, we define a stabilization problem via SOF gains in block-diagonal forms for systems with a single player, and then solve the problem of minimizing the upper bound of the cost function by cost-guaranteed cost control theory. For this problem, the necessary conditions for the sub-optimality are established using stochastic large-scale matrix equations. The obtained preliminary results are then used to study Pareto optimal strategies in cooperative games, for mean-field stochastic systems involving a large number of players. The primary contribution of this study is the derivation of a design method for decentralized strategies. Furthermore, a new low-order computational algorithm based on Newton's method is developed to obtain the decentralized strategy set. The cost degradation of the proposed decentralized SOF strategy set is then estimated. Finally, a simple numerical example is presented to demonstrate the usefulness and effectiveness of the proposed method. As a result, it is determined that the decentralized SOF strategy works well even when the number of players goes to infinity.

H∞$$ {H}_{\infty } $$ constraint Pareto optimal control for discrete‐time Markov jump linear stochastic systems in finite horizon

AbstractThis paper mainly focuses on discrete‐time Markov jump linear stochastic systems (DMJLSSs) with external disturbances and multiplicative noise. Due to the multi‐player in the systems and multi‐objective cost function, the strategy design for these systems is more difficult than the traditional Markov jump stochastic systems. We combine theory with Pareto control and use the weighted sum method of the objective functional of each player to solve the problem of Pareto cooperative game. Four coupled difference matrix‐valued recursion equations (CDMREs) are derived by stochastic bounded real lemma (SBRL). Then, a sufficient and necessary condition for the existence of the Pareto optimal strategy is obtained, and the Pareto solution for every controller is derived under this strategy. A simulation example is given to verify the correctness of the theory.

Privileged or ordinary carrier: strategic choice in a competitive environment

ABSTRACT Facing the increasing demand for ocean transportation, transport participants are seeking new ways of cooperation to improve overall productivity. In this study, we suppose a terminal operator would propose an agreement, in which carriers who choose to sign the agreement with the terminal operator could be a privileged carrier, otherwise they can only be an ordinary one. The berth requirements of privileged carriers will be satisfied in priority, resulting in certain operation efficiency improvements. A non-cooperative model is proposed to investigate two competing carriers of two transportation chains about whether to be the privileged carrier. It is noticed that the equilibrium strategies for two carriers are always the same. The operation efficiency and intensity of competition are the two key factors influencing the optimal strategy. When the efficiency improvement is at an appropriate level, it is more profitable for carriers to sign the agreement with the terminal operator. When the operation efficiency is at a high level and intensity of competition between two carriers is comparatively greater, the Pareto-optimal strategy will be selected to be the ordinary carrier. Furthermore, we discuss some extensions to prove the robustness of our main insights.

New algorithm for checking Pareto optimality in bimatrix games

Bimatrix games have had theoretical importance and important applications since the very beginning of game theory to date. Pareto optimal strategy vectors represent a reasonable and frequently applied solution concept (basically in the cooperative approach). Particularly, it often arises whether a non-cooperative solution can be improved in cooperative sense, i.e. it is Pareto optimal or not. However, in concrete cases it may be hard to determine the Pareto optimal strategy vectors or at least check the Pareto optimality of a given strategy vector. In the present paper, the Pareto optimality of the strategy pairs in general n × m (n = 2,3, ldots; m = 2,3, ldots) bimatrix games is studied. First of all an elementary proof is provided for a theorem, which makes the proposed Pareto optimality checking algorithm simpler. Then a nonlinear transform is proposed, which makes the algorithm even more convenient in the important case of 2 × 2 bimatrix games (and for certain other cases). Two numerical examples present the practical applicability of the checking algorithm. The problem of 2 × 2 bimatrix games can be solved even by hand. For larger games, numerous computational tools are available in the practice to apply the checking algorithm in exact or at least approximate way.