Pareto Optimality Conditions Research Articles

Prioritized optimization by Nash games : towards an adaptive multi-objective strategy

This work is part of the development of a two-phase multi-objective differentiable optimization method. The first phase is classical: it corresponds to the optimization of a set of primary cost functions, subject to nonlinear equality constraints, and it yields at least one known Pareto-optimal solution xA*. This study focuses on the second phase, which is introduced to permit to reduce another set of cost functions, considered as secondary, by the determination of a continuum of Nash equilibria, {x̅ε} (ε≥ 0), in a way such that: firstly, x̅0=xA* (compatibility), and secondly, for ε sufficiently small, the Pareto-optimality condition of the primary cost functions remains O(ε2), whereas the secondary cost functions are linearly decreasing functions of ε. The theoretical results are recalled and the method is applied numerically to a Super-Sonic Business Jet (SSBJ) sizing problem to optimize the flight performance.

Some Approaches for Fuzzy Multiobjective Programming Problems

In this paper we discuss two approaches to bring a balance between effectiveness and efficiency while solving a multiobjective programming problem with fuzzy objective functions. To convert the original fuzzy optimization problem into deterministic terms, the first approach makes use of the Nearest Interval Approximation Operator (Approximation approach) for fuzzy numbers and the second one takes advantage of an Embedding Theorem for fuzzy numbers (Equivalence approach). The resulting optimization problem related to the first approach is handled via Karush- Kuhn-Tucker like conditions for Pareto Optimality obtained for the resulting interval optimization problem. A Galerkin like scheme is used to tackle the deterministic counterpart associated to the second approach. Our approaches enable both faithful representation of reality and computational tractability. They are thus in sharp contrast with many existing methods that are either effective or efficient but not both. Numerical examples are also supplemented for the sake of illustration.

Cooperative Game Approach to Robust Control Design for Fuzzy Dynamical Systems.

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

Determining transmission line path alternatives using a valley-finding algorithm

Since new (Power) Transmission Lines (TLs) can have a long-term effect on the makeup of a landscape and on the human living space, it should be expected that the route of any new TL will be based on objective criteria that take into account the views of the public. Geographic Information Science (GIScience) provides powerful tools that assist in the determination of feasible locations for new TLs based on objective criteria and georeferenced data by combining methods from Multi-Criteria Decision Analysis (MCDA) and Least Cost Path (LCP) analysis. If such an approach is applied, the LCP analysis usually yields one optimal result. However, stakeholders and decision-makers prefer to compare multiple distinct path alternatives in order to find a solution that will be acceptable to as many stakeholders as possible.We have developed a method that calculates spatially distinct and Pareto optimal path alternatives based on the same cost surface using an algorithm for determining valleys on a Digital Elevation Model (DEM) to determine local low-cost points, which were then connected to a network graph by geometrical rules. Finally, we selected all non-dominated path alternatives that represented Pareto optimal conditions regarding a specific main objective. We then asked ten expert stakeholders to cross-compare the calculated path alternatives and assess our novel method. The concept of applying linear programming to obtain Pareto optimal path alternatives yielded routings that were mostly preferred over the LCP and had a greater likelihood of being realized than the results obtained by conducting the LCP analysis. The stakeholders determined the method's key concept to be useful and assert it a high potential to support planning, matter-of-fact argumentation, and discussions about TL routing.

Magnitude of inefficiency

Various types of inefficiencies of a system state like the Nash equilibrium (NE) exist, such as social inefficiency, Pareto inefficiency, etc. (A system state is inefficient if it is inferior to another realizable state.) Firstly, this article presents a general procedure to obtain each inefficiency measure. The procedure brings as each inefficiency measure, the maximum degree of corresponding inferiority of the state to some other. We examine the procedure in the game-theory context. Vastly-many people use the social-inefficiency measure (represented by the price of anarchy [PoA]). However, it cannot always serve as a Pareto-inefficiency measure. Contrarily, the Pareto-inefficiency measures are yet to establish. Secondly, we follow the procedure (to which PoA also conforms) and obtain Pareto-inefficiency measures. We confirm that they distinguish Pareto inefficiencies that PoA cannot always distinguish. We show a fixed relation between the values of the measures. Further, if a state is proportional to a Pareto-optimal state, proposed measures of strict Pareto inefficiency and Pareto inefficiency behave in identical and straightforward ways. Then, their value is the proportionality constant. Using examples, we examine the measures.

Optimizing wheat production and reducing environmental impacts through scientist-farmer engagement: Lessons from the North China Plain.

Producing high economic benefits and high grain yields with limited environmental impacts is crucial for feeding the world's growing population. Yet it remains challenging to improve the performance of one objective without creating unintended consequences for other objectives. This is especially difficult for smallholders navigating a diverse array of environmental and personal demands. This study demonstrates how combining participatory research through the Science and Technology Backyards (STB) approach with Pareto‐based ranking modeling can increase smallholder production while also reducing environmental impact. Through an intensive farmer survey in a 1 × 1 km grid in Quzhou County, we demonstrate that farmers engaged in STBs performed better according to multiple objectives (i.e., optimizing overall grain yield, benefit‐cost ratio, and GHG emissions, without compromising any one of these objectives) than farmer's not engaged in STBs. Moreover, we used a Pareto optimization approach (OPT) to determine the optimal smallholder scenario. We found that under OPT, grain yield could reach 9.5 t/ha, with a benefit‐cost ratio of 2.1, a 100% N recovery efficiency, and 7,395 kg CO2eq ha−1 GHG emissions. With OPT as a final goal, our research team worked with STB farmers to improve economic and environmental outcomes without compromising yield. Our findings demonstrate that no significant difference was obtained between farmers engaged in STBs and these under OPT. Compared with non‐STB farmers, STB farmers’ grain yield improved by 18%, benefit‐cost ratio improved by 26% due to improved N recovery efficiency, and GHG emissions were reduced by 31%. These improvements demonstrate the power of scientist–farmer engagement for optimizing wheat production. Such engagement allows farmers to modify their agronomic practices to more closely match Pareto optimal conditions, thus improving environmental and economic benefits without compromising yield. Our results provide solid evidence of the potential for sustainable wheat production by combining modeling with participatory research.

Multiagent Collaborative Governance for Targeted Poverty Alleviation from the Perspective of Stakeholders

As a social problem involving a wide range of objects, targeted poverty alleviation governance needs to clearly define stakeholders and identify their behaviour choices, so as to seek a multiagent collaborative governance strategy, and strive to jointly promote the realization of a targeted poverty alleviation goals in an atmosphere to win-win cooperation and benefit sharing. By constructing a three-subject evolutionary game model of local government, social organization, and poverty group in the process of targeted poverty alleviation, this paper discusses the influence of their behavioural decisions on multisubject collaborative governance of targeted poverty alleviation and selects samples to carry out simulation experiments on the model. The results show that, first, superior government support has little effect on the evolution of tripartite competition, and the conclusion is inconsistent with the general cognition. However, the enhancement of support from local governments and social organizations can effectively promote the transformation of the willingness of the poor groups to cooperate. Second, a modest increase in the punishment of social organizations and poor groups can have a binding effect on the behavioural strategy choices of both sides and ultimately promote the process of targeted poverty alleviation. Third, the increase in the benefits of social organizations and poor groups can significantly improve the willingness of both sides to cooperate, so the “endogenous driving force” of the poor groups should be enhanced to achieve the Pareto optimal state of targeted poverty alleviation.

Pareto Assumption for Constrained PSO-Based Locomotive Resistance Minimization

The mechanical resistance of a locomotive is crucial for power consumption. It is desirable to maintain this resistance at a minimum value for energy efficiency under optimal operation conditions. The optimal conditions can be found by particle swarm optimization with constraints. The particle swarm optimization method is a highly preferred type of heuristic algorithm because of its advantages, such as fewer parameters, faster speed, and a simpler flow diagram. However, fast convergence can be misleading in finding the optimum solution in some cases. Pareto analysis is used in this proposed study to prevent missing the target. When the literature is searched, it is seen that there are various studies using this method. However, in all of these studies, the results of the particle swarm method have been interpreted as whether or not they complied with Pareto’s 80/20 rule. The validity of the Pareto analysis is taken as an assumption, and with the help of this assumption, the coefficients of a locomotive’s mathematical equation were changed, and finally the results were found by applying the particle herd optimization method. Finally, a novel hybrid method has been created by including the Pareto optimality condition to particle swarm optimization. The results are compared with this innovative hybrid method of Pareto and particle swarm and the results found using only the particle swarm method.

Multi-objective robust generalised H 2 control

A novel multi-objective robust control problem is studied for systems with norm-bounded structured uncertainty and robust generalised norms as criteria. Necessary conditions for Pareto optimality are formulated from which it follows that Pareto optimal solutions are to be among optimal solutions for scalar multi-objective costs in the form of Germeyer convolution. The upper bounds of the multi-objective costs are used to compute Pareto suboptimal controllers in terms of linear matrix inequalities, while the lower bounds to estimate a ‘difference’ between Pareto suboptimal and unavailable Pareto optimal controllers. Two-criteria robust control problem for a mathematical model of the rotor rotating in active magnetic bearings is considered as an application of this theory.

Necessary/sufficient conditions for Pareto optimality in finite horizon mean-field type stochastic differential game

This paper is concerned with necessary and sufficient conditions for the existence of Pareto solutions in finite horizon mean-field type stochastic cooperative differential game. Based on the equivalent characterization of Pareto optimality, the problem is transformed into a set of constrained mean-field type stochastic optimal control problems with a special structure. Utilizing the mean-field type stochastic minimum principle, the necessary conditions are put forward. Under certain convex assumptions, it is shown that the necessary conditions are also sufficient ones. Next, the indefinite linear quadratic (LQ) case is studied. It is pointed out that the solvability of two related generalized differential Riccati equations (GDREs) provides a sufficient condition under which Pareto efficient strategies are equivalent to weighted sum optimal controls. In addition, all Pareto solutions are obtained based on the solutions of two generalized differential Lyapunov equations (GDLEs). At last, an example sheds light on the effectiveness of the theoretical results.

On weak Pareto optimality of nonatomic routing networks

This paper establishes several sufficient conditions for the weak Pareto optimality of Nash equilibria in nonatomic routing games on single- and multi-commodity networks, where a Nash equilibrium (NE) is weakly Pareto optimal (WPO) if under it no deviation of all players could make everybody better off. The results provide theoretical and technical bases for characterizing graphical structures for nonatomic routing games to admit WPO NEs. We prove that the NE of every nonatomic routing game on a single or multi-commodity network is WPO (regardless of the choices of nonnegative, continuous, nondecreasing latency functions on network links) if the network does not have two links x, y and three paths each of which goes from some origin to some destination such that the intersections of the three paths with $$\{x,y\}$$ are $$\{x\},\{y\}$$ and $$\{x,y\}$$, respectively. This sufficient condition leads to an alternative proof of the recent result that the NE of every 2-commodity nonatomic routing game on any undirected cycle is WPO. We verify a general property satisfied by all feasible 2-commodity routings (not necessarily controlled by selfish players) on undirected cycles, which roughly says that no feasible routing can “dominate” another in some sense. The property is crucial for proving the weak Pareto optimality associated to the building blocks of undirected graphs on which all NEs w.r.t. two commodities are WPO.

The Economic Development of Urban Planning in China

To study the enlightenment of development economics on the economic development of urban planning, firstly, the research background and significance of the enlightenment of development economics on the economic development of urban planning are introduced. Secondly, through the main method of literature review, social investigation method, theoretical model analysis method and so on, combined with relevant theory of economics and related data analysis, it is found that economic theory can effectively explain the problems existing in the urban planning, avoid possible problems in urban planning, and provide effective theory basis for the development of the city. In this study, the theoretical value of the sub-optimal theoretical model, the supply and demand analysis model and the marginal analysis model under the pareto optimal state in the economic development of urban planning is mainly studied. A large number of theories and research results confirm that to do a good job in urban planning must be guided by relevant economic theories, which will make the progress of urban planning more rapid.

A multi-objective framework for multidimensional vulnerability assessment – Case of a coastal district of West Bengal, India

Vulnerability assessment for disaster studies pertaining to natural hazards has evolved as a discipline in itself. The multidimensional approach for the design of a vulnerability framework is widely accepted and used, where the prevalently used dimensions are economic, social, physical, environmental. Although the dimensions of vulnerability are distinct, these are commonly aggregated together to compute the overall vulnerability of a place (i.e. composite vulnerability). It is observed this practice leads to loss of information and averaging out of scores obtained from individual dimensions of vulnerability. This study proposes a new framework for assessing multidimensional vulnerability of a region in a multi-objective framework. Individual dimension of vulnerability is computed using a new aggregator function proposed in the study. The proposed methodology has been demonstrated using the case study of a coastal district (South 24 Parganas) in West Bengal, India. It is one of the most impoverished districts of the state and has been exposed to multiple incidences of catastrophic events like tropical cyclones, storm surges and flooding. The vulnerability indices for each dimension of vulnerability were calculated using the proposed aggregator function. Pareto optimality conditions were used to obtain a Pareto frontier from where the Blocks having highest overall vulnerability were selected. This method was repeatedly used to sort the vulnerabilities of all the constituent Blocks of the district in varying levels of vulnerabilities. It was observed that Gosaba, Patharprotima, Kultali, Canning-II, Namkhana and Sagar were the most vulnerable Blocks in the district. This methodology posits that the hierarchy-based clustering system obtained from non-weighted Pareto optimality conditions is better in terms of evaluating the vulnerability of a region. It provides a system of evaluation which is free from decision maker's prejudices and guards it against loss of information - thus eliminating two weaknesses of conventional aggregation methods. It also makes it easier to arrive at specific disaster management policies.

Grouping detection and forecasting security controls using unrestricted cooperative bargains

Security controls are widely used to minimize the effects generated by unwanted events, such as malicious network traffic. However, incompatibilities between these controls make integration actions (grouping) difficult in order to improve results. This problem becomes more evident when the evaluated controls are of different types, for example, detection and forecasting. In these cases, the scientific literature is still rare. Our hypothesis to solve the problem is based on the analysis of events at two levels of abstraction: the technical level and the strategic level. Our proposal, called Strategic Grouping Architecture (SGA), uses negotiations based on Unrestricted Cooperative Bargains (UCB) to carry out a balancing that leads to the best choices of configuration and results considering the evaluated controls. As a proof of concept, we created a ranking-based experiment to group detection and prediction controls in a real scenario. The application of the SGA in the ranking resulted in anticipated predictions of attacks with a hit rate from 99.95%. As comparison with other methods, we change the ranking data into a noncooperative game and the results have reached the Nash Equilibrium (NE) and Pareto optimal state, showing the reliability of the architecture. •Effective grouping of detection security controls with predictive controls.•The use of Unrestricted Cooperative Bargain (UCB) processes to balance grouping results.•The implementation of a ranking to predict attacks in a detection environment with two filters.

Linear Quadratic Pareto Game of the Stochastic Systems in Infinite Horizon

This paper investigates the necessary/sufficient conditions for Pareto optimality in the infinite horizon linear quadratic stochastic differential game. Based on the necessary and sufficient characterization of the Pareto optimality, the problem is transformed into a set of constrained stochastic optimal control problems with a special structure. Under the assumption about the Lagrange multipliers, utilizing the stochastic Pontryagin maximum principle, the necessary conditions for the existence of the Pareto efficient strategies are presented. Furthermore, a condition is introduced to guarantee that the element zero does not belong to the Lagrange multiplier set. In addition, the necessary conditions, the convexity condition on the weighted sum cost functional and a transversality condition provide the sufficient conditions for a control to be Pareto efficient. The characterization of Pareto efficient strategies and Pareto solutions is also studied. If the system is stabilizable, then the solvability of the related generalized algebraic Riccati equation provides a sufficient condition under which all Pareto efficient strategies can be obtained by the weighted sum optimality method and all Pareto solutions can be derived based on the solutions of an introduced algebraic Lyapunov equation.

Parallel proximal point methods for systems of vector optimization problems on Hadamard manifolds without convexity

ABSTRACTIn this paper, the local weak Pareto optimality conditions for nonsmooth vector optimization problems are presented on Hadamard manifolds. Some convergence results of the parallel proximal point algorithms for finding a solution of vector optimization problems are established.

Thin-walled tubes under torsion: multi-objective optimal design

The lightweight design of a thin-walled tube under torsion is addressed in the paper. A multi-objective optimization approach is adopted to minimize the mass while maximizing the structural stiffness of the thin walled tube. Constraints on available room (maximum diameter), safety (admissible stress), elastic stability (buckling), minimum thickness (forced by manufacturing technologies) are included in the problem. The analytical solution of the multi-objective optimization problem is obtained by applying a relaxed formulation of the Fritz John conditions for Pareto-optimality. Relatively simple analytical expressions of the Pareto-optimal set are derived both in the design variables (tube diameter and wall thickness) and objective functions (mass and compliance) domain. Simple practical formulae are provided to the designer for the preliminary design of thin-walled tubes under torsion. Finally, the comparative lightweight design of tubes made from different materials is presented and an application of the derived formulae to a simple engineering problem is discussed.

Multi-objective generalized [formula omitted] control

Multi-objective control problem with generalized H2-norms as criteria, as well as its dual problem with generalized γ0-norms, is studied. By using a scalar multi-objective cost function in the form of Germeyer convolution we derive necessary conditions for Pareto optimality and characterize Pareto optimal controllers in terms of LMIs as optimal solutions for this function. Optimal protection of a high storey building from vibration is then considered in the novel multi-objective framework as an application of the approach proposed.

Design-oriented regression models for H2O2 decontamination processes in sterile drug product manufacturing considering rapidity and sterility

We developed regression models for designing rapid and effective H2O2 decontamination processes in the manufacturing of sterile drug products such as injectables. Decontamination, which is typically performed by using H2O2, is a critical changeover process used to establish a sterile environment for filling products. In the process, there is a trade-off relationship between the duration of the process and the level of sterility assurance that needs to be considered in the design. Our model defines these two items as objective functions and the parameters describing the profile of H2O2 injection and the initial humidity as design variables. Our model also considers aeration, i.e., removal of H2O2 from the environment, as a part of the entire process. This design-oriented modeling considering the entire process is the novelty of the work. Experiments were performed using an industrial isolator to develop and validate a set of regression models that describe the relationship between the design variables and the objective functions. In the application of the model, Pareto-optimal conditions could be indicated given the target H2O2 concentration in aeration, which is useful for the makers of drugs and/or isolators for designing decontamination processes.

Necessary and sufficient conditions for Pareto optimality of the stochastic systems in finite horizon

This paper is concerned with the necessary and sufficient conditions for the Pareto optimality in the finite horizon stochastic cooperative differential game. Based on the necessary and sufficient characterization of the Pareto optimality, the problem is transformed into a set of constrained stochastic optimal control problems with a special structure. Utilizing the stochastic Pontryagin minimum principle, the necessary conditions for the existence of the Pareto solutions are put forward. Under certain convex assumptions, it is shown that the necessary conditions are also sufficient ones. Next, we study the indefinite linear quadratic (LQ) case. It is pointed out that the solvability of the related generalized differential Riccati equation (GDRE) provides the sufficient condition under which all Pareto efficient strategies can be obtained by the weighted sum optimality method. Two examples shed light on the effectiveness of theoretical results.