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For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data, and an optimizer, for example, a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs. [ABSTRACT FROM AUTHOR]

In this study, we have carried out a comparative analysis of a fixed bed reactor (FBR) and reverse flow chromatographic reactor (RFCR) for a series reaction. This comparison has been carried out using mathematical model based single and multi-objective optimization. In addition, since the model merely approximates the actual process, there is an inherent presence of uncertainty in it. To account for the uncertainty, optimization is done considering the uncertainty in the key model parameters. Three objective functions are used in this work for the comparative study, namely yield, selectivity, and conversion. The decision variables used in the optimization problem are the inlet concentration, Damkohler number, and dimensionless switching time. The multi-objective optimization results have been analysed in terms of optimal Pareto fronts for three bi-objective and one tri-objective optimization problems. A detailed analysis of the Pareto fronts for both the reactors is presented for five distinct representative Pareto points. The results of the work indicated the superiority of RFCR over FBR. In particular, a representative Pareto point solution of 3-objective problem in RFCR corresponds to 51.36% higher yield, 27.06% higher selectivity and 19.15% higher conversion as compared to FBR. [Display omitted] • Multi-objective optimization study of reverse flow chromatographic reactor and fixed bed reactor. • Process criteria for the multi-objective study include the maximization of yield, selectivity, and conversion. • Optimization variables include switching time, Damkohler number and inlet concentration. • RFCR shows 51.39%, 27.06%, and 19.15% improvement in yield, selectivity, and conversion, respectively as compared to FBR. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonmonotone gradient method for smooth constrained multiobjective optimization problems. Under mild assumptions, we demonstrate the Pareto stationarity of the accumulation point of the sequence generated by this method, while the convergence of the full sequence to a weak Pareto optimal solution of the problem is proven when the function is convex. Further, by imposing some assumptions on the gradients of the objective functions and the search directions, the linear convergence of the function value sequence to the optimal value is provided. The initial point in the convergence results established here can be any one in the constraint set. [ABSTRACT FROM AUTHOR]

• Virtual water strategies might lead to economic decline. • A framework is established to identify the non-inferior solutions for the strategies. • Optimized strategies benefit the tradeoff between water conservation and economy. Despite the effectiveness of virtual water strategies for water resource conservation, this approach has not yet been widely adopted in real-world water resource management. One major reason is that previous research on this approach emphasized its water conservation effects, but understated its economic impacts. In the present study, we combined a computable general equilibrium model with Pareto optimality analysis to establish an analytical framework. This framework can help planners to quantify the trade-offs between water resource conservation and economic development, and identify non-inferior solutions for virtual water strategies. We used the Luanhe River Basin as a case study, and considered three strategy sub-modes (promote-imports, limit-production, and dual-policy) and five water-intensive agricultural sub-sectors (cotton, oilseeds, melons and fruits, grains, and vegetables). We found that although the virtual water strategy can improve water conservation, it has negative effects on economic development; compared with the promote-imports modes, the limit-production and dual-policy modes were non-inferior choices; cotton was an inferior agricultural sub-sector to implement the virtual water strategy. [ABSTRACT FROM AUTHOR]

Ethanol is among the largest fermentation product used worldwide, accounting for more than 90 % of all biofuel produced in the last decade. However current production methods of ethanol are unable to meet the requirements of increasing global demand, because of low yields on glucose sources. In this work, we present an in silico multi-objective optimization and analyses of eight genome-scale metabolic networks for the overproduction of ethanol within the engineered cell. We introduce MOME (multi-objective metabolic engineering) algorithm, that models both gene knockouts and enzymes up and down regulation using the Redirector framework. In a multi-step approach, MOME tackles the multi-objective optimization of biomass and ethanol production in the engineered strain; and performs genetic design and clustering analyses on the optimization results. We find in silico E. coli Pareto optimal strains with a knockout cost of 14 characterized by an ethanol production up to 19.74 mmol gDW - 1 h - 1 ( + 832.88 % with respect to wild-type) and biomass production of 0.02 h - 1 ( - 98.06 % ). The analyses on E. coli highlighted a single knockout strategy producing 16.49 mmol gDW - 1 h - 1 ( + 679.29 % ) ethanol, with biomass equals to 0.23 h - 1 ( - 77.45 % ). We also discuss results obtained by applying MOME to metabolic models of: (i) S. aureus; (ii) S. enterica; (iii) Y. pestis; (iv) S. cerevisiae; (v) C. reinhardtii; (vi) Y. lipolytica. We finally present a set of simulations in which constrains over essential genes and minimum allowable biomass were included. A bound over the maximum allowable biomass was also added, along with other settings representing rich media compositions. In the same conditions the maximum improvement in ethanol production is + 195.24 % . [ABSTRACT FROM AUTHOR]

The advantages of the simultaneous integration of production and time-lapse seismic data for history matching have been demonstrated in a number of previous studies. Production data provide accurate observations at particular spatial locations (wells), while seismic data enable global, though filtered/noisy, estimates of state variables. In this work, we present an efficient computational tool for bi-objective history matching, in which data misfits for both production and seismic measurements are minimized using an adjoint-gradient approach. This enables us to obtain a set of Pareto optimal solutions defining the optimal trade-off between production and seismic data misfits (which are, to some extent, conflicting). The impact of noise structure and noise level on Pareto optimal solutions is investigated in detail. We discuss the existence of the “best” trade-off solution, or least-conflicting posterior model, which corresponds to the history-matched model that is expected to provide the least-conflicting forecast of future reservoir performance. The overall framework is successfully applied in 2D and 3D compositional simulation problems to provide a single least-conflicting posterior model and, for the 2D case, multiple samples from the posterior distribution using the randomized maximum likelihood method. [ABSTRACT FROM AUTHOR]

Bubbly Markov equilibria (BME) are recursive equilibria on the natural state space which admit a non-trivial bubble. The present paper studies the existence and properties of BME in a general class of overlapping generations economies with capital accumulation and stochastic production shocks. Using monotone methods, we develop a general approach to construct Markov equilibria and provide necessary and sufficient conditions for these equilibria to be bubbly. Our main result shows that a BME exists whenever the bubbleless equilibrium is Pareto inefficient due to either overaccumulation of capital or inefficient risk sharing between generations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Wireless multihop networks (WMHNs) have to strike a trade-off among diverse and often conflicting quality-of-service requirements. The resultant solutions may be included by the Pareto front under the concept of Pareto optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as non-deterministic polynomial-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms has been proposed, namely the non-dominated quantum optimization and the non-dominated quantum iterative optimization. However, their complexity is proportional to $\sqrt {N}$ , where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in “polynomial time.” As a remedy, we devise a dynamic programming framework and propose the so-called evolutionary quantum pareto optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction. [ABSTRACT FROM AUTHOR]

We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity , indicating the maximum number of courses and applicants they can be assigned to, respectively. We thus essentially have a many-to-many bipartite matching problem with one-sided preferences, which has applications to the assignment of students to optional courses at a university. We consider additive preferences and lexicographic preferences as two means of extending preferences over individual courses to preferences over bundles of courses. We additionally focus on the case that courses have prerequisite constraints: we will mainly treat these constraints as compulsory, but we also allow alternative prerequisites. We further study the case where courses may be corequisites. For these extensions to the basic problem, we present the following algorithmic results, which are mainly concerned with the computation of Pareto optimal matchings (POMs). Firstly, we consider compulsory prerequisites. For additive preferences, we show that the problem of finding a POM is NP-hard. On the other hand, in the case of lexicographic preferences we give a polynomial-time algorithm for finding a POM, based on the well-known sequential mechanism. However we show that the problem of deciding whether a given matching is Pareto optimal is co-NP-complete. We further prove that finding a maximum cardinality (Pareto optimal) matching is NP-hard. Under alternative prerequisites, we show that finding a POM is NP-hard for either additive or lexicographic preferences. Finally we consider corequisites. We prove that, as in the case of compulsory prerequisites, finding a POM is NP-hard for additive preferences, though solvable in polynomial time for lexicographic preferences. In the latter case, the problem of finding a maximum cardinality POM is NP-hard and very difficult to approximate. [ABSTRACT FROM AUTHOR]

Typical design for manufacturing applications requires simultaneous optimization of conflicting performance objectives: Design variations that improve one performance metric may decrease another performance metric. In these scenarios, there is no unique optimal design but rather a set of designs that are optimal for different trade-offs (called Pareto-optimal). In this work, we propose a novel approach to discover the Pareto front, allowing designers to navigate the landscape of compromises efficiently. Our approach is based on a first-order approximation of the Pareto front, which allows entire neighborhoods rather than individual points on the Pareto front to be captured. In addition to allowing for efficient discovery of the Pareto front and the corresponding mapping to the design space, this approach allows us to represent the entire trade-off manifold as a small collection of patches that comprise a high-quality and piecewise-smooth approximation. We illustrate how this technique can be used for navigating performance trade-offs in computer-aided design (CAD) models. [ABSTRACT FROM AUTHOR]

A constrained multi-objective optimization approach is applied to optimize the exergy efficiency and material costs of thermocline packed-bed thermal-energy storage systems using air as the heat-transfer fluid. The axisymmetric packed-bed’s height, top and bottom radii, insulation-layer thicknesses, and particle diameter were chosen as design variables. The competing objectives of maximizing the exergy efficiency and minimizing the material costs were treated by a Pareto front. The Pareto front allows identifying the most efficient design for a given cost or the cheapest design for a given efficiency and is an important tool to find the best overall design of storage systems for a specific application. Constraints were imposed to obtain storage systems with specified capacities and limits on the air outflow temperatures during charging and discharging. The results showed that a storage shaped as a truncated cone with the smallest cross-section at the top has a higher exergy efficiency than storages shaped as cylinders or truncated cones with the largest cross-section at the top. The higher efficiency is attributed to the axial temperature distribution in the packed bed and the associated conduction heat losses across the insulated walls. The optimization of an industrial-scale storage allowed identifying a design with an exergy efficiency that was only 4.8% below that of the most efficient design, but a cost that was 81.3% lower than the cost of the most efficient design. Compared to brute-force design approaches, the optimization procedure can reduce the computational time by 91–99%. [ABSTRACT FROM AUTHOR]

In this paper, we present a multi-objective solution of the Pareto front for a certain class of discrete-time ergodic controllable Markov chains. For solving the problem, we transform the original multi-objective problem into an equivalent nonlinear programming problem implementing the Lagrange principle. We then propose to adopt the Tikhonov’s regularization method to ensure the convergence of the cost functions to a unique point into the Pareto front. We show that Pareto policies are characterized as optimal policies. One of the fundamental problems related to the construction of the Pareto front is the existence and characterization of both, Pareto and strong Pareto policies. By introducing the Tikhonov’s regularizator, we ensure the existence of strong Pareto policies. This paper proposes a real solution to this problem. We formulate the original problem considering several constraints: (a) we employ the c-variable method for the introduction of linear constraints over the nonlinear problem and (b) restrict the cost functions, allowing points in the Pareto front to have a small distance from one another. The constraints imposed by the c-variable method make the problem computationally tractable and the restriction imposed by the small distance change ensures the continuation of the Pareto front. The resulting equation in this nonlinear system is an optimization problem for which the necessary and efficient condition of a minimum is solved using the projected gradient method. Moreover, we also prove the convergence conditions and compute the estimate rate of convergence of variables corresponding to the Lagrange principle and the Tikhonov’s regularization, respectively. We provide all the details needed to implement the proposed method in an efficient way. The usefulness of the method is successfully demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

For reinforcement learning tasks with multiple objectives, it may be advantageous to learn stochastic or non-stationary policies. This paper investigates two novel algorithms for learning non-stationary policies which produce Pareto-optimal behaviour (w-steering and Q-steering), by extending prior work based on the concept of geometric steering. Empirical results demonstrate that both new algorithms offer substantial performance improvements over stationary deterministic policies, while Q-steering significantly outperforms w-steering when the agent has no information about recurrent states within the environment. It is further demonstrated that Q-steering can be used interactively by providing a human decision-maker with a visualisation of the Pareto front and allowing them to adjust the agent’s target point during learning. To demonstrate broader applicability, the use of Q-steering in combination with function approximation is also illustrated on a task involving control of local battery storage for a residential solar power system. [ABSTRACT FROM AUTHOR]

We propose two strategies for choosing Pareto solutions of constrained multiobjective optimization problems. The first one, for general problems, furnishesbalancedoptima, i.e. feasible points that, in some sense, have the closest image to the vector whose coordinates are the objective components infima. It consists of solving a single scalar-valued problem, whose objective requires the use of a monotonic function which can be chosen within a large class of functions. The second one, for practical problems for which there is a preference among the objective’s components to be minimized, gives us points that satisfy this order criterion. The procedure requires the sequential minimization of all these functions. We also study other special Pareto solutions, thesub-balancedpoints, which are a generalization of the balanced optima. [ABSTRACT FROM AUTHOR]

This research work is devoted to significant open problems in the general Efficiency presented inside the best appropriate environment of the infinite dimensional Ordered Vector Spaces. Following our refined recent results, we especially use the largest class of the Convex Cones discovered till now in separated Locally Convex Spaces, named by us "Isac's Cones", and ensuring the existence together with important properties for the efficient points under completeness instead of compactness. These Open problems are also generated by the new links between the General Efficiency, the Vector (Strong) Optimization and the Choquet Boundaries, since the Efficiency is strongly related to the General Optimization, the Potential Theory and conversely, with projections in the new recent and future fields of Scientific Research: Theory and Applications of the Generalized Dynamical Systems, Fixed points Theory, the Best Approximation Theory, the study of the Conically Bounded Sets, the study of the Nuclearity for the Topological Vector Spaces. [ABSTRACT FROM AUTHOR]

We consider the allocation of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationship between two geometric objects of fair division: The Individual Pieces Set (IPS) and the Radon–Nykodim Set (RNS). The algorithm can be considered as an extension of the Adjusted Winner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness. [ABSTRACT FROM AUTHOR]

Spatial patterning often occurs in ecosystems as a result of a selforganizing process caused by feedback between organisms and the physical environment. Here, we show that the spatial patterns observable in centuries-old Balinese rice terraces are also created by feedback between farmers' decisions and the ecology of the paddies, which triggers a transition from local to globalscale control of water shortages and rice pests. We propose an evolutionary game, based on local farmers' decisions that predicts specific power laws in spatial patterning that are also seen in a multispectral image analysis of Balinese rice terraces. The model shows how feedbacks between human decisions and ecosystem processes can evolve toward an optimal state in which total harvests are maximized and the system approaches Pareto optimality. It helps explain how multiscale cooperation from the community to the watershed scale could persist for centuries, and why the disruption of this self-organizing system by the Green Revolution caused chaos in irrigation and devastating losses from pests. The model shows that adaptation in a coupled human-natural system can trigger self-organized criticality (SOC). In previous exogenously driven SOC models, adaptation plays no role, and no optimization occurs. In contrast, adaptive SOC is a self-organizing process where local adaptations drive the system toward local and global optima. [ABSTRACT FROM AUTHOR]

A new equivalent definition of proper efficiency is presented. With the aid of the new definition of properness, a transformation technique is proved to transform a multi-objective problem to a more convenient one. Some conditions are determined under which the original and the transformed problems have the same Pareto and properly efficient solutions. This transformation could be employed for the sake of convexification and simplification in order to improve the computational efficiency for solving the given problem. Moreover, some existing results about the weighted sum method in the multi-objective optimization literature are generalized using the special case of the proposed transformation scheme. [ABSTRACT FROM AUTHOR]

Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values. [ABSTRACT FROM AUTHOR]

We propose a decision-making framework to compute compromise solutions that balance conflicting priorities of multiple stakeholders on multiple objectives. In our setting, we shape the stakeholder dissatisfaction distribution by solving a conditional-value-at-risk (CVaR) minimization problem. The CVaR problem is parameterized by a probability level that shapes the tail of the dissatisfaction distribution. The proposed approach allows us to compute a family of compromise solutions and generalizes multi-stakeholder settings previously proposed in the literature that minimize average and worst-case dissatisfactions. We use the concept of the CVaR norm to give a geometric interpretation to this problem and use the properties of this norm to prove that the CVaR minimization problem yields Pareto optimal solutions for any choice of the probability level. We discuss a broad range of potential applications of the framework that involve complex decision-making processes. We demonstrate the developments using a biowaste facility location case study in which we seek to balance stakeholder priorities on transportation, safety, water quality, and capital costs. [ABSTRACT FROM AUTHOR]

We study a class of optimization problems involving linked recursive preferences in a continuous-time Brownian setting. Such links can arise when preferences depend directly on the level or volatility of wealth, in principal-agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first-order conditions, which are also sufficient under additional conditions ensuring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations. [ABSTRACT FROM AUTHOR]

We characterize the space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions where efficiency is not required. We examine a model with two players and k nonidentical items (2k outcomes), multidimensional types, private values, non-negative prices, and quasilinear preferences for the players with one relaxation - the players are subject to publicly-known budget constraints. We show that if it is publicly known that the players value the bundles more than the smaller of their budgets then the studied space includes one type of mechanism: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. Interestingly the above basic properties are a weaker requirement than it may initially appear, as the property of Pareto optimality in our model of budget-constrained players and non-negative prices do not coincide with welfare maximization, i.e., efficiency as such is a much weaker requirement. [ABSTRACT FROM AUTHOR]

Consider a many-to-many matching market that involves two finite disjoint sets, a set A of applicants and a set C of courses. Each applicant has preferences on the different sets of courses she can attend, while each course has a quota of applicants that it can admit. In this paper, we examine Pareto optimal matchings (briefly POM) in the context of such markets, that can also incorporate additional constraints, e.g., each course bearing some cost and each applicant having a limited budget available. We provide necessary and sufficient conditions for a many-to-many matching to be Pareto optimal and show that checking whether a given matching is Pareto optimal can be accomplished in O ( ∣ A ∣ 2 ⋅ ∣ C ∣ 2 ) time. Moreover, we provide a generalized version of serial dictatorship, which can be used to obtain any many-to-many POM. We also study some structural questions related to POM. We show that, unlike in the one-to-one case, finding a maximum cardinality POM is NP-hard for many-to-many markets. [ABSTRACT FROM AUTHOR]

Purpose -- This paper aims to compare Pareto optimality for altruistic and individualistic societies to show whether it is possible to have Pareto improvement through altruistic acts even after free market equilibrium. Design/methodology/approach -- The paper follows conceptual, axiomatic and theoretical approaches to show Pareto efficiency in altruistic versus individualistic societies. The paper first outlines the welfare axioms of Islamic economics compared to those of capitalism. Second, it defines Pareto efficiency within capitalist and Islamic economic systems. Third, it compares and contrasts the concept in the two systems based on their epistemological and anthropological worldviews. Fourth, it shows how -- even under the efficient allocation of material goods -- room for Pareto improvement still exists through the redistribution of resources. Finally, it demonstrates optimum income transfer for social welfare maximization. Findings -- The paper shows that Islamic economics relying on certain welfare axioms aim for an altruistic society. It then theoretically proves that social well-being would be greater in such an altruistic society in comparison to an individualistic society promoted by capitalism, holding everything else constant. The paper clearly shows that free market equilibrium does not maximize social utility. It theoretically demonstrates that even under efficient allocation of material goods, there is still room for Pareto improvement through redistribution of resources. It reveals that optimum income transfer might not be possible through voluntary altruistic behaviors unless people transcend self-interest and begin to value social interest as important as their own interest. Therefore, the paper suggests a role for the government to reach optimum-level income transfer for social welfare maximization. Research limitations/implications -- The paper is purely theoretical. Its main limitation is not to be empirically tested. Future studies might shed light on the issue through empirical evidence Practical implications -- Pareto improvement provides important guidance or at least moral justification for welfare programs. The paper might directly affect welfare policy of Muslim countries. Social implications -- The paper suggests income transfer through altruistic acts would provide higher social welfare. Therefore, it is in the best interest of nations to promote altruistic behaviors and support voluntary welfare programs for higher social utility. Originality/value -- The paper contributes to the Islamic moral economy doctrine by proving that altruistic behaviors encouraged by Islamic teaching could provide higher social welfare. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic optimal control problem of finding optimal dividend policies of an insurance company in discrete time with the use of general Lipschitz payoff functions involving indicators of profitability and risk. To construct positional optimal controls and to evaluate the performance indicators, the dynamic programming method is validated. The convergence rate of the successive approximation method in finding generally unbounded Bellman functions is estimated. The Pareto-optimal set of the problem is numerically approximated by so-called barrier-proportional control strategies. [ABSTRACT FROM AUTHOR]

We develop a population-based algorithm for the optimization of multiple, nonconvex, nondifferentiable, and possibly discontinuous objective functions. The algorithm employs Markov kernels, Hit-and-Run, and Pattern Hit-and-Run for exploration of the solution space and Pareto ordering rules for the selection of the population and to update the approximate Pareto optimal list. Our multiobjective interacting particle algorithm asymptotically converges to the stationary distribution associated with the Pareto ordering rules. We present numerical benchmark results on test problems. [ABSTRACT FROM AUTHOR]

We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent different and conflicting objectives associated with the scenarios. We utilize the interactive classification-based multiobjective optimization method NIMBUS for assessing the relative optimality of the current solution in different scenarios. This information can be utilized when considering the next step of the overall solution process. Decision making is performed by giving special attention to individual scenarios. We demonstrate our method with an example in portfolio optimization. [ABSTRACT FROM AUTHOR]

Abstract: A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coalition formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to various results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants. [Copyright &y& Elsevier]

The basic concepts and methods for multi-criteria synthesis of complex thin-walled ship structures in concept and preliminary design are presented. The principal steps in the definition of the design model, the selected general requirements on the design procedure and balanced and applicable combinations of design models are elaborated. The paper also provides an introduction to the basic theory, mappings, non-dominance concepts (Pareto frontier), spaces and sets used for the mathematical definition of design problems (DPs) together with the unified taxonomy applicable in the handling of complex DPs. System identification from the multi-stakeholder perspectives of owner and society and the formulations and solutions of structural DP are discussed. [ABSTRACT FROM PUBLISHER]

We consider the problem of approximating Pareto surfaces of convex multicriteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that optimally limit the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem can be solved by enumerative techniques but at a cost that increases exponentially with the number of objectives. We present an algorithm for solving the Pareto surface approximation problem that is practical with 10 or less conflicting objectives, motivated by an application to radiation therapy optimization. Our enumerative scheme is, in a sense, dual to a family of previous algorithms. The proposed technique retains the quality of the best previous algorithm in this class while solving fewer subproblems. A further improvement is provided by a procedure for discarding subproblems based on reusing information from previous solves. The combined effect of the enhancements is empirically demonstrated to reduce the computational expense of solving the Pareto surface approximation problem by orders of magnitude. For problems where the objectives have positive curvature, an improved bound on the approximation error is demonstrated using transformations of the initial objectives with strictly increasing and concave functions. [ABSTRACT FROM AUTHOR]

Abstract: A new method is proposed for approximating a Pareto front of a bound constrained biobjective optimization problem (BOP) where the evaluation of the objective functions is very expensive and/or the structure of the objective functions either cannot be exploited or not known. The method employs a hybrid optimization approach using two direct search techniques (dividing rectangles and mesh adaptive direct search). The algorithm iteratively formulates and solves several single objective optimization problems of the original BOP by using an adaptive weighting scheme, and moves closer to the true Pareto front at the end of each iteration. The method is tested on problems from the literature designed to illustrate some of the inherent difficulties in biobjective optimization such as a nonconvex or disjoint Pareto front, local Pareto front, or a nonuniform Pareto front. Finally, the algorithm is compared with a recent biobjective optimization algorithm, BiMADS, that generates an approximation of the Pareto front by solving a series of single objective formulations of the original BOP. Results show that the proposed algorithm efficiently generates a set of evenly distributed globally Pareto optimal solutions for a diverse types of problems. The accuracy and the distribution of the solutions obtained can be improved further with a relaxed budget in terms of true function evaluations. [Copyright &y& Elsevier]

Reconstruction of architectural structures from photographs has recently experienced intensive efforts in computer vision research. This is achieved through the solution of nonlinear least squares (NLS) problems to obtain accurate structure and motion estimates. In Photogrammetry, NLS contribute to the determination of the 3-dimensional (3D) terrain models from the images taken from photographs. The traditional NLS approach for solving the resection-intersection problem based on implicit formulation on the one hand suffers from the lack of provision by which the involved variables can be weighted. On the other hand, incorporation of explicit formulation expresses the objectives to be minimized in different forms, thus resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may conflict in a Pareto sense, namely, a small change in the parameters results in the increase of one objective and a decrease of the other, as is often the case in multi-objective problems. Such is often the case with error-in-all-variable (EIV) models, e.g., in the resection-intersection problem where such change in the parameters could be caused by errors in both image and reference coordinates. This study proposes the Pareto optimal approach as a possible improvement to the solution of the resection-intersection problem, where it provides simultaneous estimation of the coordinates and orientation parameters of the cameras in a two or multistation camera system on the basis of a properly weighted multi-objective function. This objective represents the weighted sum of the square of the direct explicit differences of the measured and computed ground as well as the image coordinates. The effectiveness of the proposed method is demonstrated by two camera calibration problems, where the internal and external orientation parameters are estimated on the basis of the collinearity equations, employing the data of a Manhattan-type test field as well as the data of an outdoor, real case experiment. In addition, an architectural structural reconstruction of the Merton college court in Oxford (UK) via estimation of camera matrices is also presented. Although these two problems are different, where the first case considers the error reduction of the image and spatial coordinates, while the second case considers the precision of the space coordinates, the Pareto optimality can handle both problems in a general and flexible way. [ABSTRACT FROM AUTHOR]

In some geodetic and geoinformatic parametric modeling, the objectives to be minimized are often expressed in different forms, resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may compete in a Pareto sense, namely a small change in the parameters results in the increase of one objective and a decrease of the other, as frequently occurs in multiobjective problems. Such is the case with errors-in-all-variables (EIV) models, e.g., in the geodetic and photogrammetric coordinate transformation problems often solved using total least squares solution (TLS) as opposed to ordinary least squares solution (OLS). In this contribution, the application of Pareto optimality to solving parameter estimation for linear models with EIV is presented. The method is tested to solve two well-known geodetic problems of linear regression and linear conformal coordinate transformation. The results are compared with those from OLS, Reduced Major Axis Regression (TLS solution), and the least geometric mean deviation (GMD) approach. It is shown that the TLS and GMD solutions applied to the EIV models are just special cases of the Pareto optimal solution, since both of them belong to the Pareto-set of the problems. The Pareto balanced optimum (PBO) solution as a member of this Pareto optimal solution set has special features and is numerically equal to the GMD solution. [ABSTRACT FROM AUTHOR]

We introduce and study a family of models for multiexpert multiobjective/criteria decision making. These models use a concept of weight robustness to generate a risk-averse decision. In particular, the multiexpert multicriteria robust weighted sum approach (McRow) introduced in this paper identifies a (robust) Pareto decision that minimizes the worst-case weighted sum of objectives over a given weight region. The corresponding objective value, called the robust value of a decision, is shown to be increasing and concave in the weight set. We study compact reformulations of the McRow model with polyhedral and conic descriptions of the weight regions. The McRow model is developed further for stochastic multiexpert multicriteria decision making by allowing ambiguity or randomness in the weight region as well as the objective functions. The properties of the proposed approach are illustrated with a few textbook examples. The usefulness of the stochastic McRow model is demonstrated using a disaster planning example and an agriculture revenue management example. [ABSTRACT FROM AUTHOR]

We compare unanimity rule and majority rule in their abilities to produce Pareto superior and Pareto optimal alternatives in fixed number of rounds of voting using a two-dimensional spatial voting model with random proposals, sincere proposals, and strategic proposals. Our findings show that for random or sincere proposals, majority rule is at least as likely to select a Pareto optimal outcome as unanimity rule. For strategic proposals, the subgame perfect equilibrium under unanimity rule is Pareto optimal. For other k-majority rules, the outcome is Pareto optimal or very close to it. For outcomes that are both Pareto optimal and Pareto superior, unanimity rule outperforms majority rule. [ABSTRACT FROM AUTHOR]

Abstract: We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubelʼs “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible. [Copyright &y& Elsevier]

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto-Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In the proposed approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO). We compare PLO to the existing algorithm DIRECT. We show that, in contrast to PLO, the DIRECT algorithm considers only a subset of PO decisions that are selected by a heuristic rule depending on an adjustable parameter. It means that some PO decisions are preferred to others. By contrast, PLO regards all PO decisions without preferences and is naturally suited to utilize highly parallel computing. [ABSTRACT FROM AUTHOR]

Abstract: Pareto optimality was introduced in order to find the better equilibrium between performance and robustness of linear controllers by the simultaneous minimization of the quadratic-error and quadratic-control functions integrals. The Pareto optimization problem was solved setting the characteristic matrix eigenvalues in the region of left complex semi plane where |Im/Re|<1 as constraint. 2D Pareto fronts were built with the quadratic-error function integral vs. quadratic-control function integral. The proposed method was applied for tuning linear controllers of three chemical reactors with different kinetic equations and mix patterns. In the three situations, the Pareto optimality procedure improved the controllers’ performance and robustness with respect to controllers previously tuned by different methods. [Copyright &y& Elsevier]

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature are obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems. [ABSTRACT FROM PUBLISHER]

The present paper formulates a consensus moderation system based on the negotiation of the actors involved. There are a series of steps in the moderation process, the first of which is constructing a front of Pareto optimal solutions. Since this in itself will likely not lead to consensus in a real life scenario, Kaldor-Hicks compromises are then detected. Compromises are recommended at every iteration of the negotiation process which can lead to a lengthy negotiation time, which is addressed by using a recommendation engine based on the previous behavior of the actor. [ABSTRACT FROM AUTHOR]

ABSTRACT With increasing interest in the implementation/functionality of a contaminant warning system for water distribution systems, questions exist over the application to a real distribution system. A methodology is described to assess the impacts of changes in the numbers of sensors, on the time delay required to detect a contaminant intrusion event and to maximize sensor detection redundancy as protection against false positives. The methodology is used to explore the point of diminishing marginal return of detection likelihood, and the average time delay of detected intrusion events. Pareto front performance improvement with increasing numbers of sensors (from 2 through 50) is characterized through a case study application to the City of Guelph water distribution system (WDS). The results provide a methodology for utilities to employ for decisions on the number of sensors to use for a system. Within the two scenarios applied, five and four sensors are shown to be the point of diminishing marginal return for Guelph WDS in terms of the Pareto front performance improvement, detection likelihood, and the average time delay for the case study. Nevertheless, given that the timeframe to detect a contamination event may be lengthy, placing more sensors than the point of diminishing marginal return may be appropriate. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the data gathering problem in wireless networks, where data generated at the nodes has to be collected at a single sink. We investigate the relationship between routing optimality and fair resource management. In particular, we prove that for energy-balanced data propagation, Pareto optimal routing and flow maximization are equivalent, and also prove that flow maximization is equivalent to maximizing the network lifetime. We algebraically characterize the network structures in which energy-balanced data flows are maximal. Moreover, we algebraically characterize communication links which are not used by an optimal flow. This leads to the characterization of minimal network structures supporting the maximal flows. We note that energy-balance, although implying global optimality, is a local property that can be computed efficiently and in a distributed manner. We suggest online distributed algorithms for energy-balance in different optimal network structures and numerically show their stability in particular setting. We remark that although the results obtained in this paper have a direct consequence in energy saving for wireless networks they do not limit themselves to this type of networks neither to energy as a resource. As a matter of fact, the results are much more general and can be used for any type of network and different types of resources. [Copyright &y& Elsevier]

n approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. [ABSTRACT FROM AUTHOR]

Pareto optimality is an important property in game theory and mechanism design, which can be utilized to design resource allocation strategies in wireless systems. We analyze the structure of the boundary points of certain utility sets based on interference functions. We particularly investigate the cases with no power constraints, with individual power constraints, and with a total power constraint. We display the dependency between Pareto optimality and interference coupling in wireless systems. An axiomatic framework of interference functions and a global dependency matrix is used to characterize interference coupling in wireless systems. The relationship between interference-balancing functions and Pareto optimality of the boundary points is elucidated. Among other results, it is shown that the boundary points of utility sets with individual power constraints and with strictly monotonic interference functions are Pareto-optimal if and only if the corresponding restricted global dependency matrix is irreducible. The obtained results provide certain insight when suitable algorithms can be designed for network utility maximization. [ABSTRACT FROM PUBLISHER]

We consider settings in which T multi-antenna transmitters and K single-antenna receivers concurrently utilize the available communication resources. Each transmitter sends useful information only to its intended receivers and can degrade the performance of unintended systems. Here, we assume the performance measures associated with each receiver are monotonic with the received power gains. In general, the joint performance of the systems is desired to be Pareto optimal. However, designing Pareto optimal resource allocation schemes is known to be difficult. In order to reduce the complexity of achieving efficient operating points, we show that it is sufficient to consider rank-1 transmit covariance matrices and propose a framework for determining the efficient beamforming vectors. These beamforming vectors are thereby also parameterized by T(K-1) real-valued parameters each between zero and one. The framework is based on analyzing each transmitter's power gain-region which is composed of all jointly achievable power gains at the receivers. The efficient beamforming vectors are on a specific boundary section of the power gain-region, and in certain scenarios it is shown that it is necessary to perform additional power allocation on the beamforming vectors. Two examples which include broadcast and multicast data as well as a cognitive radio application scenario illustrate the results. [ABSTRACT FROM AUTHOR]

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607-637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford's results support Schelling's intuition on the reasons of disagreement: it may arise if players' commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling's original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices. [ABSTRACT FROM AUTHOR]

Abstract: This article proposes a novel multiobjective real coded genetic fuzzy clustering scheme for segmentation of multispectral magnetic resonance image (MRI) of the human brain. The proposed technique is able to automatically evolve the number of clusters along with the clustering result. The multiobjective variable string length clustering technique encodes the cluster centers in its chromosomes and simultaneously optimizes the global fuzzy compactness and fuzzy separation among the clusters. In the final generation, it produces a set of non-dominated solutions, from which the best solution in terms of a recently proposed validity index is chosen to be the final clustering solution. The corresponding chromosome length provides the number of clusters. The proposed method is applied on many simulated T1-weighted, T2-weighted and proton density-weighted normal and MS lesion MRI brain images. Superiority of the proposed method over K-means, Fuzzy C-means, Expectation Maximization, hierarchical clustering, Single Objective Genetic clustering and other recent multiobjective clustering algorithms has been demonstrated quantitatively. The automatic segmentation obtained by the proposed clustering technique is also compared with the available ground truth information. [Copyright &y& Elsevier]

This paper presents a novel approach to solve multiobjective robotic trajectory planning problems. It proposes to find the Pareto optimal set, rather than a single solution usually obtained through scalarization, e.g., weighting the objective functions. Using the trajectory planning problem for a redundant manipulator as part of a captive trajectory simulation system, the general discrete dynamic programming (DDP) approximation method presented in our previous work is shown to be a promising approach to obtain a close representation of the Pareto optimal set. When compared with the set obtained by varying the weights, the results confirm that the DDP approximation method can find approximate Pareto objective vectors, where the weighting method fails, and can generally provide a closer representation of the actual Pareto optimal set. [ABSTRACT FROM AUTHOR]

This article presents an analysis of the states of equilibrium and Pareto optimality of the solutions in the monetary-fiscal games between the fiscal and monetary authorities each having either two or three qualitatively different strategies: expansive, neutral and restrictive. Two sets of assumptions about the influence, exerted by the instruments of the monetary policy (real interest rate) and by those of the fiscal policy (budgetary deficit related to the GDP), on the state of economy (rate of economic growth and inflation) are considered. The results obtained indicate that, along with the case of the prisoner's dilemma, to which the discussion in the major publications on the subject is limited, other situations may also occur, where the independent decisions of the central bank and the government do not necessarily lead to the choice of a Pareto non-optimal solution. [ABSTRACT FROM AUTHOR]