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In this paper, a class of fractional multiobjective interval valued optimization problems with Einvexity is considered. First, the definition of the E-invex fractional interval value function is given under the interval order relation, and the existence of these fractional interval-valued functions is verified by examples. Second, we present the E-KKT necessary optimality conditions and the sufficient optimality conditions for a fractional interval-valued optimization problem (FIVPE) under E-invexity. Last, the Mond-Weir E-dual problem (DFIVPE) of (FIVPE) is established, and several E-duality theorems are obtained under E-invexity. To some extent, this paper generalizes the existing relevant results obtained recently. [ABSTRACT FROM AUTHOR]

Simple Summary: This study aimed to examine the aging process of fibrous elements in the dermis of male volunteers over a 10-year period (47–57 years). It was observed that the aging process included visible changes in the content and organization of type I collagen fibers, resulting in changes in fibroblast morphology, and changes in type III collagen and elastic fibers. For the first time, this study presents a comparison of the dynamics of changes in morphology of the dermis in the same volunteer over a time interval of 10 years. Skin aging is a complex phenomenon influenced by multiple internal and external factors that can lead to significant changes in skin structure, particularly the degradation of key extracellular matrix (ECM) components such as collagen and elastic fibers in the dermis. In this study, we aimed to meticulously assess the morphological changes within these critical fibrous ECM elements in the dermis of the same volunteer at age 47 and 10 years later (2012 to 2022). Using advanced histological staining techniques, we examined the distribution and characteristics of ECM components, including type I collagen, type III collagen, and elastic fibers. Morphological analysis, facilitated by hematoxylin and eosin staining, allowed for an accurate assessment of fiber bundle thickness and a quantification of collagen and elastic fiber areas. In addition, we used the generalized Pareto distribution for histogram modeling to refine our statistical analyses. This research represents a pioneering effort to examine changes in ECM fiber material, specifically within the male dermis over a decade-long period. Our findings reveal substantial changes in the organization of type I collagen within the ECM, providing insight into the dynamic processes underlying skin aging. [ABSTRACT FROM AUTHOR]

Nickel superalloys occupy a reasonably broad niche in the industry. One of this group's most common and well-known alloys is Inconel 718. Parts from Inconel 718 are used in aerospace, energy, automotive, and some other vital industries, which creates a demand for research and improvement of the machining conditions of this alloy. This article is devoted to the systematization and generalization of the accumulated experience of machining of Inconel 718 at turning operation. The research methodology is based on the Pareto distribution. In the study, more than 50 articles devoted to turning Inconel 718 were analyzed. The tool materials, methods, and types of coating used in turning Inconel 718 were analyzed. Finite element method modeling of processing processes has been considered. The trends in the selection of cutting parameters and the geometry of the cutting tool and finite element method modeling of processing processes have been considered. Lacunae for promising future research were formulated. [ABSTRACT FROM AUTHOR]

Copyright of Afrika Statistika is the property of Statistics & Probability African Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Afrika Statistika is the property of Statistics & Probability African Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Environmental parameters such as temperature, light, water, gas, and fertilizer in a controlled environment are important components of the greenhouse microclimate. In general, temperature and humidity are highly dependent on individual factors, and indeed it is difficult to control multiple targets simultaneously. This paper proposes an improved non dominant classification genetic algorithm II (NSGA-II) to solve this problem. The method of adaptive mutation can be set in the holding solution diversity, while still maintaining a high speed to obtain a Pareto optimal solution. Original crossover method has the global search capability is not big enough limitations, it is replaced with arithmetic crossover method, but also can make the diversity of knowledge is maintained. For improved multi-objective optimization algorithm simulation test, simulation and data analysis found: Pareto optimal distribution of cutting-edge solution set more reasonable, and its efficiency with better performance indicators have improved [ABSTRACT FROM AUTHOR]

This paper investigates infinite horizon repeated security games with one defender and multiple attacker types. The incomplete information brings uncertainty of attackers' behaviour for the defender. Under the uncertainty of attackers' behaviours, we take the worst-case analysis to minimise the defender's regret w.r.t. each attacker type. We wish to keep the regret especially small w.r.t. one attacker type, at the cost of modest additional overhead compared to others. The trade-off among the objectives requires us to build a Multi-Objective Repeated Security Game (MORSG) model. To parameterise the regret Pareto frontier, we combine the different weight vectors with different objectives and build a linear programming approach. By running the Q-iteration procedure on linear programming for each weight vector, the optimal regret Pareto frontier can be computed. We also propose an approximate approach to approximate it. The approximation analysis proves the effectiveness of the approximation approach. [ABSTRACT FROM AUTHOR]

The Pareto model, first used in socioeconomic problems, has successfully been applied in many other areas such as astronomy, biology, bibliometrics, demography, insurance, or risk management. Although there are several variants of this distribution, the current study focuses on the classic Pareto distribution, also known as the Pareto type I distribution. We propose a new class of estimators for the Pareto shape parameter, obtained through a modification of the probability weighted moment method, called the log generalized probability weighted moments method. In addition to the asymptotic distribution, Monte Carlo simulations were performed to analyze the finite sample behavior of the proposed new estimators. A comparison with the most used estimators, such as the moment, the maximum likelihood, the least squares, and the probability weighted moments estimators was also performed. In addition, the estimators were used to construct asymptotic confidence intervals. To illustrate an application of the different estimation methods to a real data set from a clinical trial complete the article. Results indicate an overall good performance of the new proposed class. [ABSTRACT FROM AUTHOR]

The aim of this study is to model the probabilistic behaviour of unusually large financial losses (extreme-risk) and gains of the South African Financial Index (J580). Risk is defined as uncertainty in return in this paper. This study makes use of Extreme Value Theory (EVT) for the period years: 1995-2018 to build models that are used to estimate extreme losses and gains. The quarterly block maxima/minima of monthly returns are fitted to the Generalised Extreme Value Distribution (GEVD). Return levels (maximum loss/gain) based on the parameters from the GEVD are estimated. A comparative analysis with the Generalised Pareto Distribution (GPD) is carried out. The study reveals that EVT provides an efficient method of forecasting potentially high risks in advance. The conclusion is that analysing extreme risk in the South African Financial Index helps investors understand its riskness better and manage to reduce the risk exposure in this portfolio. [ABSTRACT FROM AUTHOR]

Today the interest of industrial organizations increase about the quality subject and they work seriously to satisfy the customers who consider today the main factor in the business environment, by manufacturing quality products. Pareto distribution and Pareto analysis are used where The Pareto distribution is used to analysis the data of the defective motors to find the mean, variance, and standard deviation. Pareto Analysis is used as a tool to diagnose and analyse the defects type, causes of the critical defect and the root of cause of the critical cause for the air cooling motor. The air cooling motor is a one of the various products that produce by the state company for electrical products. Four main defects have been diagnosed through final inspection process by the Inspection team, these are dielectric (electrical circuit), sound (noise), loss (non- pass the electrical current) and tolerance (non-accurate tolerance). The Pareto distribution was illustrated that Dielectric defect has the highest mean but loss has the highest variance and standard deviation. The Pareto analysis was identified that the dielectric has the biggest defect with 42.24% of all defects. It has been caused by four causes, and the machine are the biggest cause, it is responsible to 50% of this defect, consumption of the rolling mold is the root of the dielectric defect with 40% of this defects. The Pareto distribution and Pareto analysis may considered an efficient tools that could use to help company management to analyse the defects data and diagnose all the causes and cause roots of the biggest defect (dielectric defect) to determine and take any necessary corrective actions that will minimize the defective products.

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented. [ABSTRACT FROM AUTHOR]

One of the most important topics in manufacturing industries is the evaluation of performance lifetimes of products. Based on a given lifetime performance index, this paper deals with evaluating the performance of a process subject to a given lower specification limit. We confine ourselves to the progressively first-failure-censored data coming from a common Pareto distribution. With both the Bayesian and the non-Bayesian approaches being investigated here, we pay more attention to Bayesian estimators under balanced type loss functions. The results are presented under the balanced versions of two well-known loss functions, namely the squared error loss and the Varian's linear-exponential (LINEX) loss. Moreover, based on the Bayesian and the non-Bayesian approaches, the problem of testing hypotheses on the lifetime performance index is studied. Also, a simulation study is performed to assess the obtained results. Finally, two illustrative examples are given. [ABSTRACT FROM AUTHOR]

In multi-objective evolutionary optimization, maintaining a good balance between convergence and diversity is particularly crucial to decision makers, especially when tackling problems with complicated Pareto sets. According to the analysis of dominance-based and decomposition-based selection mechanisms in multi-objective evolutionary algorithms, a multi-objective evolutionary algorithm based on the combination of local non-dominated rank and global decomposition is presented. The Gauss distribution model and differential evolution based on history information are employed as evolutionary operators. Various comparative experiments are conducted on 19 unconstraint test MOPs, and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types. [ABSTRACT FROM AUTHOR]

The International Swimming Federation has developed a points system that allows comparisons of results between different events. Such system is important for several reasons, since it is used as a criterion to rank swimmers in awards and selection procedures of national teams. The points system is based entirely on the world record of the correspondent event. Since it is based on only one observation, this work aims to suggest a new system, based on the probability distribution of the best performances in each event. Using extreme value theory, such distribution, under certain conditions, converges to a generalized Pareto distribution. The new performance index, based on the peaks over threshold methodology, is obtained based on the exceedance probabilities correspondent to the swimmers' times that exceed a given threshold. We work with 17 officially recognized events in 50 m pool, for each women and men, and considered all-time rankings for all events until 31 December 2016. A study on the adequacy of the proposed generalized Pareto distribution index and a comparison between the performances of Usain Bolt and Michael Phelps are also conducted. [ABSTRACT FROM AUTHOR]

Abstract Investors often co-invest in the same project together. As the payoff of the project realizes, how to share the total payoff is in consideration. With this inspiration, an investor sharing game is proposed in this paper, where investors’ payoffs relate to their investing amount and the degree of monopoly in the industry market. Economically, the degree of monopoly in the market is introduced in the game by a parameter α that affects the evolutionary process. The distribution of investing amounts is assumed to satisfy the Pareto distribution in terms of the empirical wealth distribution. The simulation on WS small-world networks shows that cooperative behaviors will prosper by the union of investors who invest less amounts in a less monopolized market. The higher power of the Pareto distribution of investing amounts also results in more cooperators in equilibriums. Furthermore, as the degree of monopoly swings, the density of cooperators is higher and more stable in a more random small-world network. The findings may be helpful in understanding the effect of network structure on the emergence of cooperation. [ABSTRACT FROM AUTHOR]

Abstract This paper establishes the possibility of utilizing energy harvesting from mechanical vibrations to estimate extreme value responses of the host structure and demonstrates the calibration of these estimates for excitation spectra typical to natural systems. For illustrative purposes, a cantilever type energy harvester is considered for wind excitation. The extreme value estimates are established through a Generalized Pareto Distribution (GPD). Classically well-known Kaimal and Davenport spectra for wind have been considered in this paper for comparison purposes. The applicability of GPD for processes with short-range dependence is explored in both linear and nonlinear systems. The work also demonstrates how return levels can be mapped using energy harvesting levels and indicates that vibration energy harvesting, in its own right, has the potential to be used for extreme value analysis and estimates. The work has impact on health monitoring and assessment of built infrastructure in various stages of repair or disrepair and exposed to nature throughout their lifetime. [ABSTRACT FROM AUTHOR]

The Pareto distribution has been widely used to model data in numerous areas including actuarial science, climatology, economics, finance, and reliability. The exponential weighted moving average (EWMA) chart with variable sample size and sampling interval (VSSI) is quicker than EWMA chart, EWMA chart with variable sample size (VSS), and EWMA chart with variable sampling interval (VSI) in detecting the mean shifts of a normal process. In this study, we present an EWMA‐VSSI chart to monitor the Pareto data with estimated parameters. The average time to signal (ATS) is computed by using the Markov chain approach. The results indicate that the proposed chart performs better than the other EWMA charts with fixed sample size, VSS, and VSI in terms of ATS. The design parameters of the proposed control charts are given in order to expedite the use of the chart by practitioners. Two examples are used to illustrate the application of the proposed control charts. [ABSTRACT FROM AUTHOR]

The problem of hypothesis testing and interval estimation, based on the generalized variable method, for the reliability function of Pareto distribution using progressively type II censored data with fixed removals are considered. The confidence limits and testing procedures have to be numerically obtained; however, the required computations are simple and straightforward. There are no exact or approximate testing procedures and confidence intervals for reliability parameter of a Pareto distribution based on the progressively type-II right censored data with random or fixed removals available in the literature. In addition, generalized coverage probabilities, generalized size of the test, and adjusted and unadjusted generalized powers of the test are also discussed. Comparison of the reliability function under the classical paradigm and the generalized paradigm is done citing an illustrative example and an example based on the simulated data to demonstrate the advantages and merits of the proposed generalized variable method over the classical method. [ABSTRACT FROM AUTHOR]

The Pareto distribution is widely applied in many areas of studies such as economics and sciences. An important issues related to Pareto tail modelling is to determine the optimal threshold of the Pareto distribution. One of the methods used for determining the optimal threshold of Pareto distribution is by choosing the threshold that minimizes the goodness-of-fit statistics found based on empirical distribution function (EDF). This study involves determination of the shape parameter of the Pareto distribution using the maximum likelihood method and robust method based on the probability integral transform statistics. In addition, given the particular estimates of the shape parameter, comparison of the performance of several EDF statistics, namely, Kolmogorov–Smirnov, Kuiper, Anderson–Darling, Cramer–von Misses and Watson statistics in determining the optimal threshold in the presence of outliers is studied based on Monte Carlo simulation. Since the EDF statistics are found smallest for Kolmogorov–Smirnov or Kuiper statistics, these two EDF statistics outperformed other EDF statistics considered. The findings are illustrated using a sample of household income data of the Malaysian population. The optimal threshold found can be used to classify the high income earners in Malaysia since Pareto distribution is one of the most frequently used model to describe the upper tail of income distribution. [ABSTRACT FROM AUTHOR]

Highlights • The port investment always make the port better but may harm the liner company. • The port investment can bring Pareto gains to the supply chain. • Which port can win liner lies on the handling capacity and the time value. • The triple-win realizes at the cost of extracting more surplus of the shippers. • The port investment does not necessarily bring a greater market share to port. Abstract This paper considers a liner company that docks at one of two heterogeneous ports and selects either business cooperation or port investment. The results demonstrate that port investment always makes the port better off but may be detrimental for the liner company. Interestingly, when the liner company reaches a port investment agreement with one port, the other port also benefits. With port investment, the liner company and the two ports will raise the prices they charge to shippers, which means that the Pareto gains of the supply chain may be realized at the cost of extracting more surplus from shippers. [ABSTRACT FROM AUTHOR]

The selection mechanisms that are most commonly adopted by multi-objective evolutionary algorithms (MOEAs) are based on Pareto optimality. However, recent studies have provided theoretical and experimental evidence regarding the unsuitability of Pareto-based selection mechanisms when dealing with problems having four or more objectives. In this paper, we propose a novel MOEA designed for solving many-objective optimization problems. The selection mechanism of our approach is based on the transformation of a multi-objective optimization problem into a linear assignment problem, which is solved by the Kuhn-Munkres’ (Hungarian) algorithm. Our proposed approach is compared with respect to three state-of-the-art MOEAs, designed for solving many-objective optimization problems (i.e., problems having four or more objectives), adopting standard test problems and performance indicators taken from the specialized literature. Since one of our main aims was to analyze the scalability of our proposed approach, its validation was performed adopting test problems having from two to nine objective functions. Our preliminary experimental results indicate that our proposal is very competitive with respect to all the other MOEAs compared, obtaining the best results in several of the test problems adopted, but at a significantly lower computational cost. [ABSTRACT FROM AUTHOR]

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show that the system of particles, rescaled in an appropriate way, converges in distribution to a scaling limit that is interesting in its own right. We describe the limit object as a growing collection of "lilypads" built on a Poisson point process in ℝd. As an application of our main theorem, we show that the maximizer of the system displays the ageing property. [ABSTRACT FROM AUTHOR]

The results of this paper are the continuation of the research presented by Bieniek [Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate. Statistics. 2016;50:1206-1220]. We consider the remaining total time on test after a given failure in a life test experiment. We derive sharp upper bounds on the mean of the total time on test optimal in the class of distributions with increasing generalized failure rate with respect to generalized Pareto distributions. Specific results are obtained for distributions with increasing density and increasing failure rate. We also provide exemplary numerical values of the obtained bounds and we compare them with the corresponding bounds for distributions with decreasing generalized failure rate. [ABSTRACT FROM AUTHOR]

Pareto-based guaranteed cost control (GCC) problem of uncertain mean-field stochastic systems is investigated in infinite horizon. Firstly, the Pareto game of nominal mean-field stochastic systems is studied. Applying the convexity of the cost functionals, it is shown that all Pareto efficient solutions can be obtained by solving a weighted sum optimal control problem, based on which, Pareto-based GCC problem is solved by the GCC of the weighted sum objective functional. Secondly, applying the Karush–Kuhn–Tucker (KKT) conditions, the necessary conditions for the existence of the Pareto-based guaranteed cost controllers are derived. In particular, it turns out that all controllers are expressed as linear feedback forms involving the state and its mean based on the solutions of the cross-coupled generalized algebraic Riccati equations (CGAREs). Thirdly, this paper presents an LMI-based approach to reduce greatly the computational complexity in the controller design. Finally, two examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Extreme value analysis is an important tool for studying coastal flood risk, but requires the estimation of a threshold to define an ‘extreme’, which is traditionally undertaken visually. Such subjective judgement is not accurately reproducible, so recently a number of quantitative approaches have been proposed. This paper therefore reviews existing methods, illustrated with coastal tide‐gauge data and the Generalized Pareto Distribution, and proposes a new automated method that mimics the enduringly popular visual inspection method. In total, five different types of statistical threshold selection and their variants are evaluated by comparison to manually derived thresholds, demonstrating that the new method is a useful, complementary tool. [ABSTRACT FROM AUTHOR]

This study exploits unprecedented access to income data and a combination of newly developed statistical methods to evaluate income inequality in Egypt and test for potential top incomes biases. Income inequality in Egypt is found to be low by regional and world standards; top incomes are found to follow the Pareto distribution and do not show anomalies compared to surveys worldwide. Correcting for top incomes biases increases the Gini coefficient significantly. The magnitude of the upward correction varies between 1.1 and 4.1 percentage points depending on the choice of correction method and welfare measure. [ABSTRACT FROM AUTHOR]

In order to avoid wrong conclusions in any further analysis, it is of importance to conduct a formal comparison for characteristic quantities of the distributions. These characteristic quantities we are familiar with include mean, quantity and reliability function, and so on. In this paper, we consider two tests aiming at the comparisons for function of parameters in Pareto distribution based on record values. They are generalized p-value-based test and parametric bootstrap-based test, respectively. The resulting procedures are easy to compute and are applicable to small samples. A simulation study is conducted to investigate and compare the performance of the proposed tests. A phenomenon we note is that generalized p-value-based test almost uniformly outperforms the parametric bootstrap-based test. [ABSTRACT FROM AUTHOR]

Characterising storm surge in extreme sea states is important in offshore design. Here we estimate key surge design characteristics such as the maximum surge observed during a storm event of given extreme storm severity and covariates such as storm direction. Inferences are made using a simple non-stationary implementation of the conditional extremes model of Heffernan and Tawn (2004), comprising a set of coupled piecewise stationary marginal and dependence models defined on a partition of the covariate domain. The approach uses samples consisting of pairs of values for peaks over threshold of a conditioning variate, namely storm peak significant wave height, and the corresponding peaks over threshold of an associated value of a key surge characteristic. Each pair is allocated to a particular storm direction covariate interval, and all pairs within the same interval are assumed to exhibit common stationary marginal and conditional extreme value behaviour. Non-stationary marginal extreme value characteristics for each variate are estimated using maximum roughness-penalised generalised Pareto likelihood estimation over covariate intervals. Extremal dependence between variates on a transformed standard Gumbel scale is then estimated using maximum roughness-penalised likelihood estimation for a conditional extremes model, also piecewise stationary with respect to covariates. Sample and threshold uncertainties are quantified using a bootstrapping scheme. Marginal and conditional return value distributions, estimated using numerical integration, incorporate these uncertainties. From offshore radar-based measurements at locations in the northern, central and southern North Sea, we observe that characteristics of surge and significant wave height vary with wave direction at all locations. Surge is a larger contributor to extreme seas in the southern North Sea than in the northern North Sea in particular. There is evidence that extremal dependence between surge characteristics and significant wave height also varies with storm direction. Hence, the size of surge contribution to return values of total water level also varies with storm direction and location. [ABSTRACT FROM AUTHOR]

The derivation of conditions necessary for Pareto efficient production and exchange is a lesson frequently showcased in microeconomic theory textbooks. Traditional delivery of this lesson is, however, limited in its scope of application and can be unnecessarily convoluted. The author shows that the universe of application is greatly expanded and a more transparent logic is embraced by noting that definition of Pareto efficiency directly implies the tangency of aggregate production/endowment and aggregate weakly preferred sets. This tangency condition can itself serve as a necessary condition for Pareto optima. For convex, but not necessarily differentiable, environments this tangency condition implies nonempty intersection of multi-valued marginal rates of substitution and transformation rather than outright identity. [ABSTRACT FROM AUTHOR]

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions. [ABSTRACT FROM AUTHOR]

Consider independent random samples from (k≥2) Pareto populations with the same known shape parameter but different scale parameters. Let Xi be the smallest observation of the ith sample. The natural selection rule which selects the population associated with the largest Xi is considered. In this paper, we estimate the moments of the selected population under asymmetric scale invariant loss function. We investigate risk-unbiased, consistency and admissibility of the natural estimators for the moments of the selected population. Finally, the risk-bias’s and risks of the natural estimators are numerically computed and compared for k=2,3. [ABSTRACT FROM AUTHOR]

The inspection samples of raw material such as chemical substances in the food industry follow the inflated-Pareto distribution. To reduce the required sample size and maintain the same protection for producer and consumer, we propose three new variables sampling plans, including resubmitted sampling, repetitive group sampling (RGS), and multiple dependent state repetitive (MDSR) sampling plans. The MDSR plan outperforms the other three plans in terms of the sample size required. The proposed plans can reduce the sample size by 25–70% compared to the single sampling plan. [ABSTRACT FROM AUTHOR]

To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner. [ABSTRACT FROM AUTHOR]

The theory of non cooperative games with potential function was introduced by Monderer and Shapley in 1996. Such games have interesting properties, among which is the existence of equilibria in pure strategies. The paper by Monderer and Shapley has inspired many game theory researchers. In the present paper, many classes of multiobjective games with potential functions are studied. The notions of generalized, best-reply and Pareto potential games are introduced in a multicriteria setting. Some properties and Pareto equilibria are investigated. [ABSTRACT FROM AUTHOR]

Aquifer recharge rates and patterns are often uncertain, especially in arid areas due to sporadic and erratic rainfall. Therefore, determining the optimal groundwater abstraction using classical approaches such as Monte Carlo Simulation (MCS) requires a large number of groundwater simulations and exorbitant computational efforts. The problem becomes even more complex and time consuming for regional coastal aquifers whose domains must be discretized using high-resolution meshes. In fact, even fast evolutionary multi-objective optimization techniques generally require a large number of simulations to determine the Pareto-front among the objectives. This study explores the performance of a Decision Tree (DT) approach for the generation of the Pareto optimal solutions of groundwater extraction. This paper applies the DTs for the optimal management of the Al-Khoud coastal aquifer in Oman. The learning process of the developed DT-based model uses the output of a numerical simulation model to assess the aquifer response based on different abstraction policies. The trained DT network then utilizes the NSGA-II to determine the Pareto-optimal solutions. The simulation show that the general flux pattern in the study area is toward the sea and the hydraulic head following a similar pattern in both best and worst recharging scenarios downstream of the studied recharging dam. Statistical tests showed a good correlation between the DT-based and simulation-based results and demonstrate the capability of the DT approach to obtain high-quality solutions by incorporating a large number of recharge scenarios. Moreover, the required runtime of the DT-based approach is extremely low (5 min) compared to that of the simulation-based method (several days). This means that including additional Monte-Carlo simulations can be readily done in few minutes using the obtained DTs, instead of the long computational time needed by the simulation-based approach. [ABSTRACT FROM AUTHOR]

Differential evolution algorithm is a very popular nature inspired algorithm and it is used for solving single objective optimization problems. Due to its high convergence rate and ability to produce diverse solutions, it has been extended to solve multiobjective optimization problems. Many versions of DE were proposed however multiobjective versions, where concept of Pareto optimality is used, are most popular. Pareto Based Differential Evolution (PBDE) is one of them. Although performance of this algorithm is very good, yet its convergence rate can be further improved by minimizing the time complexity of nondominated sorting and by improving the diversity among solutions. This has been implemented by using efficient nondominated algorithm whose time complexity is better than the previous one and a new mutation scheme is implemented in DE which can provide more diversity among solutions. The proposed variant adds one more vector named as Homeostasis mutation vector in the existing mutation vectors to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escaping the situation of stagnation. Performance of proposed algorithm is evaluated on twelve benchmark test functions (bi-objective and tri-objective) on Pareto-optimal front. Performance of proposed algorithm is compared with other state-of-the-art algorithms on five multiobjective evolutionary algorithms (MOEAs). The result verifies that our proposed Homeostasis mutation strategy performs better than other state-of-the-art variants. [ABSTRACT FROM AUTHOR]

The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a non-elitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the $$(\mu + \lambda )$$ Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison with MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69 % performance increase according to the Inverse Generational Distance (IGD) metric. [ABSTRACT FROM AUTHOR]

Maximal covering location problems have efficiently been solved using evolutionary computation. The multi-stage placement of charging stations for electric cars is an instance of this problem which is addressed in this study. It is particularly challenging, because a final solution is constructed in multiple steps, stations cannot be relocated easily and intermediate solutions should be optimal with respect to certain objectives. This paper is an extended version of work published in Spieker et al. (Innovations in intelligent systems and applications (INISTA), 2015 international symposium on. IEEE, pp 1-7, 2015). In this work, it was shown that through problem decomposition, an incremental genetic algorithm benefits from having multiple intermediate stages. On the other hand, a decremental strategy does not profit from reduced computational complexity. We extend our previous work by including multi-objective optimization of multi-stage charging station placement, allowing us to not only optimize toward (weighted) demand location coverage, but also to include a second objective, taking into account traffic density. It is shown that the reachable part of the full Pareto front at each stage is bound by the solution that was chosen from the respective previous front. By careful choice of the selection strategy, a particular focus can be set. This can be exploited to comply with concrete implementation goals and to adjust the evolved strategy to both static and dynamic changes in requirements. [ABSTRACT FROM AUTHOR]

The new tilted generalized logistic distribution, also called Marshall- Olkin-Rathie-Swamee (MORS) distribution, is studied in some detail. This distribution is important because it is multimodal and generalizes the logistic distribution among others. Moments and order statistics are given. The reliability P(X < Y ), for X and Y independent generalized logistic and beta-generated MORS distributions, is obtained along with its particular cases. Also it is proved that the beta-generated MORS distribution is an infinite linear combination of a new distribution which is obtained from powers of MORS distribution. Maximum likelihood method is used to estimate the parameters of the distribution. Four applications, with real data, are presented to illustrate the applicability of the proposed distribution. For corresponding non-negative random variable, which resulted in a generalization of the Harris extended exponential (HEE) distribution, moments are obtained extending a recent result given for Marshall-Olkin exponential Weibull (MOEW) distribution. [ABSTRACT FROM AUTHOR]

When optimizing a product or process with multiple responses, a two-stage Pareto front approach is a useful strategy to evaluate and balance trade-offs between different estimated responses to seek optimum input locations for achieving the best outcomes. After objectively eliminating non-contenders in the first stage by looking for a Pareto front of superior solutions, graphical tools can be used to identify a final solution in the second subjective stage to compare options and match with user priorities. Until now, there have been limitations on the number of response variables and input factors that could effectively be visualized with existing graphical summaries. We present novel graphical tools that can be more easily scaled to higher dimensions, in both the input and response spaces, to facilitate informed decision making when simultaneously optimizing multiple responses. A key aspect of these graphics is that the potential solutions can be flexibly sorted to investigate specific queries, and that multiple aspects of the solutions can be simultaneously considered. Recommendations are made about how to evaluate the impact of the uncertainty associated with the estimated response surfaces on decision making with higher dimensions. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose a new scalarization technique for nonconvex multiobjective optimization problems and establish its theoretical properties. By combining our new scalarization approach with existing grid generation techniques, we design new algorithms for constructing reliable approximations of the Pareto fronts of three- and four-objective optimization problems. Our algorithms can be extended for problems with more objective functions to minimize. Four three-objective algorithms are formed by pairing up the new scalarization technique and three existing scalarization techniques with a grid of weights generated over the convex hull of individual minima (the CHIM grid) due to Das and Dennis. Four more algorithms are obtained by using, instead of the CHIM grid, the grid in the successive boundary generation algorithm (the SBG grid) by Mueller-Gritschneder, Graeb, and Schlichtmann. The new algorithms seem to perform better than existing algorithms, in terms of computational time and accuracy in constructing the boundary and the interior of the Pareto front. The advantages are tested, in particular, through a problem whose Pareto front has a hole in it. A rocket injector design problem with four objective functions illustrates the effectiveness of our new approach further. [ABSTRACT FROM AUTHOR]

The problem of estimation after selection arises when we select a population from the given k populations by a selection rule, and estimate the parameter of the selected population. In this paper we consider the problem of estimation of the scale parameter of the selected Pareto population $$\theta _{M}$$ (or $$\theta _{J}$$ ) under squared log error loss function. The uniformly minimum risk unbiased (UMRU) estimator of $$\theta _{M}$$ and $$\theta _{J}$$ are obtained. In the case of $$k=2,$$ we give a sufficient condition for minimaxity of an estimator of $$\theta _{M}$$ and $$\theta _{J},$$ and show that the UMRU and natural estimators of $$\theta _{J}$$ are minimax. Also the class of linear admissible estimators of $$\theta _{M}$$ and $$\theta _{J}$$ are obtained which contain the natural estimator. By using the Brewester-Ziedeck technique we find sufficient condition for inadmissibility of some scale and permutation invariant estimators of $$\theta _{J},$$ and show that the UMRU estimator of $$\theta _{J}$$ is inadmissible. Finally, we compare the risk of the obtained estimators numerically, and discuss the results for selected uniform population. [ABSTRACT FROM AUTHOR]