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Nonlinear optimization is becoming more challenging in information sciences and various industrial applications, but nonlinear problems solved by the classical particle swarm‐based methods are usually characterized by low efficiency, accuracy, and convergence speed in specific issues. To solve these problems and enhance the nonlinear optimization performance, an improved metaheuristic particle swarm optimization (PSO) model is proposed here. First, the optimization principles and model of the new method are introduced, and algorithms of the improved PSO are presented by updating the displacement and velocity of the moving particle according to Euler–Maruyama (EM) principle rather than traditional standard normal distribution. Then, the influence of the model parameters, input dimensions, and different nonlinear problems on the PSO optimization characterizations are studied by Pareto set solving and optimization performance comparison. The analysis regarding diverse nonlinear problems and optimization methods manifests that the improved method is capable of solving various nonlinear problems especially for multiobjective models, while the robustness and reliability can always keep consistent regardless of the change of model parameters. Finally, the performance evaluation is exhibited by the case study of nonlinear parameter optimization, 3 groups of CEC benchmark problems, and rank‐sum test for 6 comparable optimization algorithms, which all verify its effectiveness and reliability, as well as the significance and great application promise. The results show that the new proposed PSO method has the fastest convergence speed and least iteration numbers in searching for the global best solution of 9 nonlinear problems among 8 different optimization models indicated by the p values smaller than 0.05. Additionally, the main conclusions showing the calculation efficiency, stability, robustness, and great application promise of the proposed method are summarized, and future work is discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of generating an evenly distributed set of Pareto solutions. It appears in real-life applications related to multi-objective optimization when it is important to represent the entire Pareto front with a minimal cost. There exist only a few algorithms which are able to tackle this problem in a general formulation. The Directed Search Domain (DSD) algorithm has proved to be efficient and quite universal. It has successfully been applied to different challengeable test cases. In this paper for the first time the DSD approach is systematically extended and applied to problems with higher dimensions. The modified algorithm does not have any formal limitation on the number of objective functions that is important for practical applications. The efficacy of the algorithm is demonstrated on a number of test cases. [ABSTRACT FROM AUTHOR]

The object of the research is to increase the level of productivity of teamwork due to the effective selection of participants who demonstrate the highest level of productivity in cooperation. The presented research is aimed at the mathematical formalization of the problem of team formation based on the results of a series of competitions using graph-theoretic approaches. Each competition in this series involves teams with the same number of participants. The composition of the team necessarily changes for each subsequent competition. After the competitive series, the obtained information about the teams’ composition and their results is evaluated for the success of the interaction of the participants, which can be used in the formation of successful teams. A graph-theoretic formalization of the team formation problem on a complete undirected weighted graph has been developed. The set of vertices of this graph corresponds to the set of potential participants. Each edge is weighted with a number that reflects the quality of the interaction between the two participants. A valid solution is to cover the graph with cliques, the size of which is determined by the number of team members. A mathematical model of a two-criterion problem with MAXSUM and MAXMIN criteria was built, where the first criterion evaluates the overall success of the created teams, the second criterion evaluates the «weakest link», allowing to choose the option that maximizes the minimum edge weights for each clique. A two-criterion objective function defines a Pareto set consisting of all Pareto optima in the set of admissible solutions. The algorithmic problem of finding the complete set of alternatives, which is a subset of the Pareto set of minimum power when the condition of equality of the objective functions for the complete set of alternatives and the Pareto set is fulfilled, is considered. The weight of the edges of the graph is calculated using the scores obtained during the series of competitions. In practice, the research results can be used as a basis for the development of team building techniques. [ABSTRACT FROM AUTHOR]

Due to the continual advancements in the Internet of Things (IoT), which generate enormous volumes of data, the cloud computing infrastructure recently has received the most significance. to meet the demands made by the network of IoT devices. It is anticipated that the planned Fog computing system would constitute the next development in cloud computing. The optimal distribution of computing capacity to reduce processing times and operating costs is one of the tasks that fog computing confronts. In the IoT, fog computing is a decentralized computing approach that moves data storage and processing closer to the network's edge. This research article discusses a unique technique for lowering operating expenses and improving work scheduling in a cloud-fog environment. Non-dominated sorting genetic algorithm II (NSGA-II) is a proposal that is presented in this paper. Its purpose is to allocate service requests with the multi-objective of minimising finishing time and running cost. Determining the Pareto front that is associated with a group of perfect solutions, which are sometimes referred to as non-dominated solutions or Pareto sets, is the fundamental objective of the Pareto NSGA-II. There is a contradiction between the environmental and economic performances, which is shown by the Pareto set of suboptimal solutions that are the consequence of the bi-objective issue. [ABSTRACT FROM AUTHOR]

Hydropower compensating for wind and solar power is an efficient approach to overcoming challenges in the integration of sustainable energy. Our study proposes a multi-objective scheduling model for the complementary operation of wind–photovoltaic–hydro systems. The model aims to maximize the total generation while minimizing the mean square deviation of the system output and grid load. Taking wind and solar bases and key peak-shaving cascade hydropower stations in Hubei Province as a case study, various multi-objective Pareto solution sets were obtained for different scheduling periods. The analysis dissects the relationship between total generation and the stability of residual load after adjustment by the wind–photovoltaic–hydro systems. Furthermore, the study analyzes the role that a complementary system should play in the power grid and discusses the effect of cascade hydropower scheduling methods on the operational characteristics of multi-energy complementary systems. [ABSTRACT FROM AUTHOR]

The digitalization of the economy reduces the cost of doing business by automating the relevant processes, but any transformation creates new risks and economic instability. Economic instability leads to a drop in the standard of living and, as a result, negatively affects the activities of trade enterprises. Small and medium businesses are especially sensitive to any changes. The decrease in demand for most everyday goods has a painful effect on the activities of small and medium-sized businesses and leads to the emergence of new risks. These risks have a significant impact on reducing the profitability of enterprises. Therefore, it is important for each enterprise to diversify the activities of the enterprise, which includes the expansion of the product range, the reorientation of sales markets and the optimal distribution of goods between divisions of one enterprise.The subject of the article is multi-criteria models of a diversified portfolio that minimize the risks that arise in the era of the digital economy when managing retail chains. To formalize the problem, five models are proposed that differ in vector objective functions, both in the quantity and quality of the selected criteria. The aim of the work is to analyze the problem of choosing criteria in the corresponding multicriteria or vector diversification problems. The article examines the advantages of introducing an additional criterion of entropy maximization into the criteria of the classical two-criteria model of portfolio theory, which characterizes the degree of diversity of the portfolio composition. A complex combination of methods of classical portfolio theory and multicriteria optimization is applied. The results include a comparison of three methods for solving the following problems: criteria convolution, successive concessions, and computer simulation of the Pareto set. Conclusions: the results obtained will be useful for automating the risk management of retail chains. The practical value is that the obtained results of real data for the network have demonstrated the possibility of using the developed tool for automatic allocation of resources in the form of pareto-optimal portfolios in order to minimize risks.

In this paper, an axiomatic approach to Pareto set reduction problem is considered. The reduction is based on accounting for preferences of a decision maker which are modeled with the use of a type-2 fuzzy binary relation. This relation is only partially known through a set of so-called information quanta. Since these quanta are provided by the decision maker, it must be verified that they are consistent with the requirements of the axiomatic approach — the axioms of rational choice. Several theorems giving necessary and sufficient conditions of quanta consistency are proved. Ideas for dealing with inconsistencies are discussed with a few examples. [ABSTRACT FROM AUTHOR]

This paper proposes an augmented Lagrangian method to compute Pareto optimal sets of multiobjective optimization problems. The method neither requires a prior information about the locations of the Pareto surface nor the convexity of the objective and constraint functions. To generate Pareto optimal points, we convert a multiobjective optimization problem into a set of direction-based parametric scalar optimization problems by using the cone method. Subsequently, we apply the augmented Lagrangian method to the direction-based parametric problems to transform them into unconstrained problems. Transformed augmented Lagrangian subproblems are then solved by the steepest descent method with a max-type nonmonotone line search method. A step-wise algorithmic implementation of the proposed method is provided. We discuss the convergence property of the proposed algorithm with regard to a feasibility measure and the global Pareto optimality. Under a few common assumptions, we prove that any subsequential limit of the sequence generated by the proposed algorithm is the global minimizer of an infeasibility measure corresponding to each direction. In addition, the obtained limit is found to be a global minimizer when the feasible region of the given multiobjective optimization problem is nonempty. It is observed that the solution of the proposed method is not affected by variable scaling. The efficiency of the proposed algorithm is shown by solving standard test problems. As a realistic application, we employ the proposed method on a deterministic unemployment optimal control model with the implementation of government policies to create employment and vacancies as their controls. [ABSTRACT FROM AUTHOR]

Many practical optimisation problems have conflicting objectives, which should be addressed by multi-criteria optimisation (MCO), i.e. by determining the set of best compromises, the Pareto set (PS), along with its picture in parameter space (PSPS). In previous work on low-dimensional MCO problems, we have found characteristic topological features of the PS and PSPS, which depend on the dimensionality of the parameter space M and the objective space N. E.g., M = 2 and N = 3 yields triangles with needle-like extensions. The reasons for these topological features were unknown so far. Here, we show that they are to be expected if all objective functions of the MCO satisfy two conditions: (a) they can be approximated by quadratic functions and (b) one of the eigenvalues of the Hessian matrix evaluated at the function's minimum is small compared to the other eigenvalues. Objective functions which meet conditions (a) and (b) have a valley-like topology, for which the valley lies in the direction of the eigenvector corresponding to the lowest eigenvalue. The PSPS can be estimated by starting at the minimum of an objective function, following the valley, and combining these lines for all objective functions. The PS is obtained by evaluating the objective functions. We believe that the conditions (a) and (b) are met in many practical problems and discuss an example from molecular modelling. The improved understanding of the features of these MCO problems opens the route for designing methods for swiftly finding estimates of their PS and PSPS. [ABSTRACT FROM AUTHOR]

Novel algorithms for adaptive approximation and interactive navigation of Pareto sets are applied to various homogeneous distillation processes with recycle streams within an industrial flowsheet simulator. The adaptive approximation scheme shows that the Pareto set consists of both convex and non‐convex regions when the product purities are maximised while minimising the total heat duties. It is illustrated how such Pareto sets can be navigated interactively using a ray tracing technique. Our results suggest that the occurrence of non‐convex regions in the Pareto sets is due to recycle streams in the flowsheets and is therefore the rule rather than the exception in multi‐objective optimisation of flowsheet simulations in chemical engineering. [ABSTRACT FROM AUTHOR]

Previous investigations of the authors surveyed the possibility of applying interval methods to seek the Paretofront of a multicriterial nonlinear problem. An efficient algorithm has been proposed and its implementation in a multicore environment has been done and tested. This paper has two goals. First one is to tune the developed algorithm to increase the speedup of the multi-threaded variant. The second one is to extend the algorithm to compute not only the Paretofront (in the criteria space), but also the Pareto-set (in the decision space). Numerical results for suitable test problems are presented.

Cloud manufacturing is a consumer-centric requirement-driven manufacturing paradigm that integrates distributed resources for providing services to consumers in an on-demand manner. Scheduling of multiple tasks is an important technical means for satisfying consumer requirements in cloud manufacturing. However, high individualised requirements and the associated complex task structures complicate the task scheduling in cloud manufacturing. This paper establishes a more comprehensive model for scheduling multiple distinct tasks with complicated manufacturing processes. The hierarchical relationships (a mixture of dependency and independency) of subtasks within tasks are considered. The objectives involve three kinds of time and cost factors, namely processing time, setup time, transfer time and the respective cost. In addition, service quality is also considered into the optimisation objective. Two multi-objective-meta-heuristic algorithms, i.e. ACO-based multi-objective algorithm (MACO) and NSGA-II-based multi-objective algorithm (MGA), are designed to solve the scheduling problem. A detailed analysis of the performance of the two algorithms is performed by applying them to several different scheduling instances. Experimental results indicate that in most cases the MACO algorithm can obtain a more diverse set of Pareto solutions hence offering more alternatives to meet widely different users' needs. [ABSTRACT FROM AUTHOR]

The crude distillation unit (CDU) plays a significant role in the petroleum refinery. Decision variables of this unit have an effect on the final product quality, quantity, and energy consumption. The aim of this work is to increase the profit of the refinery proportionally with reducing emissions by getting high distillate products through selection of the optimal conditions. Two goal functions in three cases, namely, profit, CO2 emission, energy cost, and total distillate are considered. Therefore, the multi‐objective particle swarm optimization (MOPSO) algorithm is implemented by using MATLAB to optimize the CDU unit and then linked to an ASPEN HYSYS simulator. The effect of the temperature of preheated crude is demonstrated in the Pareto front. Also, the influence of the other variables, i.e., reflux ratio, atmospheric stripper steam, and amount of fuel burnt, is investigated. [ABSTRACT FROM AUTHOR]

BackgroundThe beam quality determined by the beamline status greatly affects the experimental results of macromolecular X-ray crystallography (MX). At present, the optimization of the crystallography beamline of Shanghai Synchrotron Radiation Facility (SSRF) is manually operated by the beamline staffs, which is time-consuming and laborious. X-ray diffractive (XRD) beamline of SSRF realized single-objective automatic optimization of flux based on differential evolution, but this scheme still has certain limitations for MX beamline.PurposeThis study aims to design and implement an automatic optimization procedure based on non-dominated sorting genetic algorithm-II (NSGA-II) on the crystallography beamline system.MethodsFirstly, based on NSGA-II, a multi-objective automatic optimization model of the beamline was established. Then, an automatic optimization procedure was designed and implemented by using Python for the beamline system. Finally, this optimization procedure was tested on BL10U2 of SSRF to optimize the beam flux and position by adjusting the beamline optical components.ResultsThe test results show that the automatic optimization can find the correct optimization objectives Pareto set with two optimized measures of beam flux and beam position within 30 min, and the optimization efficiency is greatly improved when compared with that of manual or previous optimization.ConclusionsNSGA-II based automatic optimization procedure simplifies the optical optimization of beamline and improves the operation efficiency of the crystallography beamlines at SSRF.

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical methods can be helpful. This article proposes Pareto Front (PF) and Pareto Set (PS) estimation methods using Bayesian Additive Regression Trees (BART), which is a nonparametric model whose assumptions are typically less restrictive than popular alternatives, such as Gaussian Processes (GPs). These less restrictive assumptions allow BART to handle scenarios (e.g., high-dimensional input spaces, nonsmooth responses, large datasets) that GPs find difficult. The performance of our BART-based method is compared to a GP-based method using analytic test functions, demonstrating convincing advantages. Finally, our BART-based methodology is applied to a motivating engineering problem. , which include a theorem proof, algorithms, and R code, for this article are available online. [ABSTRACT FROM AUTHOR]

ith the rapid development of radio frequency identification (RFID) technology,in a variety of special environments (such as factories,warehouses,prisons,etc.),the demand for optimal deployment of RFID reader antennas has attracted extensive attention.In order to solve the problems in the deployment of RFID reader antenna,such as difficult deployment,many constraints and difficult to find the optimal solution and Pareto front,this paper proposes an optimized deployment method of RFID reader antenna based on the improved multi-objective SALP swarm algorithm (MSSA).The multi-objective optimization deployment model of RFID reader antenna is constructed in advance,and the optimization target is set.The multi-objective tympana algorithm is used to train the optimal deployment model of RFID reader antenna.The separation operator is introduced to optimize the search ability,and the non dominated solutions satisfying the conditions are searched continuously through iteration,and the Pareto solution set satisfying the conditions is constructed,which is the optimization result.The results show that the proposed algorithm has faster convergence rate than the algorithms of BA-OM,PSO and MC-BFO without the prior knowledge,coverage rate increases by 33%,28% and 20% respectively.Compared with the same type of hybrid firefly (HMOFA) algorithm for Pareto solution set,the load balancing is increased by 7.14%,the economic benefit is increased by 59.74%,and the reader interfe-rence is reduced by 34.04%.

In this paper a bi-criterion fuzzy scheduling problem was presented and the problem under consideration is total fuzzy completion time and maximum earliness, where the processing times and the due dates are triangular fuzzy numbers. Each of jobs is to be processed without interruption on a single machine and becomes available for processing at time zero. A new definition of fuzzy numbers was given namely m-strongly positive fuzzy numbers, through this definition we found an interval which restricts the range of the fuzzy lower bound and presented a relation between the fuzzy lower bound and the fuzzy optimal solution with number of efficient solutions. Also we found the exact solution of the problem through finding the Pareto set.

A multiobjective problem of integer linear programming with parametric optimality is addressed. The parameterization is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as extreme and Pareto. The admissible perturbation in such problem is formed by a set of additive matrices, with arbitrary H\"{o}lder's norms specified in the solution and criterion spaces. The lower and upper bounds for the radius of strong stability are obtained with some important corollaries concerning previously known results.

An algorithm is developed for finding the structure of the optimal subset in the knapsack problem based on the proposed multicriteria optimization model. A two-criteria relation of preference between elements of the set of initial data is introduced. This set has been split into separate Pareto layers. The depth concept of the elements dominance of an individual Pareto layer is formulated. Based on it, conditions are determined under which the solution to the knapsack problem includes the first Pareto layers. They are defined on a given set of initial data. The structure of the optimal subset is presented, which includes individual Pareto layers. Pareto layers are built in the introduced preference space. This does not require algorithms for enumerating the elements of the initial set. Such algorithms are used when finding only some part of the optimal subset. This reduces the number of operations required to solve the considered combinatorial problem. The method for determining the found Pareto layers shows that the number of operations depends on the volume of the knapsack and the structure of the Pareto layers, into which the set of initial data in the entered two-criteria space is divided.

In this study, the optimization of heat transfer in serpentine micro heat exchangers using the genetic algorithm based multi-objective optimization was investigated. The effects of geometric parameters of the serpentine microchannels including curvature radius and straight length between the bends on friction factor (f) and Nusselt number (Nu) were investigated experimentally. As was expected, increasing the heat transfer rate and pressure drop occurs simultaneously, which leads to the more energy required for pumping. Hence, both phenomena should be considered at the same time. The constants of two empirical equations for estimating Nusselt number and friction factor were obtained by the genetic algorithm searching method. The mean relative error of 7.49% and 9.76% were calculated for Nu and f correlation, respectively. These empirical equations were employed in two objective functions for genetic algorithm based multi-objective optimization. The optimum geometrical parameters of the investigated serpentine microchannels which lead to a trade-off between heat transfer and pressure drop were presented.

We investigate the bicriteria discrete optimization problems in the context of the axiomatic approach reducing the Pareto set. The degree of the reduction with respect to values of the coefficient of compromise is evaluated for the special structures and general case of the Pareto set. We apply the results to the set covering problems and the vehicle routing problems. [ABSTRACT FROM AUTHOR]

A multicriteria investment Boolean problem of minimizing lost profits with parameterized efficiency and different types of risks is formulated. The lower and upper bounds on the radius of the strong stability of efficient portfolios are obtained. Several earlier known results regarding strong stability of Pareto efficient and extreme portfolios are confirmed. [ABSTRACT FROM AUTHOR]

We consider multicriteria minimax optimization problems with criteria in the form of the maxima of functionals given by the induced norms of linear operators taking the system inputs and/or initial state to the outputs. It is shown that replacing the difficult minimization of the linear convolution of such criteria by the minimization of the maximum of the linear convolution of the corresponding functionals leads to suboptimal solutions with an estimate of the degree of suboptimality with respect to Pareto optimal solutions. This approach is applied to Pareto suboptimal control design for linear finite-horizon time-varying and infinite-horizon time-invariant continuous- and discrete-time systems with uncertain initial states and/or disturbances. Numerical simulation results are presented. [ABSTRACT FROM AUTHOR]

The knapsack problem is analyzed on the basis of the mathematical model, which uses the means of multicriterial optimization. The method which defines possible redundancy of the initial data set is offered for the problem. The algorithm of the transition to the task with a changed set of initial data is developed. The algorithm of pareto elements division into subsets with ordered upper and lower criteria borders is executed. The complexity estimation of proposed algorithms is realized and the general approach to the knapsack problem solving is presented.

It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs. [ABSTRACT FROM AUTHOR]

A multiobjective problem of integer linear programming with parametric optimality is addressed. The parameterization is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as extreme and Pareto. The admissible perturbation in such problem is formed by a set of additive matrices, with arbitrary Hölder's norms specified in the solution and criterion spaces. The lower and upper bounds for the radius of strong stability are obtained with some important corollaries concerning previously known results. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective network design problem with environmental considerations for urban networks with queues. A spatial queuing link model is introduced to take account of the spatial effect of queuing. With this more realistic link performance function capturing spatial queuing, the network equilibrium flow patterns can be more accurately identified. Furthermore, to better estimate vehicle emissions, this paper proposes a refined emission estimation model, which distinguishes between travel speeds in free-running state and queue-forming state over a link. A multi-objective bi-level programming is then developed, in which the upper-level problem optimizes the investment decisions, whereas the lower-level problem characterizes the user equilibrium with spatial queuing delays. The metaheuristic of non-dominated sorting genetic algorithm II (NSGA-II) is adopted to solve the multi-objective network design problem. Numerical tests on the Sioux Falls network and the Barcelona network confirm the effectiveness of our proposed model and algorithm in identifying queuing equilibrium flows and Pareto optimal solutions. The refined models and valuable information about trade-offs among objectives are particularly helpful for environmentally sustainable transport network planning. [ABSTRACT FROM AUTHOR]

Firstly, according to the particle structure information in the muiti-objective particle swarm opiimzzaiion algorithm, using nondominated soluiion sets to construct the topological structure between individual particle neighborhoods, a star-structured muiti-objective particle swarm opiimizaiion algorithm is proposed for solving multi-modal multi-objective problems. Secondly, in view of the difficulty of selecting the global optimal individual in the muiti-objective particle swarm, an evaluation method for the uniformity of the distribution of non-dominated solution sets is proposed. The evaluation result determines the global optimal individual corresponding to the current particle. Finally, combining two methods, a star topology multi-objective particle swarm optimization algorithm with uniform calculation method is proposed. The test function analyzes the convergence of the algorithm and shows that the improved algorithm converges faster than the original algorithm. Experimental results show that the algorithm can take into account the distribution of the problem object space and decision space, and effectively solve the multi-modal multi-objective problem. [ABSTRACT FROM AUTHOR]

A universal computational procedure is used to construct numerical methods for Pareto set approximation. The numerical methods are developed relying on the assumptions necessary for proving the convergence of the universal procedure to the Pareto set. [ABSTRACT FROM AUTHOR]

We consider a multicriteria integer linear programming problem with a parametrized optimality principle which is implemented by means of partitioning the partial criteria set into non-empty subsets, inside which relations on the set of solutions are based on the Pareto minimum. The introduction of this principle allows us to connect such classical selection functions as Pareto and aggregative-extremal. A quantitative analysis of two types of stability of the problem to perturbations of the parameters of objective functions is given under the assumption that an arbitrary lp-Holder norm, 1 = p = 8, is given in the solution space, and the Chebyshev norm is given in the criteria space. The formulas for the radii of quasistability and strong quasi-stability are obtained. Criteria of these types of stability are given as corollaries. [ABSTRACT FROM AUTHOR]