Set Of Approximate Solutions Research Articles

Kinetic modeling of the plasma pharmacokinetic profiles of ADAMTS13 fragment and its Fc-fusion counterpart in mice.

Introduction: Fusion of the fragment crystallizable (Fc) to protein therapeutics is commonly used to extend the circulation time by enhancing neonatal Fc-receptor (FcRn)-mediated endosomal recycling and slowing renal clearance. This study applied kinetic modeling to gain insights into the cellular processing contributing to the observed pharmacokinetic (PK) differences between the novel recombinant ADAMTS13 fragment (MDTCS) and its Fc-fusion protein (MDTCS-Fc). Methods: For MDTCS and MDTCS-Fc, their plasma PK profiles were obtained at two dose levels following intravenous administration of the respective proteins to mice. The plasma PK profiles of MDTCS were fitted to a kinetic model with three unknown protein-dependent parameters representing the fraction recycled (FR) and the rate constants for endocytosis (kup, for the uptake into the endosomes) and for the transfer from the plasma to the interstitial fluid (kpi). For MDTCS-Fc, the model was modified to include an additional parameter for binding to FcRn. Parameter optimization was done using the Cluster Gauss-Newton Method (CGNM), an algorithm that identifies multiple sets of approximate solutions ("accepted" parameter sets) to nonlinear least-squares problems. Results: As expected, the kinetic modeling results yielded the FR of MDTCS-Fc to be 2.8-fold greater than that of MDTCS (0.8497 and 0.3061, respectively). In addition, MDTCS-Fc was predicted to undergo endocytosis (the uptake into the endosomes) at a slower rate than MDTCS. Sensitivity analyses identified the association rate constant (kon) between MDTCS-Fc and FcRn as a potentially important factor influencing the plasma half-life in vivo. Discussion: Our analyses suggested that Fc fusion to MDTCS leads to changes in not only the FR but also the uptake into the endosomes, impacting the systemic plasma PK profiles. These findings may be used to develop recombinant protein therapeutics with extended circulation time.

Multiobjective Combinatorial Optimization Using a Single Deep Reinforcement Learning Model.

This article proposes utilizing a single deep reinforcement learning model to solve combinatorial multiobjective optimization problems. We use the well-known multiobjective traveling salesman problem (MOTSP) as an example. Our proposed method employs an encoder-decoder framework to learn the mapping from the MOTSP instance to its Pareto-optimal set. Specifically, it leverages a novel routing encoder to extract information for both the entire multiobjective aspect and every individual objective from the MOTSP instance. The global embeddings and each objective's embeddings are adaptively aggregated via a routing network to form the subproblems' embedding that can well represent the MOTSP features. Using a modified context embedding, the subproblems' embeddings are fed into a decoder to produce a set of approximate Pareto-optimal solutions in parallel. Additionally, we develop a Top-k baseline to enable more efficient data utilization and lightweight training for our proposed method. We compare our method with heuristic-based and learning-based ones on various types of MOTSP instances, and the experimental results show that our method can solve MOTSP instances in real-time and outperform the other algorithms, especially on large-scale problem instances.

Superiorization with a Projected Subgradient Algorithm on the Solution Sets of Common Fixed Point Problems

In this work, we investigate a minimization problem with a convex objective function on a domain, which is the solution set of a common fixed point problem with a finite family of nonexpansive mappings. Our algorithm is a combination of a projected subgradient algorithm and string-averaging projection method with variable strings and variable weights. This algorithm generates a sequence of iterates which are approximate solutions of the corresponding fixed point problem. Additionally, either this sequence also has a minimizing subsequence for our optimization problem or the sequence is strictly Fejer monotone regarding the approximate solution set of the common fixed point problem.

Integrating stop planning, timetabling and rolling stock planning on high-speed railway lines: A multi-objective optimization approach

Designing railway operational planning is a complex and challenging task to cope with fluctuating passenger demand and satisfy actual operational requirements. Focusing on high-speed railway (HSR) lines, this paper proposes an integrated modeling framework for phase-oriented railway operational planning. The framework simultaneously optimizes the stop planning, train timetable problem (TTP) and rolling stock planning (RSP). A multi-objective optimization model, with macro passenger demand, two train speed levels, and overtaking operations taken into account, is formulated to minimize the total train running distance, train dwell time, and rolling stock resources. The constraints involve the train operation zones, train operation process, passenger demand, rolling stock circulation conditions, and actual operational requirements. The proposed model is addressed using a framework based on the ε-constraint method, from which an approximate Pareto-optimal solution set is obtained. A case study on the Beijing-Shanghai HSR corridor demonstrates the effectiveness of the proposed approach and reveals some trade-offs between the proposed objectives.

Multi-objective optimal dispatch strategy for power systems with Spatio-temporal distribution of air pollutants

Accurate and effective pollutant emission control models are key in mitigating the environmental impact of energy supply systems. This paper proposes a novel high-dimensional multi-objective optimal dispatching strategy for power systems considering the spatial and temporal distribution of multiple pollutants. Firstly, a spatial and temporal distribution model of pollutants in thermal power plants is constructed, which is truly applicable to power dispatch. For modeling the pollution situation, the daily changes in the atmospheric boundary layer are taken into account, fully reflecting the pollutant dispersion characteristics of thermal power plants and improving the result accuracy. Next, a high-dimensional multi-objective optimization model is developed to simultaneously reduce the cost of power generation, carbon emission and the impact air quality from VOCs (volatile organic compounds), SO2 and NO2. This model combines the spatial and temporal distribution characteristics of various pollutants and environmental capacity. Finally, a representative high-dimensional multi-objective optimization algorithm is employed to obtain an approximate Pareto-optimal solution set. And a multi-objective decision method is proposed to filter the compromise solution. The results show that the APCs of VOCs, SO2 and NO2 are reduced by 27.5%, 10.13% and 23.16%, respectively, in the pollution day model. On non-pollution days, the proposed scheduling method not only effectively improves air quality, but also achieves cost savings of $1276.59 and reduces CO2 emission by 0.168 × 104t compared to the emission limitation method. The proposed scheduling method can not only effectively improve air quality, but also make corresponding adjustments according to the spatial and temporal changes of environmental capacity, which can truly realize economic and environmental-friendly power scheduling.

Multi-objective medical supplies distribution open vehicle routing problem with fairness and timeliness under major public health emergencies

Fair and timely delivery of supplies plays a critical role under major public health emergencies. In this paper, aiming at fairness and timeliness, an optimization model of open vehicle routing problem for medical supplies distribution is established considering the urgency of the demand. We adopt a differential evolutionary algorithm with fast non-dominated solution sorting to solve the proposed model, obtaining an approximate Pareto optimal solution set. Through the comparison of algorithms, the results showed that the differential evolutionary algorithm with non-dominated sorting is superior with a shorter runtime and more diverse solutions, while the epsilon constraint method has more accurate solutions. In the case verification, the quality of the solutions of both algorithms was within the acceptable range, but the runtime of the epsilon constraint method was too long to be applicable. The results can provide theoretical suggestions and practical guidance for decision-makers in emergency supplies distribution.

Stability of the approximate solution sets for set optimization problems with the perturbations of feasible set and objective mapping

The aim of this paper is to study stability of the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems with respect to the perturbations of feasible sets and objective mappings. We introduce a new metric between two set-valued mappings by utilizing a Hausdorff-type distance proposed by Han [A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems. Appl Anal. 2022;101:1243–1260]. The new metric between two set-valued mappings allows us to discuss set optimization problems with respect to the perturbation of objective mappings. Then, we establish semicontinuity and Lipschitz continuity of l-minimal approximate solution mapping and weak l-minimal approximate solution mapping to parametric set optimization problems by using the scalarization method and a density result. Finally, our main results are applied to stability of the approximate solution sets for vector optimization problems.

Individualized requirement-driven multi-task scheduling in cloud manufacturing using an extended multifactorial evolutionary algorithm

Cloud manufacturing is an emerging manufacturing paradigm, which enables the simultaneous processing of multiple manufacturing tasks based on customer requirements through centralized management and planning of manufacturing services provided by distributed enterprises. How to optimally schedule the multiple manufacturing tasks is an important problem in cloud manufacturing. As cloud manufacturing is a demand-driven manufacturing mode and the requirement of each customer is highly individualized, a new individualized requirement-driven cloud manufacturing multi-task scheduling (IRCMMS) model is proposed in this study. It aims to benefit not only individual customers but also the whole system. To solve the proposed model, an extended multifactorial evolutionary algorithm is designed to obtain the approximate optimal Pareto solution set, which offers more alternatives for the cloud manufacturing system. Experimental results based on different simulation instances confirm the feasibility and effectiveness of the IRCMMS model as well as the efficiency of the algorithm in solving the IRCMMS model.

Levitin-Polyak Well-Posedness for Parametric Set Optimization Problem

The aim of this paper is to introduce two notions of Levitin$-$Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlev\'{e}$-$Kuratowski convergence of sequences of approximate solution sets are also established.

Generalized well-posedness for parametric fuzzy generalized multiobjective games

The purpose of this article is to study well-posedness for parametric fuzzy generalized multiobjective games. First, we introduce the concepts of the well-posedness and well-posedness in the generalized sense for parametric fuzzy generalized multiobjective games. Then, under suitable conditions, we establish some sufficient conditions for the well-posedness and the well-posedness in the generalized sense for such problem. Further, results on metric characterization of the well-posedness and the well-posedness in the generalized sense for parametric fuzzy generalized multiobjective games in terms of the behavior of the approximate solution sets are also obtained. Finally, we state results on the well-posedness in the generalized sense for the parametric fuzzy generalized multiobjective games by using the Kuratowski measure of noncompactness. Examples are given to illustrate our results. The results presented in the paper are new.

An ensemble forecasting system for short-term power load based on multi-objective optimizer and fuzzy granulation

As an irreplaceable power source, electricity is responsible for sustaining the national economy and social development, and the precondition for the power system’s stable operation is to perform an accurate short-term load forecast (STLF). However, with the increasing forms of social power consumption and the emergence of large-scale sustainable resources on the grid, which make STLF increasingly challenging as the power load exhibits greater stochasticity and instability. Therefore, a novel STLF system is developed in this paper, which incorporates data fuzzy granulation, a high-performance optimizer for integrating forecasting sequences, point and interval forecasts. Moreover, the performance tests of the optimization algorithm verify that our proposed optimizer can obtain more approximate solution sets to the real Pareto front and outshines the traditional optimization algorithm concerning convergence and diversity. Load data from three regions of Australia demonstrate that our developed system can remarkably contribute to the accuracy and stability of the STLF, and also quantify the volatility and uncertainty of the power load, which allows power workers to better capture the fluctuation interval of future loads and effectively enhance the flexibility of grid operation.

Closed-form critical response of elastic-plastic shear building with viscous damper under pseudo-double impulse for simulating resonant response under near-fault fling-step motion

A set of approximate closed-form solutions of the maximum interstory drifts under the critical pseudo-double impulse (PDI) is derived for non-proportionally damped multi-story shear building models with bilinear hysteresis. The use of PDI and the closed-form solutions efficiently and accurately enable the capture of the critical responses of elastic-plastic multi-degree-of-freedom (MDOF) systems under the one-cycle sine wave, which substitutes for the main part of near-fault fling-step motions. The formulation of the closed-form maximum interstory drifts is based on the energy balance law. In the formulation, a quadratic function approximation of the damping force-interstory drift relation is introduced together with an updated mode-controlled energy-based approach (UMEA). While UMEA was proposed in the previous paper to derive the approximate maximum interstory drifts of undamped elastic-plastic MDOF systems under the critical PDI, it is extended so that it can be applied to non-proportionally damped MDOF systems. It is demonstrated that the proposed method can estimate the maximum interstory drifts of elastic-plastic non-proportionally damped MDOF systems under the critical PDI and the corresponding one-cycle sine wave with high accuracy. The estimation by the proposed method can be conducted much more efficiently and stably than the time-history response analysis (THRA). It is also shown that the hysteretic energy dissipation is not large enough to reduce the maximum interstory drifts. Finally, it is demonstrated that the proposed method can accurately estimate the maximum interstory drifts of elastic-plastic moment-resisting frames with viscous dampers under the resonant one-cycle sine wave.

A*pex: Efficient Approximate Multi-Objective Search on Graphs

In multi-objective search, edges are annotated with cost vectors consisting of multiple cost components. A path dominates another path with the same start and goal vertices iff the component-wise sum of the cost vectors of the edges of the former path is ``less than'' the component-wise sum of the cost vectors of the edges of the latter path. The Pareto-optimal solution set is the set of all undominated paths from a given start vertex to a given goal vertex. Its size can be exponential in the size of the graph being searched, which makes multi-objective search time-consuming. In this paper, we therefore study how to find an approximate Pareto-optimal solution set for a user-provided vector of approximation factors. The size of such a solution set can be significantly smaller than the size of the Pareto-optimal solution set, which enables the design of approximate multi-objective search algorithms that are efficient and produce small solution sets. We present such an algorithm in this paper which we call A*pex and which builds on PP-A*, a state-of-the-art approximate bi-objective search algorithm (where there are only two cost components) but (1) makes PP-A* more efficient for bi-objective search and (2) generalizes it to multi-objective search for any number of cost components. We first analyze the correctness of A*pex and then experimentally demonstrate its efficiency advantage over existing approximate algorithms for bi- and tri-objective search.

On the solvability of weakly linear systems of fuzzy relation equations☆

Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on finding solutions and solvability criteria for such systems. The situation is quite different with the so-called weakly linear systems, in which an unknown fuzzy relation is on both sides of the equation or inequality. Precisely, the scholars have only given the characterization of the set of exact solutions to such systems. This paper describes the set of fuzzy relations that solve weakly linear systems to a certain degree and provides ways to compute them. We pay special attention to developing the algorithms for computing fuzzy preorders and fuzzy equivalences that are solutions to some extent to weakly linear systems. We establish additional properties for the set of such approximate solutions over some particular types of complete residuated lattices. We demonstrate the advantage of this approach via many examples that arise from the problem of aggregation of fuzzy networks.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

Novel exact and approximate solutions to the family of the forced damped Kawahara equation and modeling strong nonlinear waves in a plasma

In this investigation, a set of novel exact and approximate analytic solutions to the family of the forced damped Kawahara equation (KE) are derived in detail. This work is divided into four main parts: in the first part, the ansatz method is employed to obtain some novel exact solutions to the integrable Extended KE (EKE). In this part, we use some different hypotheses to derive many exact traveling wave solutions (including solitary waves (SWs) and cnoidal waves (CWs)). In the second part, the ansatz method is devoted for deriving some exact SWs and CWs solutions to the forced KE. In the same part, two different general formulas to the analytical approximations to the forced damped KE are obtained. In the third part, the family of forced damped modified KE (mKE) is analyzed comprehensively via several different techniques in order to obtain several approximations. At the beginning, two different general formulas with different accuracy to the forced damped mKE are derived. Also, a particular soliton solution to the forced damped mKE is obtained using a direct ansatz. After that, a general formula for the approximate solution to the forced undamped mKE is obtained. In the fourth part, we focus our efforts on obtaining some approximations to forced EKE. The validity of all exact solutions is checked. Moreover, the maximum global residual error to the analytical approximations is estimated. This investigation can help all researchers interested in studying the characteristics of many nonlinear phenomena in various fields of science such as physics of plasmas, physics of fluids, nonlinear optics, Veins and capillaries, Oceans and seas, etc.

A Hybrid Heuristic for a Two-Agent Multi-Skill Resource-Constrained Scheduling Problem

This paper addresses an industrial case of the two-agent scheduling problem with a global objective function. Each agent manages one or several projects and competes with another agent for the use of common multi-skilled employees. There is a pool of employees, each of which can perform a set of skills with heterogeneous performance levels. The objectives of the two agents are both to minimize the total weighted tardiness of its tasks. Furthermore, We assume that some constraints (soft constraints) can be violated when there is no feasible schedule for the problem. Thus, the global objective function minimizes the constraint violations by reducing the undesirable deviations in the soft constraints from their respective goals. The overall objective is to find a schedule that minimizes both agents objective functions (local objectives) and the global objective function. We provide a mixed-integer goal programming (MIGP) formulation for the problem. In addition, we present a hybrid algorithm combining an exact procedure, a greedy heuristic, and a genetic algorithm to find an approximate Pareto solution set. We compare the performance of the hybrid algorithm against the corresponding MIGP formulation with simulated instances derived from real-world instances.

A multi-objective open vehicle routing problem with overbooking: Exact and heuristic solution approaches for an employee transportation problem

We address a bus routing problem, where individuals need to be gathered from spatially distributed pickup points and transported to a workplace. The problem is modeled as an open vehicle routing problem. Overbooking is allowed because the total seat capacity of the buses is limited. The problem is treated as a multi-objective optimization problem, where the total distance traveled by the buses and the total number of straphangers in the buses are minimized. We develop a mixed integer programming (MIP) model and employ the ε-constraint method to generate the Pareto-optimal frontier. Due to the high computational requirements of the exact model, two heuristic approaches are developed: a heuristic algorithm that is based on a cluster-first and route-second algorithm and a multi-objective evolutionary algorithm. We also develop another MIP model that provides an alternative bound to evaluate the quality of the heuristics’ solutions. Experiments on a small and a moderate-sized problem show that the heuristics are fast and approximate the optimal solutions well. The heuristic approaches are then used to solve the actual problem having 103 pickup points, 50 buses and 1986 individuals. A set of approximate solutions whose total transportation distances are at most 14% worse than the best lower bounds are obtained.

Bicriteria scheduling of a material handling robot in an m-machine cell to minimize the energy consumption of the robot and the cycle time

This study considers a flowshop type production system consisting of m machines. A material handling robot transports the parts between the machines and loads and unloads the machines. We consider the sequencing of the robot moves and determining the speeds of these moves simultaneously. These decisions affect both the robot’s energy consumption and the production speed of the system. In this study, these two objectives are considered simultaneously. We propose a second order cone programming formulation to find Pareto efficient solutions. We also develop a heuristic algorithm that finds a set of approximate Pareto efficient solutions. The conic formulation can find robot schedules for small cells with less number of machines in reasonable computation times. Our heuristic algorithm can generate a large set of approximate Pareto efficient solutions in a very short computational time. Proposed solution approaches help the decision-maker to achieve the best trade-off between the throughput of a cell and the energy efficiency of a material handling robot.

LP well-posed controlled systems for bounded quasi-equilibrium problems and their application to traffic networks

The aim of this paper is to establish the Levitin–Polyak well-posedness (LP well-posedness, for short) for two new classes of controlled systems of the bounded quasi-equilibrium problems, and two new classes of associated optimal control problems. First, we introduce two classes of the bounded quasi-equilibrium problems, and show, under suitable conditions, the equivalence between the LP well-posedness and existence of solution to these problems. Results on metric characterization of the LP well-posedness and LP well-posedness in the generalized sense for such problems in terms of the behavior of the approximate solution sets are provided. Second, we establish two classes of optimal control problems for systems described by the generalized bounded quasi-equilibrium problems. We also studied the LP well-posedness and LP well-posedness in the generalized sense for these problems. Finally, as a real-world application, we study the special case of controlled systems of the bounded traffic network problems.