Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

Research on the Multidimensional Constraint Stability of Bridge Structure Modeling based on Optimization Model

In this paper, we conduct research on the multidimensional constraint stability of bridge structure modeling based on the optimization model. The current internal and the external research results to the truss web structure, the high internode the aspect ratio and the stiffness of the middle truss brace of the truss web, deffection of composite beams of the impact of stress is a very important problem in the design of the bridge. Structural health monitoring is the use of the field of the non-destructive sensing technology, including the structural response, including structural system characteristics analysis, to achieve the purpose of monitoring structural damage or degradation. Under this basis, this paper proposes the new idea on the modelling and simulates the performance.

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.

Try and error-based scheduling algorithm for cluster tools of wafer fabrications with residency time constraints

To improve the productivity of cluster tools in semiconductor fabrications,on the basis of stating scheduling problems,a try and error-based scheduling algorithm was proposed with residency time constraints and an objective of minimizing Makespan for the wafer jobs in cluster tools.Firstly,mathematical formulations of scheduling problems were presented by using assumptions and definitions of a scheduling domain.Resource conflicts were analyzed in the built scheduling model,and policies to solve resource conflicts were built.A scheduling algorithm was developed.Finally,the performances of the proposed algorithm were evaluated and compared with those of other methods by simulations.Experiment results indicate that the proposed algorithm is effective and practical in solving the scheduling problem of the cluster tools.

An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT

Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

IMRT Optimization with Both Fractionation and Cumulative Constraints

Radiation therapy plans are optimized as a single treatment plan, but delivered over 30 - 50 treatment sessions (known as fractions). This paper proposes a new mixed-integer linear programming model to simultaneously incorporate fractionation and cumulative constraints in Intensity Modulated Radiation Therapy (IMRT) planning optimization used in cancer treatment. The method is compared against a standard practice of posing only cumulative limits in the optimization. In a prostate case, incorporating both forms of limits into planning converted an undeliverable plan obtained by considering only the cumulative limits into a deliverable one within 3% of the value obtained by ignoring the fraction size limits. A two-phase boosting strategy is studied as well, where the first phase aims to radiate primary and secondary targets simultaneously, and the second phase aims to escalate the tumor dose. Using of the simultaneous strategy on both phases, the dose difference between the primary and secondary targets was enhanced, with better sparing of the rectum and bladder.

Constraints in Lean Optimization Method Tested on a Real Engineering Problem

Optimizing a vehicle includes testing millions of parameters with hundreds of constraints of the performance. In this article, 162 parameters are optimized with 5 constraints using Lean Optimization combined with Linear Programming. The method converges in this example in about 100 evaluations. This is less than the gradient method needs for its first step.

Optimization based scheduling for a class of production systems with integral constraints

Operation scheduling for a class of production systems with"instantly consumed"products is very important.It is challenging to satisfy the real time system demand and to consider the realizability of the production schedules.This paper formulates a new model for optimization based production scheduling problems with integral constraints.Based on the detailed analysis of the production rate constraints,it is proved that this type of optimization problems is equivalent to a smooth nonlinear programming problem.The reachable upper and lower bounds of the production amount in every period can be expressed as functions of two variables,i.e.,the production rate at the start and end of that period.It is also proved that the gradients of these functions are monotonic,and their convexity or concavity is guaranteed.When the production cost function is convex,this type of optimization problems is equivalent to a convex programming problem.With the above analysis,a two-stage solution method is developed to solve the production scheduling problems with integral constraints,and in many applications the global optimal solution can be obtained efficiently.With the new model and solution method,the difficulties caused by the constraints on production rate can be overcome and the optimal schedule can be obtained with the real time system demand satisfied.Numerical testing for scheduling of electric power production systems is performed and the testing results are discussed.It is demonstrated that the new model and solution method are effective.

Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE

The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.

An Effective Feature Modeling Approach for 3D Structural Topology Design Optimization

This paper presents a feature modeling approach to address the 3D structural topology design optimization withfeature constraints. In the proposed algorithm, various features are formed into searchable shape features bythe feature modeling technology, and the models of feature elements are established. The feature elements thatmeet the design requirements are found by employing a feature matching technology, and the constraint factorscombined with the pseudo density of elements are initialized according to the optimized feature elements. Then,through controlling the constraint factors and utilizing the optimization criterion method along with the filteringtechnology of independent mesh, the structural design optimization is implemented. The present feature modelingapproach is applied to the feature-based structural topology optimization using empirical data. Meanwhile, theimproved mathematical model based on the density method with the constraint factors and the correspondingsolution processes are also presented. Compared with the traditional method which requires complicated constraintprocessing, the present approach is flexibly applied to the 3D structural design optimization with added holesby changing the constraint factors, thus it can design a structure with predetermined features more directly andeasily. Numerical examples show effectiveness of the proposed feature modeling approach, which is suitable for thepractical engineering design.

Shuffled complex evolution coupled with stochastic ranking for reservoir scheduling problems

This paper introduces an optimization method(SCE-SR)that combines shuffled complex evolution(SCE)and stochastic ranking(SR)to solve constrained reservoir scheduling problems,ranking individuals with both objectives and constrains considered.A specialized strategy is used in the evolution process to ensure that the optimal results are feasible individuals.This method is suitable for handling multiple conflicting constraints,and is easy to implement,requiring little parameter tuning.The search properties of the method are ensured through the combination of deterministic and probabilistic approaches.The proposed SCE-SR was tested against hydropower scheduling problems of a single reservoir and a multi-reservoir system,and its performance is compared with that of two classical methods(the dynamic programming and genetic algorithm).The results show that the SCE-SR method is an effective and efficient method for optimizing hydropower generation and locating feasible regions quickly,with sufficient global convergence properties and robustness.The operation schedules obtained satisfy the basic scheduling requirements of reservoirs.

Task scheduling for multi-electro-magnetic detection satellite with a combined algorithm

Task scheduling for electro-magnetic detection satellite is a typical combinatorial optimization problem. The count of constraints that need to be taken into account is of large scale. An algorithm combined integer programming with constraint programming is presented. This algorithm is deployed in this problem through two steps. The first step is to decompose the original problem into master and sub-problem using the logic-based Benders decomposition; then a circus combines master and sub-problem solving process together, and the connection between them is general Benders cut. This hybrid algorithm is tested by a set of derived experiments. The result is compared with corresponding outcomes generated by the strength Pareto evolutionary algorithm and the pure constraint programming solver GECODE, which is an open source software. These tests and comparisons yield promising effect.

Multimodal processes optimization subject to fuzzy operation time constraints:declarative modeling approach

We present an extension of the resource-constrained multi-product scheduling problem for an automated guided vehicle(AGV) served flow shop, where multiple material handling transport modes provide movement of work pieces between machining centers in the multimodal transportation network(MTN). The multimodal processes behind the multi-product production flow executed in an MTN can be seen as processes realized by using various local periodically functioning processes. The considered network of repetitively acting local transportation modes encompassing MTN's structure provides a framework for multimodal processes scheduling treated in terms of optimization of the AGVs fleet scheduling problem subject to fuzzy operation time constraints. In the considered case, both production takt and operation execution time are described by imprecise data. The aim of the paper is to present a constraint propagation(CP) driven approach to multi-robot task allocation providing a prompt service to a set of routine queries stated in both direct and reverse way. Illustrative examples taking into account an uncertain specification of robots and workers operation time are provided.

Towards Prevention of Sportsmen Burnout:Formal Analysis of Sub-Optimal Tournament Scheduling

Scheduling a sports tournament is a complex optimization problem,which requires a large number of hard constraints to satisfy.Despite the availability of several such constraints in the literature,there remains a gap sincemost of the new sports events pose their own unique set of requirements,and demand novel constraints.Specifically talking of the strictly time bound events,ensuring fairness between the different teams in terms of their rest days,traveling,and the number of successive games they play,becomes a difficult task to resolve,and demands attention.In this work,we present a similar situation with a recently played sports event,where a suboptimal schedule favored some of the sides more than the others.We introduce various competitive parameters to draw a fairness comparison between the sides and propose a weighting criterion to point out the sides that enjoyed this schedule more than the others.Furthermore,we use root mean squared error between an ideal schedule and the actual ones for each side to determine unfairness in the distribution of rest days across their entire schedules.The latter is crucial,since successively playing a large number of games may lead to sportsmen burnout,which must be prevented.

A Multi-Criteria Decision Making for the Unrelated Parallel Machines Scheduling Problem

In this paper, we propose a multi-criteria machine-schedules decision making method that can be applied to a produc-tion environment involving several unrelated parallel machines and we will focus on three objectives: minimizing makespan, total flow time, and total number of tardy jobs. The decision making method consists of three phases. In the first phase, a mathematical model of a single machine scheduling problem, of which the objective is a weighted sum of the three objectives, is constructed. Such a model will be repeatedly solved by the CPLEX in the proposed Multi-Objective Simulated Annealing (MOSA) algorithm. In the second phase, the MOSA that integrates job clustering method, job group scheduling method, and job group – machine assignment method, is employed to obtain a set of non-dominated group schedules. During this phase, CPLEX software and the bipartite weighted matching algorithm are used repeatedly as parts of the MOSA algorithm. In the last phase, the technique of data envelopment analysis is applied to determine the most preferable schedule. A practical example is then presented in order to demonstrate the applicability of the proposed decision making method.

Fair Scheduling Models for Doubles Group Competitions

This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n + 2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.

Land Use Structure Optimization Under Systematic Framework

This paper puts forward the concept of land use structure optimization under space_time coupling through analyzing the systematic characteristic of land use structure optimization.It mainly expounds the construction of land use structure optimization model at different levels.Lastly,this paper explains the practicableness of land use structure optimization under systematic framework through the example of Qionghai city.