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The flexible job shop scheduling problem with sequencing flexibility and position-based learning effect is considered in the present work. In [K. A. G. Araujo, E. G. Birgin, and D. P. Ronconi, Technical Report MCDO02022024, 2024], models, constructive heuristics, and benchmark instances for the same problem were introduced. In the present work, we are concerned with the development of effective and efficient methods for its resolution. For this purpose, a local search method and four trajectory metaheuristics are considered. In the local search, we show that the classical strategy of only reallocating operations that are part of the critical path can miss better quality neighbors, as opposed to what happens in the case where there is no learning effect. Consequently, we analyze an alternative type of neighborhood reduction that eliminates only neighbors that are not better than the current solution. In addition, we also suggest a neighborhood cut and experimentally verify that this significantly reduces the neighborhood size, bringing efficiency, with minimal loss in effectiveness. Extensive numerical experiments with the local search and the metaheuristics are carried on. The experiments show that tabu search, built on the reduced neighborhood, when applied to large-sized instances, stands out in relation to other the other three metaheuristics, namely, iterated local search, greedy randomized adaptive search procedure, and simulating annealing. Experiments with classical instances without sequencing flexibility show that the introduced methods also stand out in relation to methods from the literature. All the methods introduced, as well as the instances and solutions found, are freely available. As a whole, we build a test suite that can be used in future work.

This paper addresses the flexible job shop scheduling problem with sequencing flexibility and position-based learning effect. In this variant of the flexible job shop scheduling problem, precedence constraints of the operations constituting a job are given by an arbitrary directed acyclic graph, in opposition to the classical case in which a total order is imposed. Additionally, it is assumed that the processing time of an operation in a machine is subject to a learning process such that the larger the position of the operation in the machine, the faster the operation is processed. Mixed integer programming and constraint programming models are presented and compared in the present work. In addition, constructive heuristics are introduced to provide an initial solution to the models' solvers. Sets of benchmark instances are also introduced. The problem considered corresponds to modern problems of great relevance in the printing industry. The models and instances presented are intended to support the development of new heuristic and metaheuristics methods for this problem.

Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets defined through intersections of smooth sets, and formulate precise conditions to avoid singular situations. This allows us to define a general framework for solving optimization problems depending on minimization diagrams. The particular case of Voronoi diagrams is discussed to illustrate the general theory. A variety of numerical experiments is presented. The experiments include constructing Voronoi diagrams with cells of equal size, cells satisfying conditions on the relative size of their edges or their internal angles, cells with the midpoints of pairs of Voronoi and Delaunay edges as close as possible, or cells of varying sizes governed by a given function. Overall, the experiments show that the proposed methodology allows the construction of customized Voronoi diagrams using off-the-shelf well-established optimization algorithms.

The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of balls. This allows us to obtain analytical expressions for first- and second-order derivatives using nonsmooth shape optimization techniques under appropriate regularity assumptions. Singular cases are also studied using asymptotic analysis. For the case of regions given by the union of disjoint convex polygons, algorithms based on Voronoi diagrams that do not rely on approximations are given to compute the derivatives. Extensive numerical experiments illustrate the capabilities and limitations of the introduced approach.

Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely used test bed compares the presented approach with its plain (i.e. non-accelerated) version that makes part of the R package BB. Additional numerical experiments compare the proposed method with NITSOL, a state-of-the-art solver for nonlinear systems. The comparison shows that the acceleration process greatly improves the robustness of its counterpart included in the existent R package. As a by-product, an interface is provided between R and the consolidated CUTEst collection, which contains over a thousand nonlinear programming problems of all types and represents a standard for evaluating the performance of optimization methods.

Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently, these methods are attractive for solving large-scale nonlinear systems. However, the convergence of these algorithms may be slow in critical cases; therefore, acceleration procedures are welcome. In this paper, we suggest to employ a variation of the Sequential Secant Method in order to accelerate Sequential Residual Methods. The performance of the resulting algorithm is illustrated by applying it to the solution of very large problems coming from the discretization of partial differential equations.

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- and high-precision evaluations. In the present research, it is recognized that many problems with expensive objective functions are nonsmooth and, sometimes, even discontinuous. Having this in mind, the Inexact Restoration approach is extended to the nonsmooth or discontinuous case. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that take advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam.

In this work, the online printing shop scheduling problem is considered. This challenging real problem, that appears in the nowadays printing industry, can be seen as a flexible job shop scheduling problem with sequence flexibility in which precedence constraints among operations of a job are given by an arbitrary directed acyclic graph. In addition, several complicating particularities such as periods of unavailability of the machines, resumable operations, sequence-dependent setup times, partial overlapping among operations with precedence constraints, release times, and fixed operations are also present in the addressed problem. In the present work, mixed integer linear programming and constraint programming models for the minimization of the makespan are presented. Modeling the problem is twofold. On the one hand, the problem is precisely defined. On the other hand, the capabilities and limitations of a commercial software for solving the models are analyzed. Extensive numerical experiments with small-, medium-, and large-sized instances are presented. Numerical experiments show that the commercial solver is able to optimally solve only a fraction of the small-sized instances when considering the mixed integer linear programming model; while all small-sized and a fraction of the medium-sized instances are optimally solved when considering the constraint programming formulation of the problem. Moreover, the commercial solver is able to deliver feasible solutions for the large-sized instances that are of the size of the instances that appear in practice.

In this work, the online printing shop scheduling problem introduced in (Lunardi et al., Mixed Integer Linear Programming and Constraint Programming Models for the Online Printing Shop Scheduling Problem, Computers & Operations Research, to appear) is considered. This challenging real scheduling problem, that emerged in the nowadays printing industry, corresponds to a flexible job shop scheduling problem with sequencing flexibility; and it presents several complicating specificities such as resumable operations, periods of unavailability of the machines, sequence-dependent setup times, partial overlapping between operations with precedence constraints, and fixed operations, among others. A local search strategy and metaheuristic approaches for the problem are proposed and evaluated. Based on a common representation scheme, trajectory and populational metaheuristics are considered. Extensive numerical experiments with large-sized instances show that the proposed methods are suitable for solving practical instances of the problem; and that they outperform a half-heuristic-half-exact off-the-shelf solver by a large extent. Numerical experiments with classical instances of the flexible job shop scheduling problem show that the introduced methods are also competitive when applied to this particular case.

A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by \"Ozg\"uven, \"Ozbakir, and Yavuz (Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Applied Mathematical Modelling, 34:1539--1548, 2010), using instances from the literature and instances inspired by real data from the printing industry., Comment: 15 pages, 2 figures, 4 tables. Optimization Letters, 2013