Journal of Global Optimization最新文献

Maintenance and production exert reciprocal influence in practical manufacturing applications. However, decisions regarding production scheduling and maintenance planning are often made separately, leading to frequent conflicts between production and maintenance plans. This paper investigates an integrated production scheduling and maintenance planning problem for a parallel machine system, considering both deteriorating jobs and deteriorating maintenance activities. Additionally, the problem features constraints on the number of available maintenance activities due to maintenance budget limitations. The objective is to determine the optimal scheduling and maintenance plan that minimizes the makespan. To tackle this complex problem, we initially delve into the special case where jobs and maintenance activities are already assigned to machines. In our endeavor to minimize the makespan for each machine, we uncover some crucial structural properties and present a polynomial-time algorithm. Subsequently, we develop a hybrid algorithm that combines Whale Optimization Algorithm and Variable Neighborhood Search (WOA–VNS) to address the assignment challenge encompassing jobs and maintenance activities within the parallel machine environment. A series of rigorous comparative experiments are conducted to assess the effectiveness of the proposed algorithm. The results conclusively demonstrate the superior performance of the WOA–VNS algorithm over the WOA, VNS, ABC, and ACO algorithms in addressing the presented problem.

A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container. Moreover, specified ratios between the placed spheres of different radii must be satisfied. A corresponding mixed-integer nonlinear programming model is formulated. It enables the exact solution of small instances. For larger instances, a heuristic strategy is proposed, which relies on techniques for the generation of feasible points and the decomposition of open dimension problems. Numerical results are presented to demonstrate the viability of the approach.

Nonlinear dependence on a probability measure has recently been encountered with increasing intensity in stochastic optimization. This type of dependence corresponds to many situations in applications; it can appear in problems static (one-stage), dynamic with finite (multi-stage) or infinite horizon, and single- and multi-objective ones. Moreover, the nonlinear dependence can appear not only in the objective functions but also in the constraint sets. In this paper, we will consider static one-objective problems in which the nonlinear dependence appears in the objective function and may also appear in the constraint sets. In detail, we consider “deterministic” constraint sets, whose dependence on the probability measure is nonlinear, constraint sets determined by second-order stochastic dominance, and sets given by mean-risk problems. The last mentioned instance means that the constraint set corresponds to solutions which guarantee acceptable values of both criteria. To obtain relevant assertions, we employ the stability results given by the Wasserstein metric, based on the ( {{mathcal {L}}}_{1} ) norm. We mainly focus on the case in which a solution has to be obtained on the basis of the data and of investigating a relationship between the original problem and its empirical version.

A procedure is presented for finding the shortest network connecting three given undirected points, subject to a curvature constraint on both the path joining two of the points and the path that connects to the third point. The problem is a generalisation of the Fermat–Torricelli problem and is related to a shortest curvature-constrained path problem that was solved by Dubins. The procedure has the potential to be applied to the optimal design of decline networks in underground mines.

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater’s condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.

Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We focus on two convex relaxations, namely the reformulation–linearization technique (RLT) relaxation and the SDP-RLT relaxation obtained by combining the Shor relaxation with the RLT relaxation. Both relaxations yield lower bounds on the optimal value of a quadratic program with box constraints. We show that each component of each vertex of the RLT relaxation lies in the set ({0,frac{1}{2},1}). We present complete algebraic descriptions of the set of instances that admit exact RLT relaxations as well as those that admit exact SDP-RLT relaxations. We show that our descriptions can be converted into algorithms for efficiently constructing instances with (1) exact RLT relaxations, (2) inexact RLT relaxations, (3) exact SDP-RLT relaxations, and (4) exact SDP-RLT but inexact RLT relaxations. Our preliminary computational experiments illustrate that our algorithms are capable of generating computationally challenging instances for state-of-the-art solvers.

We propose a second-order method for unconditional minimization of functions f(z) of complex arguments. We call it the mixed Newton method due to the use of the mixed Wirtinger derivative (frac{partial ^2f}{partial {bar{z}}partial z}) for computation of the search direction, as opposed to the full Hessian (frac{partial ^2f}{partial (z,{bar{z}})^2}) in the classical Newton method. The method has been developed for specific applications in wireless network communications, but its global convergence properties are shown to be superior on a more general class of functions f, namely sums of squares of absolute values of holomorphic functions. In particular, for such objective functions minima are surrounded by attraction basins, while the iterates are repelled from other types of critical points. We provide formulas for the asymptotic convergence rate and show that in the scalar case the method reduces to the well-known complex Newton method for the search of zeros of holomorphic functions. In this case, it exhibits generically fractal global convergence patterns.