The increasing penetration of renewable energy and rising electricity demand are driving the need to integrate new buses and transmission lines into transmission grids. These trends are reshaping transmission expansion planning (TEP), motivating the development of effective methodologies to manage the resulting complexity. This paper introduces the longest shortest-path connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of TEP using valid inequalities (VIs). Traditional approaches for determining big-M coefficients in disconnected TEP networks typically rely on solving the computationally intensive longest path problem (LPP). In contrast, LSPC circumvents these limitations by efficiently identifying relevant power-flow paths between disconnected buses within the expansion network. We demonstrate that the VIs generated from these identified paths dominate those derived from LPP-based methods and other existing approaches.
A direct search method for local unconstrained optimization of nonsmooth functions is presented. The method performs forward tracking line searches along a sequence of poll directions, where the lengths of many poll directions are bounded away from zero. Convergence is shown under mild conditions when the poll directions are generated from any scrambled Halton sequence. An arbitrary step is incorporated into the method, allowing other line searches to be used to accelerate the convergence rate. This paper compares the performance of the Sobol, standard Halton and a scrambled Halton poll sequences with no arbitrary step. Numerical trials show the latter performs similarly to the Sobol sequence and outperforms the standard Halton sequence.
When the follower problem in a bilevel program admits multiple optimal solutions, the leader’s outcome depends on how ties are resolved. This yields the classical optimistic/pessimistic ambiguity and makes the model unstable (ill-posed) from a predictive viewpoint. We study linear–linear bilevel programs without additional upper-level coupling constraints involving the follower variables and propose a stabilization mechanism that preserves the follower’s linear objective as a primary criterion, while resolving ties within the follower optimal set through a strictly convex quadratic rule. This tie-break selects a unique follower reaction and can be anchored to implement any prescribed follower optimum (e.g., a leader-favorable one). We then interpret stabilization as a semi-cooperation contract: in the presence of a (possibly unknown) secondary preference used by the follower to break ties, the leader may need to compensate the follower to accept the leader-chosen tie-break. We define the price of semi-cooperation as the minimal transfer ensuring acceptance, and we derive explicit formulas and robust bounds under preference uncertainty. A computational illustration highlights stabilization and pricing behavior on randomly generated instances.
Complex information systems often operate in cooperative environments where participants’ involvement is uncertain and may occur at multiple probabilistic participation levels. The purpose of this paper is to introduce a congruent optimization approach for cooperative games with probabilistic participation levels. We first define a new characteristic function with probabilistic participation proportional forms of cooperative games with probabilistic participation levels. The congruent contribution excess of players is introduced. An optimization problem is constructed by minimizing the variance of the congruent contribution excess of players. A new solution named the congruent value is proposed. Then, we establish the axiomatization of the congruent value. An interesting result that shows the relationship between the congruent value and the equal division value is explored. Considering the influence of the probabilistic participation level of players, the probabilistic weighted congruent value is developed. The axiomatization of the probabilistic weighted congruent value is provided. Some ideal properties of the proposed value are discussed.
We introduce three novel variants of the projection extragradient algorithm for solving equilibrium problems in real Hilbert spaces, without imposing any generalized monotonicity assumptions on the bifunctions involved. The proposed approach replaces the traditional shrinking projection step with a projection onto the intersection of the feasible set and a suitably chosen half-space, offering a more flexible and effective strategy. To address cases where the bifunctions do not satisfy a Lipschitz-type condition, we incorporate a general linesearch mechanism for determining the step size. When the bifunctions are of Lipschitz-type with known constants, this linesearch is rendered unnecessary; in the absence of such constants, we propose an adaptive step size rule. All three algorithms are rigorously proven to converge strongly to a solution, even without assuming the joint weak continuity of the bifunction-an assumption often required in existing literature. Numerical examples are presented to illustrate the efficiency and practical performance of the proposed methods.
We propose a simple proof of the worst-case iteration complexity for the Difference of Convex functions Algorithm DCA for unconstrained minimization, showing that the global rate of convergence of the norm of the objective function’s gradients at the iterates converge to zero like o(1/k). A small example is also provided indicating that the rate cannot be improved.
This paper introduces an innovative mathematical model aimed at optimizing assembly line balancing and scheduling in Human-Robot Collaboration (HRC) environments. In today’s manufacturing landscape, HRC is critical for boosting both productivity and flexibility. The presented model focuses on minimizing the cycle time while adhering to operational and financial constraints and addressing task allocation with setup times in complex, multi-station, and multi-mode assembly lines. The model is validated across various scenarios, demonstrating enhanced throughput and resource utilization. In conclusion, this study provides a practical framework to provide more adaptable and efficient assembly lines by optimizing HRC scheduling.
This study presents an accurate hybrid classification approach for dry bean varieties by integrating a lightweight one-dimensional Residual Network (1D-ResNet) with pre-extracted morphological features. The proposed architecture is designed to investigate how residual learning contributes to incremental feature refinement and stable optimization in low-dimensional morphological tabular data. By incorporating skip connections, the model facilitates effective modeling of nonlinear feature interactions while maintaining training stability. The framework operates directly on geometric and shape-based descriptors without relying on image-based representation learning. Experimental results over 10 independent runs demonstrate an average classification accuracy of 95.70
In the classical nonatomic routing game model on a simple network, we seek to determine for how many different levels of demand the equilibrium distribution of selfish users on the network can coincide with the optimal one. To this end, we study the Price of Anarchy as a function of the traffic inflow, in the special case of two-link parallel networks and polynomial costs. We obtain, in the most simple cases, some sharp bounds on the number of solutions.
This paper addresses binary stochastic difference-of-convex (DC) programming problems with applications to stochastic shortest path routing. We propose two complementary approaches: a Sample Average Approximation (SAA)—based method that reformulates the problem into a large-sum DC program with binary variables, solved via DCA and stochastic DCA (SDCA) combined with an exact penalty technique; and a stochastic approximation (SA)—based approach that directly tackles the original stochastic DC problem through iterative stochastic DCA with penalized DC constraints. Numerical experiments on benchmark stochastic shortest path problems demonstrate the effectiveness and scalability of the proposed algorithms. The results highlight the efficiency and versatility of DCA for solving discrete stochastic DC programs, especially in large-scale settings.
The increasing integration of electric vehicles into transportation fleets poses new challenges in the classical Vehicle Routing Problem, primarily due to the nonlinearity of the battery charging process. In the literature, the piecewise linear approximation and a formulation based on paths of charging stations are established approaches to deal with this complex function. In this paper, we address the Electric Vehicle Routing Problem using a realistic non-linear charging function, and we present an alternative exact method of linearising it by using Perspective Cuts. Additionally, we present a preprocessing algorithm for the elimination of dominated paths, i.e., paths that cannot be present in an optimal solution. The logic of our preprocessing, unlike previous methods, does not depend on the piecewise linear approximation. The proposed methods are validated through computational experiments on benchmark instances, demonstrating their effectiveness in improving model accuracy while maintaining computational tractability.
In this work, we propose a Stackelberg-like model for a resource allocation problem over an urban region. The model incorporates transportation costs, distribution costs, and utility functions. A social planner aims to minimize the total cost while maximizing the welfare of the population that receives the resource. The resulting formulation is a bilevel optimization problem—also known as a Stackelberg game in game theory. The existence of the best-response function is established by means of results from optimal transport theory.
In this paper, we introduce ROS-GPU, a novel large-scale image classification algorithm that replaces the conventional multi-layer perceptron (MLP) classification head with an ensemble of Random Oblique Stumps (ROS) trained using a GPU-optimized Multi-Class Linear Discriminant Analysis (MC-LDA). Unlike prior ROS-based approaches, the proposed algorithm unifies oblique stump construction and multi-class discrimination through a fully parallel One-Versus-All (OVA) MC-LDA formulation, specifically designed for efficient execution on modern GPU architectures. To address class imbalance in large-scale multi-class datasets, the algorithm incorporates an under-sampling strategy within the OVA scheme to improve class balance and stabilize scalable stump learning. The proposed ROS-GPU algorithm is implemented using CUDA and cuBLAS and is evaluated on the ImageNet benchmark. Experimental results demonstrate that ROS-GPU significantly reduces training time while achieving competitive classification accuracy compared to established learning methods. In particular, ROS-GPU completes ImageNet training in 5.86 min while attaining an accuracy of 89.44
We introduce the integrated block relocation and fleet allocation problem with soft precedence constraints, which jointly determines the unloading sequence of items and their assignment to a heterogeneous fleet of capacity-limited vehicles. The new problem aims at maximizing the number of delivered items while minimizing violations of a given item precedence order. Items with different destinations cannot be allocated to the same vehicle. The problem finds applications in logistic operations in steel plants and container terminals, as well as in humanitarian supply operations in the context of natural or industrial disasters. We formalize the problem as a lexicographic bi-objective model, providing two compact integer linear programming formulations reflecting different modeling perspectives, two reformulations and a family of valid inequalities. The models incurring the best dual bounds are used as backbone for a Kernel Search heuristic exploiting problem-specific structural properties. Computational experiments on a benchmark derived from the block relocation literature show that the exact models solve most instances to optimality within one hour, while the heuristic provides high-quality solutions with short runtimes and near-optimal gaps, making it an effective and reproducible approach for larger instances.
Motivated by a recent FIFPRO (the International Federation of Professional Footballers’ Associations) report on the adverse effects of international travel load and time-zone crossings on player performance and physical well-being, this paper develops an optimization framework to reduce the total distance traveled by national teams in the FIFA World Cup 2026. We propose a mixed integer programming model that minimizes the total internal distance traveled by the 48 teams in the group stage, subject to the structural constraints implied by FIFA’s official schedule. Computational results yield a feasible schedule that reduces total internal travel distance by 50 https://igorlucindo.github.io/fifa-world-cup-2026-scheduler-APP/ .
This paper studies a novel integrated production scheduling and vehicle routing problem with order acceptance. The problem entails selecting a subset of orders for acceptance, followed by determining a production schedule and delivery plan that adheres to the committed due dates. The objective is to maximize the revenue from accepted orders. To address this NP-hard problem, this paper proposes a mixed-integer linear programming (MILP) model and develops an enhanced adaptive general variable neighborhood search (AGVNS) algorithm incorporating a novel adaptive shaking mechanism. Experimental results demonstrate that the proposed algorithm achieves both high solution quality and computational efficiency.
In this paper, we study a stochastic parallel machine scheduling problem denoted as Pm|r_j, p_j stoch|∑ w_j E(C_j) , where the processing time of each job follows a general discrete distribution. To address this problem, we develop an exact solution approach by extending the set partitioning model. Unlike its deterministic counterpart, the computation of the expected completion time E(C_j) in this stochastic setting is highly complex and nonlinear, rendering traditional solution methods inapplicable. To overcome this challenge, we propose a branch-and-price algorithm to solve the problem efficiently. Specifically, we introduce a series of approximations for E(C_j) that can be computed significantly faster than the exact value. These approximations are employed to identify promising job sequences and to prune less profitable ones in the pricing subproblem of the column generation procedure. Computational experiments demonstrate that the proposed algorithm can solve large-scale instances of the stochastic parallel machine scheduling problem within a reasonable time. Furthermore, we show that our proposed method can be easily adapted to related problems such as Pm|r_j, d_j, p_j stoch|∑ w_j E(T_j) and Pm|r_j, d_j, p_j stoch|∑ w_j E(U_j) .
In this paper, we consider a class of stochastic inverse linear semidefinite optimal value problems, in which the forward problem is a linear semidefinite programming problem (LSDP), and the data in its constraints is affected by a random variable. Under some mild assumptions for LSDP, the corresponding inverse optimal value problem can be reformulated as a mathematical program with stochastic linear semidefinite complementarity constraints (MPSLSDCC). By employing the techniques of sample average approximation (SAA), we construct a series of smooth SAA subproblems and transform them into nonlinear semidefinite programming problems by utilizing the smooth Fischer-Burmeister function for linear semidefinite complementarity constraints. In addition, we prove that the sequence of global minimizer (respectively, KKT point) of these SAA subproblems converge with probability one (w.p.1) to a global minimizer (respectively, an S-stationary point) of MPSLSDCC under mild assumptions. Finally, some numerical experiments are presented to show the ability of our method for solving the given stochastic linear semidefinite inverse optimal value problems.
We present an effective warm-starting scheme for solving large linear complementarity problems (LCPs) arising from Nash equilibrium problems. The approach generates high-quality starting points that, when passed to the PATH solver, yield substantial reductions in computational time and variance. Our warm-start routine reformulates each agent’s linear program (LP) using strong duality, leading to a master problem with bilinear constraints that is equivalent to the original LCP. Bilinear terms emerge, for example, from system-level variables in the overall equilibrium problem that are exogenous to individual agent optimization problems. Approximate solutions are obtained using the difference-of-convex function algorithm for bilinear terms (DCA-BL) or a spatial branch-and-bound method (SBB). Unlike conventional bilinear approximation schemes, such as McCormick envelopes, DCA-BL does not rely on tight variable bounds. We test the scheme on a realistic LCP instance derived from a stochastic natural gas equilibrium model with nearly 100,000 variables. Without warm starts, PATH struggles to solve these instances within 24 h. With DCA-BL or SBB warm starts, solution times drop significantly; the largest instance is solved in about one hour after two hours of warm start. While both warm-start approaches yield faster and less variable computational times, experiments suggest that DCA-BL provides the best starting point, as measured by the resulting PATH runtime. Although demonstrated on a specific LCP, the warm-start method extends to any LCP derived from the KKT conditions of LPs for each agent combined with linear system-level constraints.
