Mathematical Programming Research Articles

Solving the minimum labeling global cut problem by mathematical programming

AbstractAn edge‐labeled graph (ELG) is a graph such that is the set of vertices, is the set of edges, is the set of labels (colors), and each edge has a label associated. Given an ELG , the goal of the minimum labeling global cut problem (MLGCP) is to find a subset such that the removal of all edges with labels in disconnects and is minimum. This work proposes three new mathematical formulations for the MLGCP, namely PART, VC, and TE as well as branch‐and‐cut algorithms to solve them. Additionally, a theoretical study was carried out on the MLGCP input graph, leading to the concept of chromatic closure, used in preprocessing algorithms for this model PART. Finally, a comprehensive polyhedral investigation of the model is performed. The computational experiments showed that the model, adopting the chromatic closure concept and its branch‐and‐cut algorithm, can solve small to average‐sized instances in reasonable times.

Complex Instruction: developing teachers’ professional knowledge and practice in Brazil

ABSTRACT ‘Programa de Especialização Docente Brasil’ (PED Brasil) is a learning and professional development program in mathematics or science education for primary or secondary in-service schoolteachers. Designed to be a teacher education program that addresses issues related to educational quality and equity in racially, socially, and academically diverse Brazilian schools, PED Brasil intended to craft a program with a signature pedagogy that could be capable of shaping the ways of thinking and acting in the teaching profession. PED Brasil does it by integrating different dimensions of knowledge and demonstrating various aspects of professional practice, considering the democratic society we aim to build. In this paper, we analyse how PED Brasil has adopted Complex Instruction as its signature pedagogy.

A Raster-Based Multi-Objective Spatial Optimization Framework for Offshore Wind Farm Site-Prospecting

Siting an offshore wind project is considered a complex planning problem with multiple interrelated objectives and constraints. Hence, compactness and contiguity are indispensable properties in spatial modeling for Renewable Energy Sources (RES) planning processes. The proposed methodology demonstrates the development of a raster-based spatial optimization model for future Offshore Wind Farm (OWF) multi-objective site-prospecting in terms of the simulated Annual Energy Production (AEP), Wind Power Variability (WPV) and the Depth Profile (DP) towards an integer mathematical programming approach. Geographic Information Systems (GIS), statistical modeling, and spatial optimization techniques are fused as a unified framework that allows exploring rigorously and systematically multiple alternatives for OWF planning. The stochastic generation scheme uses a Generalized Hurst-Kolmogorov (GHK) process embedded in a Symmetric-Moving-Average (SMA) model, which is used for the simulation of a wind process, as extracted from the UERRA (MESCAN-SURFEX) reanalysis data. The generated AEP and WPV, along with the bathymetry raster surfaces, are then transferred into the multi-objective spatial optimization algorithm via the Gurobi optimizer. Using a weighted spatial optimization approach, considering and guaranteeing compactness and continuity of the optimal solutions, the final optimal areas (clusters) are extracted for the North and Central Aegean Sea. The optimal OWF clusters, show increased AEP and minimum WPV, particularly across offshore areas from the North-East Aegean (around Lemnos Island) to the Central Aegean Sea (Cyclades Islands). All areas have a Hurst parameter in the range of 0.55–0.63, indicating greater long-term positive autocorrelation in specific areas of the North Aegean Sea.

Robust Semi-Infinite Interval Equilibrium Problem Involving Data Uncertainty: Optimality Conditions and Duality

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from the literature. We introduce the dual robust version of the above problem, prove the Mond–Weir-type weak and strong duality theorems, and illustrate our results with an example.

Design of Integrated Energy–Water Systems Using Automated Targeting Modeling Considering the Energy–Water–Carbon Nexus

The swift expansion of the global population and economy has spurred growing requirements for energy and water in recent decades. Inefficient energy and water consumption, however, has led to an increase in CO2 emissions. Hence, the socio-economic development of a country must consider the interconnections between energy, water and carbon, as there are mutual dependencies among these three elements. This work considers the nexus between energy, water and carbon in the design of integrated energy–water systems using a new automated targeting modeling (ATM) framework. ATM incorporates the advantages of the insight-based Pinch method and a mathematical programming approach to provide visual understanding for a thorough analysis of the problem while guaranteeing accurate solutions. Minimum targets of power and water based on the integrated network operation were established by the ATM, with corresponding carbon emissions. A specific goal of annual carbon emissions reduction was set as the constraint and the ATM optimized the capacities of the components in the system accordingly to achieve minimum overall cost. The application of ATM on an industrial plant case study shows that a target of 45% reduction in the carbon discharge amount was achieved by shifting to greener fuel in the energy system at a minimum overall cost increase of 0.45% only. The framework can assist users in meeting power and water loads in their plant while planning for the appropriate decarbonization efforts at the minimum possible cost.

Evaluating didactic strategies for teaching mathematics: A Policy–Driven approach to gender equity in Panama’s education system

This article evaluates the Didactic Strategies for Teaching Mathematics (DSTM) program, designed to enhance the teaching of mathematical content in primary and secondary education in a hybrid modality. In alignment with SENACYT’s Gender-STEM-2040 Policy, which emphasizes gender equality as a foundational principle of education, this study aims to assess whether initial teacher training aligns with this policy through the use of mathematical strategies promoting gender equality. A descriptive-correlational approach was applied to a sample of 64 educators, selected based on their responses during the training, with the goal of improving teaching and data collection methodologies. Findings indicate that, although most teachers actively engage in training, an androcentric approach persists, with sexist language and a curriculum that renders girls invisible, hindering the fulfillment of the National Gender Equality Policy in Science, Technology, and Innovation of Panama (Gender-STEM Policy 2040). Additionally, through a serendipitous finding, a significant gap in student activity levels, especially in secondary school, was discovered. While in primary school, activity levels were similar between genders, a decline in active participation among girls in secondary school was observed. This discovery, not initially contemplated in the study’s objectives, provides valuable insights into gender differences in active participation, particularly in higher educational stages. The serendipity suggests the need for further exploration of social, environmental, and family factors that may influence this decrease in girls’ active participation. The article concludes with a preliminary diagnosis and a call to deepen gender equality training and the effective implementation of coeducation in Panama’s educational system.

Employing battery energy storage systems for flexible ramping products in a fully renewable energy power grid: A market mechanism and strategy analysis through multi-Agent Markov games

In high-proportion renewable energy power systems, flexible ramping products (FRPs) are critical for mitigating the volatility of renewable energy outputs and enhancing the adaptability of power systems. This paper aims to explore a fully renewable energy power system, with a battery energy storage system (BESS) as the sole provider of FRPs. An innovative market mechanism and new approaches to market equilibrium analysis are introduced. Initially, a common day-ahead (DA) market is established, covering both electricity and ancillary services with FRPs. The setup allows FRP providers to make bidding decisions and get rewarded based on actual ramping mileages. A bi-level multi-agent Markov game (MG) model is formulated. The upper level integrates the proposed strategies of wind power plants (WPP), photovoltaic power plants (PVP), and BESS, while the lower level encompasses the joint market clearing mechanism. An iterative solution algorithm, using reinforcement learning, is also introduced to address the model, effectively circumventing the privacy concerns associated with traditional mathematical programming methods. The proposed solution models and strategies are validated and demonstrated to be effective through two illustrative examples, highlighting their application and relevance in fully renewable energy power systems.

User preferences in ride-sharing mathematical models for enhanced matching

Ride-sharing services have attracted significant interest due to overcrowding, limited energy resources, and environmental concerns. This study proposes a mathematical programming model that integrates user preferences into the ride-sharing problem with transfer. Passenger transfer in ride-sharing problems addresses the limitations of the matching process, especially in less-populated areas. It allows passengers to be dropped off at meeting points and continue with another driver. Moreover, considering user preferences in ride-sharing systems is crucial for enhancing efficiency and user satisfaction. Accordingly, we propose a Preference-Driven Matching Algorithm for the matching process. Our proposed algorithm captures user preferences and provides potential matches. In addition, we introduce an Iterative Enhance-and-Optimize Algorithm capable of producing high-quality solutions within short computational times. We evaluate the efficiency of these approaches across various instances, focusing on real-scale scenarios. Based on the results, the model with preferences demonstrates effective performance compared to other methods. Our findings underscore the importance of user preferences in optimizing ride-sharing problems and highlight the trade-off between efficiency and user satisfaction. By incorporating user preferences, our approach results in higher user satisfaction, a more responsive and efficient system with reduced response times, and increased demand and revenue by servicing more users.

Maximizing the number of allowable approximation errors when building a linear regression model

Subject of research: errors in approximation of a linear regression model within the framework of a logical-algebraic approach to data analysis. Purpose of the study: to develop an algorithmic method for solving the problem of maximizing the number of permissible approximation errors using a linear-Boolean programming computer. Methods and objects of research: the object of research is a linear regression model, the methods are linear regression analysis and mathematical programming apparatus. Main results of the study: an algorithmic method is proposed for maximizing the number of permissible absolute and relative errors in approximation of a linear regression equation, which reduces to solving linear-Boolean programming problems of a dimension acceptable for practical situations. Solving generated problems of this type should not cause computational problems due to a significant number of effective software tools, for example, the LPsolve program, which is freely available on the Internet.

Mathematical crystal chemistry: A mathematical programming approach to crystal structures of inorganic compounds

Mathematical crystal chemistry: A mathematical programming approach to crystal structures of inorganic compounds

Arguing for Access: Teachers’ Perspectives on the Use of Argumentation in Elementary Mathematics

This study investigates teachers’ perspectives on the use of a mathematical argumentation teaching strategy in elementary mathematics in which students disprove mathematical statements they already know to be false. Mathematical argumentation is a process through which students develop an argument about a mathematical concept and rationalize its truth or untruth through mathematical reasoning but is if often underused in mathematics. In this study we focused on a argumentation tasks which involved providing students with number statements which they already knew to be false, and inviting them to argue, using visuals, numeric notation, and/or written explanations, why it was false. Through practical action research, seven teachers from two different schools implemented this approach in their mathematics programs to one hundred and thirty-one students over the course of five months. Findings indicate this approach was easy to implement, improved student engagement, supported learners who struggled and deepened students’ mathematical knowledge. We believe that this approach can be used as a precursor to more formal proofs and provide more access for teachers and students in exploring mathematical proofs in elementary classrooms.

Mixture-of-Experts Based Dissociation Kinetic Model for De Novo Design of HSP90 Inhibitors with Prolonged Residence Time.

The dissociation rate constant (koff) significantly impacts the drug potency and dosing frequency. This work proposes a powerful optimization-based framework for de novo drug design guided by koff. First, a comprehensive database containing 2,773 unique koff values is created. Based on the database, a novel generic dissociation kinetic model is developed with a mixture-of-experts architecture, enabling high-throughput predictions of koff with high accuracy. The developed model is then integrated with an optimization-based mathematical programming approach to design drug candidates with low koff. Finally, the τ-RAMD method is utilized to rigorously verify the designed potential drug candidates. In a case study, the framework successfully identified numerous new potential HSP90 inhibitor candidates, achieving a maximum 45.7% improvement in residence time (τ = 1/koff) compared to that of a known exceptional HSP90 inhibitor. These findings demonstrate the feasibility and effectiveness of the kinetics-guided optimization-based de novo drug design framework in designing drug candidates with prolonged τ.

Hierarchical Game Theory-Based Optimal Power Management for Both Seaports and Ships

Unlike land-based power systems, a seaport microgrid is not only equipped with extensive electrification but also connected with ships, which turns maritime power management into a comprehensive transportation-power coordination problem. To fully exploit the potential of shipboard power systems for energy efficiency improvement of seaports, a hierarchical Stackelberg game-based framework is developed in this paper to achieve efficient power management for both seaports and ships. In this framework, the seaport microgrid serves as a leader to manage the local sources and determine the price for ships to maximize revenue, considering the influence of both the power side and transportation side. On the other hand, the ships act as followers to decide the charging and service strategies for an optimal trade-off between the benefits from onboard battery charging and the ship service cost. The proposed game is solved as a bilevel optimization problem via mathematical programming with the equilibrium constraints method. The proposed algorithm's efficiency is evaluated through numerical simulations. The simulation results demonstrate that the proposed power management method can simultaneously increase the economic profits of seaports and improve the service of ships at berth. Compared to traditional energy management methods, the comprehensive benefits can be increased by approximately 36%.

On multiobjective fractional programs with vanishing constraints

The aim of this article is to combine the study of fractional programming and mathematical programs with vanishing constraints for the first time in literature. This paper deals with multiobjective fractional programs with vanishing constraints (MFPVC) involving continuously differentiable functions. Necessary and sufficient optimality conditions are derived for a feasible point to be an efficient (or local efficient) solution of the (MFPVC). A parametric dual model has been formulated and duality results are established with the primal (MFPVC).

Heat transport analysis of three-dimensional Magnetohydrodynamics nanofluid flow through an extending sheet with thermal radiation and heat source/sink

Regarding heat transformation efficiency, the hybrid nanofluid performs superior to the nanofluid. The majority of hybrid nanofluid uses are in the industrial sector, producing solar energy, cooling generators, and vehicle heat transformation. Heat transfer and nanofluid velocity are the two most crucial transport properties that must be evaluated before the first and second thermodynamics equations are applied to nanoscale fluids. The objective of this work is to investigate the characteristics of transmission of heat of magnetohydrodynamic (MHD) nanofluid (Ag/H2O)and hybrid nanofluid (Ag+Al2O3/H2O)flow on a linear extensible sheet when magnetic forces are present. Similarity variables are applied to transform a set of nonlinear dimensionless partial-differential equations to collection of ordinary-differential equations. The non-analytical solutions of these transformed equations are found utilizing the MATLAB mathematical program's bvp4c function. The impression of various physical attributes along skin friction coefficients and properties of heat transmission are analyzed. The behavior of key parameters, including surface stretching ratio, rotational and magnetic effects, for temperature and velocity, is shown using graphs and tables. In conclusion, hybrid nanofluids, which comprise silver and aluminum oxide nanoparticles dispersed in water, outperform silver-water nanofluids by around 10-15% under magnetohydrodynamic (MHD). The higher thermal conductivity of these hybrid nanofluids allows for better heat dissipation, making them an appealing option for applications that need optimal thermal management in the presence of magnetic fields.

ANALYSIS OF FLYASH AGGREGATE BEHAVIOR IN GEOPOLYMER CONCRETE BEAMS USING METHOD OF INITIAL FUNCTIONS (MATHEMATICAL PROGRAMMING)

The stipulated performance of flyash aggregates in geopolymer concrete beams (composite beam) has been explained using the Method of Initial Functions (MIF) via mathematical programming. This research has specifically focused on understanding its strength and durability characteristics. Geopolymer concrete is now being evaluated as a successful alternative in terms of sustainability in the construction sector and has used flyash, an industrial by-product, for several years as a major binder. The major theme adopted in the present research is concentrated on the mechanical and structural behavior of geopolymer concrete beams partially replaced by flyash aggregates for civil engineering applications. The present paper focuses on using the Method of Initial Functions to model and analyze beam behavior subjected to various loading conditions within a strong mathematical programming approach. In the current study, an explanatory analysis of the flexural strength, load-deflection characteristics, and crack opening profile is conducted without constructing a beam specimen by using MIF.

A Hybrid Fuzzy Mathematical Programming Approach for Manufacturing Inventory Models with Partial Trade Credit Policy and Reliability

This study introduces an inventory model for manufacturing that prioritizes product quality and cost efficiency. Utilizing fuzzy logic and mathematical programming, the model integrates fuzzy numbers to describe uncertainties associated with manufacturing costs and quality control parameters. The model extends beyond conventional inventory systems by incorporating a dynamic mechanism to halt production, employing fuzzy decision variables to optimize the economic order quantity and minimize total costs. Key innovations include the application of approaches related to graded mean integration for defuzzification and the use of Kuhn–Tucker conditions to ensure optimal solutions under complex constraints. These approaches facilitate the precise management of production rates, inventory levels, and cost factors, which are essential in achieving a balance between supply and demand. A computational analysis validates the model’s effectiveness, demonstrating cost reductions while maintaining optimal inventory levels. This underscores the potential of integrating fuzzy arithmetic with traditional optimization techniques to enhance decision making in inventory management. The model’s adaptability and accuracy indicate its broad applicability across various sectors facing similar challenges, offering a valuable tool for operational managers and decision makers to improve efficiency and reduce waste in production cycles.

Technology Adaption in Distance Teacher Training: The Impact of Demographic Factors on Learners’ Technology Adaption

Understanding how demographic characteristics influence students' technology adaptation is crucial for effective online learning. This study explored the impact of these characteristics on distance education (DE) students' technology adaptation at a sub-Saharan African university. Using a descriptive survey design with a high-reliability score (Cronbach’s Alpha = 0.898), data were collected from 200 DE students across 14 study centres. The study tested seven hypotheses, employing statistical analyses like ANOVA, t-tests, and post hoc tests. Results revealed that while gender and employment status did not significantly affect technology adaptation, age, academic programme, academic level, and study centre did. Students aged 26-35 adapted better, with those in Mathematics and English programs showing higher adaptation scores compared to those in the Postgraduate Diploma in Education (PGDE) program. Additionally, higher-level students and those from well-resourced study centres demonstrated superior adaptability. The study suggests providing targeted support based on age, academic programme, and study centre resources to enhance technology adaptation in DE. To further improve students' technology proficiency, the study recommends that DE institutions offer regular training sessions and workshops to help students navigate online platforms, use digital libraries, and maximize productivity tools.

ON THE SOLUTION UNIQUENESS IN PORTFOLIO OPTIMIZATION AND RISK ANALYSIS

In this paper, we consider the issue of solution uniqueness of the mean-deviation portfolio optimization problem and its inverse for asset returns distributed over a finite number of scenarios. Due to the asymmetry of returns, the risk is assessed by a general deviation measure introduced by Rockafellar et al. [(2006b) Optimality conditions in portfolio analysis with general deviation measures, Mathematical Programming 108, 515–540] instead of the standard deviation as in the classical Markowitz optimization problem. We demonstrate that, in general, one cannot expect the uniqueness of Pareto-optimal profit sharing in cooperative investment and the uniqueness of solutions in the mean-deviation Black–Litterman asset allocation model. For a large class of deviation measures, we provide a resolution of the above nonuniqueness issues based on the principle of law-invariance. We provide several examples illustrating the nonuniqueness and the law-invariant solution.

Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints Under Data Uncertainty

This article investigates robust optimality conditions and duality results for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (UNMPVC). Mathematical programming problems with vanishing constraints constitute a distinctive class of constrained optimization problems because of the presence of complementarity constraints. Moreover, uncertainties are inherent in various real-life problems. The aim of this article is to identify an optimal solution to an uncertain optimization problem with vanishing constraints that remains feasible in every possible future scenario. Stationary conditions are necessary conditions for optimality in mathematical programming problems with vanishing constraints. These conditions can be derived under various constraint qualifications. Employing the properties of convexificators, we introduce generalized standard Abadie constraint qualification (GS-ACQ) for the considered problem, UNMPVC. We introduce a generalized robust version of nonsmooth stationary conditions, namely a weakly stationary point, a Mordukhovich stationary point, and a strong stationary point (RS-stationary) for UNMPVC. By employing GS-ACQ, we establish the necessary conditions for a local weak Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we derive sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type and Mond–Weir-type robust dual models corresponding to the primal problem, UNMPVC.