A MIXED INTEGER PROGRAMMING MODEL FOR MULTIPLE-CLASS DISCRIMINANT ANALYSIS

New linear programming approaches are proposed as nonparametric procedures for multiple-class discriminant and classification analysis. A new MSD model minimizing the sum of the classification errors is formulated to construct discriminant functions. This model has desirable properties because it is versatile and is immune to the pathologies of some of the earlier mathematical programming models for two-class classification. It is also purely systematic and algorithmic and no user ad hoc and trial judgment is required. Furthermore, it can be used as the basis to develop other models, such as a multiple-class support vector machine and a mixed integer programming model, for discrimination and classification. A MMD model minimizing the maximum of the classification errors, although with very limited use, is also studied. These models may also be considered as generalizations of mathematical programming formulations for two-class classification. By the same approach, other mathematical programming formulations for two-class classification can be easily generalized to multiple-class formulations. Results on standard as well as randomly generated test datasets show that the MSD model is very effective in generating powerful discriminant functions.

A cutting plane algorithm for the site layout planning problem with travel barriers

In this paper, we propose a mixed integer programming (MIP) model to solve the experimental courses scheduling problem. And we use the experimental courses historical data in our information systems to solve the MIP model. The results of the numerical example demonstrate that the proposed model can reach an optimal solution in a short period of time. The MIP model can provide the decision-making support for the experimental courses arrangement.

In apparel manufacturing, cut pieces produced by the cutting process are a key input work-in-process (WIP) to the bottleneck sewing process. However, an excessive inventory of cut pieces not only requires extra storage space but also creates difficulties with shop floor control. This study determines the ideal cutting times of fabric lays by minimising the cut piece inventory under the constraint that sufficient cut pieces are produced in time to satisfy the bottleneck usage. This study proposes a mixed integer programming (MIP) model and a heuristic method to solve the problem. The solutions for most test instances of the problem that are calculated by the heuristic method are not as good as those by the MIP solver; however, the heuristic method computation times are negligible. The experiments show that the MIP model’s efficiency significantly improves by starting from an initial solution provided by the proposed heuristic method.

Integer programming models for the q-mode problem

Efficient operational planning in district heating systems (DHSs) is essential for minimizing operating costs and maximizing energy efficiency. However, since practitioners must determine future production plans under unknown future demands and costs in real-world energy systems, it is challenging to solve the production planning problems of DHSs. In this paper, we propose a multi-head attention-based TimesNet (MATN) in which a transformer decoder is incorporated that operates solely on a 24 h lookback window without requiring any future information. Specifically, the model is trained in an end-to-end manner, for which the training dataset was built by solving a mixed integer programming (MIP) model. Experimental results demonstrate that the proposed MATN model significantly outperforms baseline deep learning-based methods. A qualitative analysis of the hourly production plans further indicates that MATN generates robust operational plans that mimic those generated by an MIP model, which suggests the effectiveness of the proposed approach in terms of economic efficiency and operational stability without depending on future information.

In this paper, we propose a mixed integer programming (MIP) model for the Chicken Flock Sizing, Allocation and Scheduling Problem (CFSASP), which is an important planning problem in the broiler production supply chain. To solve the CFSASP efficiently, two variants of rolling horizon heuristics (RHHs) have been developed and applied on the case of a Norwegian broiler production company. Computational results show that the RHHs successfully obtain high-quality solutions within a reasonable time. The value of optimisation is verified through comparison with the case company's plans, where the solutions from optimisation outperforms the current solutions. Sensitivity analyses are also conducted to provide managerial insights regarding certain strategic decisions, such as how many and which days to use for hatching of chickens. Due to the promising results, the case company is now implementing an optimisation-based decision support system based on the MIP model and solution methods shown in this paper.

Integrated optimization of traffic signal timings and vehicle trajectories considering mandatory lane-changing at isolated intersections

Lattice-based algorithms for number partitioning in the hard phase

The flying sidekick traveling salesman problem with stochastic travel time: A reinforcement learning approach

A special ordered set approach for optimizing a discontinuous separable piecewise linear function

Minimizing total tardiness on a single machine with controllable processing times

Abstract. Schematic (network) maps are helpful for people to perform route planning and orientation tasks. The London Underground Map designed by Harry Beck is an excellent example of such maps. Generally, there are three approaches to generate schematic maps: manual, semi-automated (or computer-aided) and fully automated. In the past twenty years, many researchers have been devoted to the development of automated methods for generation of schematic maps. In these automated methods, various sets of constraints are used. Most of these constraints are for geometric properties of individual features (such as the lengths and orientations of lines); a few constraints are for relations between features (such as the minimum distance threshold between non-incident edges); but none are explicitly for the main structures of whole networks. It is believed that preservation of the main structure is the most important, because main structure is represented by global features which is first recognized by a pre-attentive process in human cognition – a global-to-local process (in which local features are then recognized by an attentive process). It is hypothesized here that an automated method with the preservation of main structures of networks should be able to generate schematic maps with improved clarity and aesthetics.This paper describes the development of an automated method with the preservation of the main structures of line networks. In this method, automated schematization is treated as an optimization problem and is represented as a Mixed-Integer Programming (MIP) model, which consists of an objective function and a set of constraints. The preservation of main structures is modelled into constraints (i.e., making important lines straight and orientating them to specific directions) for the model. The MIP model is imported into a commercial optimization software called “IBM ILOG CPLEX Optimization Studio” (version 12.6.3) for the acquisition of optimal solutions (i.e., coordinates of vertices and edges on schematic maps). The whole process is shown in Figure 1.Experimental evaluations have been conducted with a set of real-life data as shown in Figure 2a and 2d. Schematic maps are generated by this new method with the preservation of main structures and by an old method without the particular consideration for main structures, as shown in Figures 2b, 2c, 2e and 2f. A psychological test with a questionnaire has been conducted, which consists of questions regarding “clarity”, “recognition of major lines”, “visual simplicity” and “satisfaction”. It is found that, in all these four aspects, the map generated by new methods with preservation of main structures have higher scores than those by the old method. These improvements are proved to be significant after paired-t tests.Therefore, it is concluded that the new automated method with the preservation of main structures can generate schematic maps with significant improvement in clarity and aesthetics. This study is helpful to improve automated methods for generation of schematic maps and other visual representations.

Acceleration in energy consumption leads to a mismatch between supply and demand. This problem can be resolved by integrating Demand Side Management (DSM) programs with Energy Management Systems. DSM programs include planning, scheduling, implementing and monitoring of the demand load in a way that ensures benefits for the utility company as well as for the consumers. Tackling the Residential Load Management Problem (RLMP) is quite challenging especially while considering variants such as buildings' loads, demand uncertainty, consumers' preferences, tariff and time horizon. The Inclining Block Rate (IBR) tariff system is still used especially in developing countries. However, solving the RLMP under the IBR tariff has not received much attention in the literature. This paper addresses the RLMP under the IBR tariff while maximizing the fulfillment of the appliances' schedule with respect to budget limit. In this paper, a mixed integer programming model is proposed for scheduling of home appliances over one month under IBR as a standalone pricing tariff. The performance of the proposed model is tested using a dataset from a typical household in Egypt. Results show that the obtained schedule fulfills the consumer's usage target within the given budget limit. Various budget scenarios are investigated, and the obtained results show to what extend the budget can control the on/off status of each appliance in each time slot over one month

In this paper, we study hospital bed planning problem for a gynecological ward in China. We first proposed a mixed integer programming (MIP) model considering deterministic length of stay (LOS) to assign patients to available beds. Since statistical analysis of empirical hospitalization data reveals that variance of inpatient's LOS is significant. Therefore, based on the deterministic LOS model we further proposed a MIP model taking stochastic LOS into consideration. Both models could be solved by standard linear programming solver CPLEX. Numerical experiments of bed assignment results comparison between the two proposed models are presented. The result shows stochastic LOS model can generate better bed planning solutions with lower potential schedule conflict cost.