Renato De Leone

High Performance Algorithms and Software in Nonlinear Optimization

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSNO97) which was held in Ischia, Italy, in June, 1997. The book provides an overview of the nonlinear optimization field, including algorithms, software evaluation, implementation issues, applications, and areas of research, through authoritative papers by some of the most active and well-known researchers in the field. The papers of the Proceedings can be recommended to mathematicians, physicists, and engineers working in the fields mentioned above, as well as recommended for further reading within graduate studies.

The use of grossone in Mathematical Programming and Operations Research

The concepts of infinity and infinitesimal in mathematics date back to anciens Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev [10] for performing calculations with infinite and infinitesimal quantities, by introducing an infinite unit of measure expressed by the numeral ① (grossone). An important characteristic of this novel approach is its attention to numerical aspects. In this paper we will present some possible applications and use of ① in Operations Research and Mathematical Programming. In particular, we will show how the use of ① can be beneficial in anti–cycling procedure for the well–known simplex method for solving Linear Programming Problems and in defining exact differentiable Penalty Functions in Nonlinear Programming.

Stopping criteria for linesearch methods without derivatives

In this paper acceptability criteria for the linesearch stepsize are introduced which require only function values. Simple algorithm models based on these criteria are presented. Some modifications of criteria based on the knowledge of the directional derivative are also illustrated.

A Bus Driver Scheduling Problem: a new mathematical model and a GRASP approximate solution

This paper addresses the problem of determining the best scheduling for Bus Drivers, a

Integrating support vector machines and neural networks

\mathcal{NP}

A Partitioned ε-Relaxation Algorithm for Separable Convex

-hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491–502, 2005).

Solving a bus driver scheduling problem with randomized multistart heuristics

Support vector machines (SVMs) are a powerful technique developed in the last decade to effectively tackle classification and regression problems. In this paper we describe how support vector machines and artificial neural networks can be integrated in order to classify objects correctly. This technique has been successfully applied to the problem of determining the quality of tiles. Using an optical reader system, some features are automatically extracted, then a subset of the features is determined and the tiles are classified based on this subset.

Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications

A relaxation method for separable convex network flow problems is developed that is well-suited for problems with large variations in the magnitude of the nonlinear cost terms. The arcs are partitioned into two sets, one of which contains only arcs corresponding to strictly convex costs. The algorithm adjusts flows on the other arcs whenever possible, and terminates with primal-dual pairs that satisfy complementary slackness on the strictly convex arc set and ∈-complementary slackness on the remaining arcs. An asynchronous parallel variant of the method is also developed. Computational results demonstrate that the method is significantly more efficient on ill-conditioned networks than existing methods, solving problems with several thousand nonlinear arcs in one second or less.

Support Vector Regression for Time Series Analysis

The Bus Driver Scheduling Problem is an extremely complex part of the Transportation Planning System (e.g., [12]) that generally can be divided in different subproblems due to its complexity: Timetabling, Vehicle Scheduling, Crew Scheduling (Bus and Driver Scheduling), and Crew Rostering (see Figure 1 for the relationship between these subproblems). The transportation service is composed of a set of lines that corresponds to a bus traveling between two locations of the same city or between two cities. For each line, the frequency is determined by the demand. Then, a timetable is constructed, resulting in journeys characterized by a start and end point, and a start and end time. The Vehicle Scheduling Problem consists in finding a schedule for the buses, each schedule being defined as a bus journey starting at the depot and returning to the same depot. The objective is to minimize the total cost given by the cost of buses used for the service and running costs. Running costs can be minimized avoiding unnecessary deadheads, i.e., trips carrying no passengers. The daily schedule of each single bus is known as a running board (or vehicle block).

Probiotic-enriched foods and dietary supplement containing SYNBIO positively affects bowel habits in healthy adults: an assessment using standard statistical analysis and Support Vector Machines

Abstract A novel and interesting approach to infinite and infinitesimal numbers was recently proposed in a series of papers and a book by Sergeyev. This novel numeral system is based on the use of a new infinite unit of measure (the number grossone , indicated by the numeral ①), the number of elements of the set, IN, of natural numbers. Based on the use of ①, De Cosmis and De Leone (2012) have then proposed a new exact differentiable penalty function for constrained optimization problems. In this paper these results are specialized to the important case of quadratic problems with linear constraints. Moreover, the crucial role of Constraint Qualification conditions (well know in constraint minimization literature) is also discussed with reference to the new proposed penalty function.