A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

F-theory, GUTs, and the Weak Scale

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value mu ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 10^(8.5) GeV. Further, the B mu problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f_a ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio \mu / L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 10^12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10^1 - 10^2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10^2 - 10^3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(beta) ~ 30 +/- 7.Comment: v3: 94 pages, 9 figures, clarification of Fayet-Polonyi model and instanton corrections to axion potentia

E6,7,8 Magnetized Extra Dimensional Models

We study 10D super Yang-Mills theory with the gauge groups $E_6$, $E_7$ and $E_8$. We consider the torus/orbifold compacfitication with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.Comment: 17 pages, 1 figur

A Study of Memetic Search with Multi-parent Combination for UBQP

We present a multi-parent hybrid genetic–tabu algorithm (denoted by GTA) for the Unconstrained Binary Quadratic Programming (UBQP) problem, by incorporating tabu search into the framework of genetic algorithm. In this paper, we propose a new multi-parent combination operator for generating offspring solutions. A pool updating strategy based on a quality-and-distance criterion is used to manage the population. Experimental comparisons with leading methods for the UBQP problem on 25 large public instances demonstrate the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency

An In-Out Approach to Disjunctive Optimization

Abstract. Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to pro-vide tight bounds for Mixed-Integer Programs (MIPs). This is obtained by embedding a cut-separation module within a search scheme. The importance of a sound search scheme is well known in the Constraint Programming (CP) community. Unfortunately, the “standard ” search scheme typically used for MIP problems, known as the Kelley method, is often quite unsatisfactory because of saturation issues. In this paper we address the so-called Lift-and-Project closure for 0-1 MIPs associated with all disjunctive cuts generated from a given set of elementary disjunction. We focus on the search scheme embedding the generated cuts. In particular, we analyze a general meta-scheme for cutting plane algorithms, called in-out search, that was recently proposed by Ben-Ameur and Neto [1]. Computational results on test instances from the literature are presented, showing that using a more clever meta-scheme on top of a black-box cut generator may lead to a significant improvement

Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems

This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches

Prospect theory-based portfolio optimisation: An empirical study and analysis using intelligent algorithms

The first author was part funded by RFBR (grant 14-01-00140)

Population Heuristics

Standard heuristics in Operations Research (such as greedy, tabu search and simulated annealing) work on improving a single current solution. Population heuristics use a number of current solutions and combine them together to generate new solutions. Heuristic algorithms encountered in the literature that can generically be classified as population heuristics include genetic algorithms, hybrid genetic algorithms, memetic algorithms, scatter search algorithms and bionomic algorithms. In this tutorial paper we discuss the basic features of population heuristics and provide practical advice as to their effective use for solving Operations Research problems. 1 1. INTRODUCTION In Operations Research (OR), over the years, a number of standard heuristic algorithms have appeared. In the early years of OR heuristics were especially tailored to the problem under consideration. As OR advanced a number of basic heuristic ideas began to be formalised. These included ideas such as greedy (seek th..