Certifying optimality for convex quantum channel optimization problems

We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization problems over the set of all quantum measurements of a given system having a fixed number of measurement outcomes are obtained as a special case. In the case of linear objective functions for measurement optimization problems, our conditions reduce to the well-known Holevo-Yuen-Kennedy-Lax measurement optimality conditions. We illustrate how our conditions can be applied to various state transformation problems having non-linear objective functions based on the fidelity, trace distance, and quantum relative entropy.

OPTIMASI PENJADWALAN WAKTU KERJA MENGGUNAKAN INTEGER PROGRAMMING

Scheduling workers is one of the problems faced by every company. The regulations set by the company, the availability of the number of workers, and the division of labor are the determining factors in the scheduling system. This worker scheduling problem can be modeled as an Integer Programming problem. Integer Programming is an optimization technique with linear objective functions, linear constraint functions, and integer variables. This paper discusses the formulation of worker scheduling problems in the form of Integer Programming with workers in companies engaged in the production of Crumb Rubber with the objective function of minimizing the number of workers employed. The next model is implemented using the help of LINGO 11.0 software. The implementation results show that the model is able to produce optimal employee schedules.

Contaminant source localization via Bayesian global optimization

A Bayesian optimization approach to localize a contaminant source is proposed. The localization problem is illustrated with two 2D synthetic cases which display sharp transmissivity contrasts and specific connectivity patterns. These cases generate highly non-linear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian Process model and on the Expected Improvement criterion is used to efficiently localize the minimum of the objective function which identifies the contaminant source. In addition, the generated objective functions are made available as a benchmark to further allow the comparison of optimization algorithms on functions characterized by multiple minima and inspired by concrete field applications.

Measuring the technical efficiency of local banks in UAE using rough bi-level linear programming technique

The aim of this paper is to use a bi-level linear programming technique with rough parameters in the constraints, for measuring the technical efficiency of local banks in UAE and Egypt, while the proposed linear objective functions will be maximized for different goals. Based on Dauer's and Krueger's goal programmingmethod, the described approach was developed to deal with the bi-level decision-making problem. The concept of tolerance membership function together was used to generate the optimal solution for the problem under investigation. Also an auxiliary problem is discussed to illustrate the functionality of the proposed approach.

A Novel Wake Interaction Model for Wind Farm Layout Optimization

Optimizing the turbine layout in a wind farm is crucial to minimize wake interactions between turbines, which can lead to a significant reduction in power generation. This work is motivated by the need to develop wake interaction models that can accurately capture the wake losses in an array of wind turbines, while remaining computationally tractable for layout optimization studies. Among existing wake interaction models, the sum of squares (SS) model has been reported to be the most accurate. However, the SS model is unsuitable for wind farm layout optimization using mathematical programming methods, as it leads to non-linear objective functions. Hence, previous work has relied on approximated power calculations for optimization studies. In this work, we propose a mechanistic linear model for wake interactions based on energy balance, with coefficients determined based on publicly available data from the Horns Rev wind farm. A series of numerical tests was conducted using test cases from the wind farm layout optimization literature. Results show that the proposed model is solvable using standard mathematical programming methods, and resulted in turbine layouts with higher efficiency than those found by previous work.

A Heuristic Approach for Multi Objective Distribution Feeder Reconfiguration

The reconfiguration is an operation process used for optimization with specific objectives by means of changing the status of switches in a distribution network. This paper presents an algorithm for network recon-figuration based on the heuristic rules and fuzzy multi objective approach where each objective is normalized with inspiration from fuzzy set to cause optimization more flexible and formulized as a unique multi objective function. Also, the genetic algorithm is used for solving the suggested model, in which there is no risk of non-linear objective functions and constraints. The effectiveness of the proposed method is demonstrated through several examples in this paper.

MINKOWSKI SUM SELECTION AND FINDING

Let P,Q ⊆ ℝ2 be two n-point multisets and Ar ≥ b be a set of λ inequalities on x and y, where A ∈ ℝλ×2, [Formula: see text], and b ∈ ℝλ. Define the constrained Minkowski sum(P ⊕ Q)Ar≥ b as the multiset {(p + q)|p ∈ P, q ∈ Q,A(p + q) ≥ b }. Given P, Q, Ar ≥ b , an objective function f : ℝ2 → ℝ, and a positive integer k, the MINKOWSKI SUM SELECTION problem is to find the kth largest objective value among all objective values of points in (P ⊕ Q)Ar≥ b . Given P, Q, Ar ≥ b , an objective function f : ℝ2 → ℝ, and a real number δ, the MINKOWSKI SUM FINDING problem is to find a point (x*, y*) in (P ⊕ Q)Ar≥ b such that |f(x*,y*) - δ| is minimized. For the MINKOWSKI SUM SELECTION problem with linear objective functions, we obtain the following results: (1) optimal O(n log n)-time algorithms for λ = 1; (2) O(n log 2 n)-time deterministic algorithms and expected O(n log n)-time randomized algorithms for any fixed λ > 1. For the MINKOWSKI SUM FINDING problem with linear objective functions or objective functions of the form [Formula: see text], we construct optimal O(n log n)-time algorithms for any fixed λ ≥ 1. As a byproduct, we obtain improved algorithms for the LENGTH-CONSTRAINED SUM SELECTION problem and the DENSITY FINDING problem.