Designing optimal mixtures using generalized disjunctive programming: Hull relaxations

A general modeling framework for mixture design problems, which integrates Generalized Disjunctive Programming (GDP) into the Computer-Aided Mixture/blend Design (CAMbD) framework, was recently proposed (S. Jonuzaj, P.T. Akula, P.-M. Kleniati, C.S. Adjiman, 2016. AIChE Journal 62, 1616–1633). In this paper we derive Hull Relaxations (HR) of GDP mixture design problems as an alternative to the big-M (BM) approach presented in this earlier work. We show that in restricted mixture design problems, where the number of components is fixed and their identities and compositions are optimized, BM and HR formulations are identical. For general mixture design problems, where the optimal number of mixture components is also determined, a generic approach is employed to enable the derivation and solution of the HR formulation for problems involving functions that are not defined at zero (e.g., logarithms). The design methodology is applied successfully to two solvent design case studies: the maximization of the solubility of a drug and the separation of acetic acid from water in a liquid-liquid extraction process. Promising solvent mixtures are identified in both case studies. The HR and BM approaches are found to be effective for the formulation and solution of mixture design problems, especially via the general design problem

Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Energy-Efficient Transmission Scheduling with Strict Underflow Constraints

We consider a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source's objective is to allocate power in a manner that minimizes an expected cost measure, while satisfying strict buffer underflow constraints and a total power constraint in each slot. The expected cost measure is composed of costs associated with power consumption from transmission and packet holding costs. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user with linear power-rate curves, we show that a modified base-stock policy is optimal under the finite horizon, infinite horizon discounted, and infinite horizon average expected cost criteria. For a single user with piecewise-linear convex power-rate curves, we show that a finite generalized base-stock policy is optimal under all three expected cost criteria. We also present the sequences of critical numbers that complete the characterization of the optimal control laws in each of these cases when some additional technical conditions are satisfied. We then analyze the structure of the optimal policy for the case of two users. We conclude with a discussion of methods to identify implementable near-optimal policies for the most general case of M users.Comment: 109 pages, 11 pdf figures, template.tex is main file. We have significantly revised the paper from version 1. Additions include the case of a single receiver with piecewise-linear convex power-rate curves, the case of two receivers, and the infinite horizon average expected cost proble

Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs