A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York

Using Functional Programming to recognize Named Structure in an Optimization Problem: Application to Pooling

Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems

Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods

Exploration of Federal Sport Policy on Youth Elite Sport in Canada: A case study of Gymnastics Canada Gymnastique

A case study of Gymnastics Canada Gymnastique aided in creating a contemporary framework for youth sport policy development. Youth involved in elite sport are in a subsidiary position to those who control the sport environment, and therefore are in need of certain levels of protection. High performance youth athletes may be subject to numerous problems such as competitive anxiety, disrupted family life, and excessive physiological and psychological stress. In order to explore these issues in relation to federal sport policy, the following sub-problems were identified: (a) What are the process(es), legitimation(s) (rationale) and attribution(s) (strategies for action) of federal government sport policies (1961--2000) in relation to youth, elite athletes, and youth elite athletes? (b) What structure currently exists within Gymnastics Canada Gymnastique (GCG) in relation to youth elite athletes? (c) What issues are relevant to those affected by policy (i.e., coaches and athletes)? (d) How are the proposed process(es), emerging legitimation(s), and attribution(s) for the development of federal sport policies pertaining to youth elite athletes reflective of academic/activist approaches concerning youth sport

The Influence of the Social Determinants of Health on Para-sports Involvement Throughout the Caribbean and Americas

As the number of individuals with a disability grows worldwide, the Paralympic Games and para-sports have seen a growth in participation (WHO, 2011). However, international sporting competitions including the Paralympic Games remain dominated by developed countries (Andreff, 2001). In the last Paralympic Games, the USA, Canada, and Brazil made up nearly 70% of participants from the North and South American region with 17 of the 28 committees sending five or less participants (Maleske & Sant, 2020). The present study investigates the social and cultural determinants in the Caribbean and Americas of para-sport participation in the region and their relation to para-sport involvement. This paper presents a thematic analysis of semi-structured interviews conducted with regional committee executives and athletes to better understand how social and health determinants impact para-sport involvement. Analysis indicated there are widespread challenges to involvement in sport experienced in the Caribbean and America’s region. These include: minimal financial support and capacity; limited opportunity within educational systems; a general unfamiliarity with para-sport that is combined with a mainstream negative perception of disability; and several structural barriers reducing accessibility. These findings mirror existing literature and stress the complex combination of social and cultural factors that pose challenges to the establishment of and engagement in para-sport. Future research and program initiatives that aim to assist the region’s para-sport movement must look beyond ordinary monetary stimulus and consider contextualized support which may involve raising awareness, improving administrative structures, and promoting grassroots development of athletes and other human resources

Communal Consciousness: Using Wittgenstein to Challenge Epistemic Privacy

In the Philosophical Investigations, Ludwig Wittgenstein argues against the possibility of a private language. This argument has semantic implications for how we come to understand the meaning behind our use of mental terms. Namely, that use determines meaning prior to signification. However, an interesting part about Wittgenstein’s private language argument is what it tells us about epistemic privacy. This paper seeks to establish Wittgenstein’s private language argument in a framework which deals primarily with how we come to understand the use behind our mental terms. Once we come to understand the use behind our mental terms, we can come to understand how we come to have knowledge of mental states. The implications for epistemic privacy are twofold. The first, is that other minds are necessary when it comes to self knowledge of mental occurrences. The second, is that mental occurrences are an integral part of conscious experience. Together, these two implications provide an epistemic framework which depicts the mind as something which depends at least in part on other people. Since knowledge of mental occurrences is both dependent on the existence of mental occurrences themselves and the existence of others, minds are not epistemically private

Conflict, Forgiveness, and the Healing of Harms in C. S. Lewis’ The Chronicles of Narnia

Excerpt: In The Chronicles of Narnia, children are celebrated as models of heroic potential in the ways they realize, apologize for, and repent of sinful words and deeds. This is in keeping with C. S. Lewis’ desire that his young readers would recognize and practice these virtues as signs of the “childlike faith” Jesus expects of his disciples (Mark 10:15; Luke 18:17).92 Conversely, adults are generally shown to be owners of an obtuse conscience and a recalcitrant will

Rethinking the social value of sport events through an asset-based community development (ABCD) perspective

© 2016 Human Kinetics, Inc. With an increasing emphasis on the social value of sport and events, there has been a shift in focus regarding the management and development process of event projects as well as their associated outcomes. This shift is about emphasizing a more strategic approach to developing social benefits by recognizing and utilizing leverageable resources related to sport events as a means of fostering lasting social and economic change (Chalip, 2006; O'Brien & Chalip, 2007; Schulenkorf & Edwards, 2012). In this paper, we adapt and apply the asset-based community development (ABCD) approach as a means of developing a more action-oriented, community-based approach to leveraging the social assets of sporting events. In applying the ABCD approach, we aim to shift the focus of event-led projects away from attempts to "solve" social problems (i.e., deficit perspective) to enhancing the existing strengths of communities (i.e., strengths perspective). We reflect on case study findings that highlight the challenges and opportunities in realizing an ABCD approach for disadvantaged communities through an examination of a healthy lifestyle community event initiative in the Pacific Islands