Using a conic bundle method to accelerate both phases of a quadratic convex reformulation

We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem $(SDP)$, and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving $(SDP)$ that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm

A methodological comparison between energy and environmental performance evaluation

The European Union is working on strategies in order to increase the energy efficiency of buildings. A useful solution is to identify the energy performance of buildings through the Energy Performance Certificate (EPC), as it provides information for the comparison of buildings with different architectural typology, shape, design technology and geographic location. However, this tool does not assess the real energy consumption of the building and does not always take into account its impact on the environment. In this work, two different types of analysis were carried out: one based only on the energy efficiency and the other one based on the environmental impact. Those analyses were applied on a standard building, set in three different Italian locations, with the purpose of obtaining cross-related information. After the evaluation of the results, interventions on some parameters (walls insulation, windows frame, filler gas in the insulated glazing) have been identified in order to improve the energy behavior of the building with an acceptable environmental impact. The aim of this paper is to propose a methodology that integrates the EPC with green building rating systems, leading to a more conscious choice of retrofit interventions as a compromise between energy performances and environmental impact

Protocols for the assessment of building sustainability level. A new proposal for the Italian context

The paper aims at illustrating an innovative methodology for the development of a system to assess and rate the sustainability level of buildings, with particular reference to the Italian context. First, a review of the state of the art is presented, focusing on the existing sustainability tools, which characterize the building sector. Afterwards, the main criticalities of the current systems are pointed out, laying the basis for the setting-up of the new protocol. Consequently, the paper illustrates the process leading to the development of the new sustainability evaluation system, showing all the main steps towards its final inner structure. Finally, the research work introduces the concept of ‘benchmark’, underlining its importance within the new protocol framework. In particular, the absence of reference or limit values for some performance indicators is emphasized and a computation methodology is proposed for those performance indicators lacking of benchmark values, with respect to the Italian background. As a result, the paper provides an effective methodological and operative tool for decision makers, such as designers, constructors, developers and users of sustainability systems. The outcomes offer a contribution to the national and international development of methods and guidelines, supporting the overall sustainability evaluations in the building field

Accessing the Neighbourhood: Built Environment Performance for People with Disability

In the face of rapid urbanisation, increasing diversity of the human condition, ageing populations, failing infrastructure, and mounting evidence that the built environment affects health and well-being, the existing built environment still fails to meet the needs of people with disability. Nevertheless, in something of a parallel universe, improving built environment ‘sustainability’ performance, via measurement, receives much contemporary attention, and analysing the built environment at micro-scale (buildings), meso-scale (neighbourhood) and macro-scale (city-wide) is undertaken from various multidisciplinary perspectives. But, although built environment performance is already measured in many ways, and community inclusion is considered essential for health and well-being, accessibility performance for people with disability, at neighbourhood scale, is rarely considered. The institutional and medical models of disability help explain the inaccessibility of the existing built environment. On the other hand, the social and human rights models of disability offer insight into improving the accessibility of the existing built environment for people with disability. However, ‘disability’ and ‘built environment’ tend not to mix. People with disability continue to experience lack of meaningful involvement in research, participation in decision-making, partnership equality, and direct influence over policy, with the built environment arena increasingly becoming a private-sector activity. The actors involved, however, have little understanding of either the accessibility needs of people with disability, or the inaccessibility, particularly at neighbourhood scale, of the existing built environment. It is in this context that this paper explores the design, planning and politics of an inaccessible built environment, concluding that assessing the built environment accessibility performance for people with disability, at neighbourhood scale, is an essential component in the process of built environment accessibility improvement. Requiring collaboration between the built environment and disability knowledge domains, a new tool measuring neighbourhood accessibility, the Universal Mobility Index (UMI), has emerged and is undergoing further development

A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO)

AbstractThe “roof dual” of a QUBO (Quadratic Unconstrained Binary Optimization) problem has been introduced in [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0–1 optimization, Mathematical Programming 28 (1984) 121–155]; it provides a bound to the optimum value, along with a polynomial test of the sharpness of this bound, and (due to a “persistency” result) it also determines the values of some of the variables at the optimum. In this paper we provide a graph-theoretic approach to provide bounds, which includes as a special case the roof dual bound, and show that these bounds can be computed in O(n3) time by using network flow techniques. We also obtain a decomposition theorem for quadratic pseudo-Boolean functions, improving the persistency result of [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0–1 optimization, Mathematical Programming 28 (1984) 121–155]. Finally, we show that the proposed bounds (including roof duality) can be applied in an iterated way to obtain significantly better bounds. Computational experiments on problems up to thousands of variables are presented

Scalable Semidefinite Programming

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct algorithm for solving large SDP problems by economizing on both the storage and the arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop, the algorithm can handle SDP instances where the matrix variable has over 10¹³ entries