Heuristic Methods

The Second Annual Transpersonal Research Colloquium (TRC) was held in Northampton, UK on September 15-16, 2016. This document is the final program with presenters abstracts, bios, and contact information. For further information, see www.transpersonalresearchnetwork.com.

Some of Law and Economics’ basic claims have come to be criticized as a result of empirical findings that question their viability. Particularly, the premise that agents consistently act rationally and with their self-interest in mind seems problematic. What the consequences of the criticism mean for Law and Economics’ tenability depends largely on the questions whether (1) some elements are unassailable to the alternative’s objections and (2) the alternative is a systematic whole. It is argued that Law and Economics may be salvaged, if it is minimized and its ambitions are tempered. This means focusing on the stable, a priori, elements inherent to it.

En el presente trabajo se plantea una metodología de planeación de trayectorias para manipuladores seriales antropomórficos de seis grados de libertad y muñeca esférica enfocada en la minimización del consumo eléctrico y maximización de la manipulabilidad. Para lograr tal fin se expone un algoritmo de optimización el cual tiene como base el Algoritmo Heurístico de Kalman (AHK), cuya finalidad es encontrar la trayectoria óptima según la función multi-objetivo propuesta dentro de un espacio esférico simplificado propuesto. El algoritmo de optimización se evalúa mediante el análisis del comportamiento de dos trayectorias en el manipulador PUMA 560, simuladas en un programa desarrollado en la aplicación de Visual Basic perteneciente al software Autodesk Inventor.

The divide between counseling research and practice is often wide. Humanistic research methodologies such as heuristic inquiry resonate with clinical practice and may bridge the research‐practice chasm through focus on real‐world experience and self‐other understanding. This article illuminates principles of heuristic inquiry and implications for humanistic clinical practice and social justice.

Abstrak Slide puzzle merupakan salah satu jenis permainan puzzle yang cukup memeras otak untuk menyelesaikannya. Pemain ditantang untuk berpikir bagaimana membuat semua bagian puzzle terletak pada posisi sebenarnya dan membentuk sebuah gambar. Cara memainkannya cukup mudah, pemain hanya menggeser puzzle satu demi satu sampai akhirnya semua puzzle terletak pada posisi sebenarnya. Untuk menemukan solusi atas permasalahan slide puzzle digunakan fungsi heuristik dengan algoritma Iterative Deepening A* (IDA*), fungsi heuristik yang digunakan adalah Manhattan Distance. Algoritma IDA* memerlukan jumlah memori yang jauh lebih sedikit. Jika menghadapi masalah keterbatasan memori, maka algoritma IDA* bisa menjadi pilihan yang tepat. Kebanyakan game-game yang ada hanya memberikan kesan hiburan saja, tanpa memberikan nilai edukasi didalamnya. Untuk itu dikembangkan game slide puzzle yang memuat informasi (gambar) mengenai kebudayaan Indonesia, diantaranya rumah adat, pakaian adat, tarian adat dan senjata tradisional masing-masing Provinsi.

En un sistema de producción que cuenta con varias líneas de productos, y en el que los recursos son compartidos por los diferentes procesos de fabricación, es importante mantener en cada centro de trabajo niveles de inventario de producto en proceso bajos y cercanos a los deseados, con el fin de mantener una línea de producción ordenada. Este artículo propone una heurística de balanceo de Inventario en Proceso (WIP) basada en la ley de Little, que se encarga de mantener un nivel de WIP ideal mediante una lógica de envío y recepción de señales a lo largo de toda la línea de producción. Palabras clave: WIP, balanceo de líneas de producción, Planificación diaria

Digital learning environments are increasingly becoming popular in recent years. The rising usage of cell phones has invited researchers to design and develop learning applications and games for mobile phones. Specifically, game-based language learning is being promoted by researchers in many parts of the world. "Language Learning Serious Game (LLSG)" is based on a theoretical model constructed by the researcher that supports children learning English as a second language in a cultural context. The usability of such games is evaluated based on well-defined heuristics and other standard methods. This research aims to appraise the usability of LLSG through heuristics and think-aloud approaches while involving all essential stakeholders, including language experts, students, teachers, and game developers. The researcher proposed the heuristics in a cultural context, whereas the think-aloud review is compiled from the rigorous discussion session involving these stakeholders to evaluate the LLSG. The findings obtained from the heuristics evaluation reveal that the usability of LLSG is acceptable. On the other hand, various interesting suggestions and reviews were gathered from the discussion between experts and students. This evaluation will further improve the future versions of the game.

“Being Ma” lives at the nexus of ma and the lived body. (1) Of Shinto Zen origin, 'ma' concept of spacetime permeates traditional forms of Japanese Fine Arts. (2) The essence of 'ma' reappears in the contemporary Butoh dance philosophy, and has migrated as spatial-temporal perspective in a number of movement art practices outer-borders of Japan. “Being Ma” attempts at describing a porous, fluid, indescribable concept as experienced in its relationship along and between the artistic intents of a moving body in spacetime.
'Ma' is a contributing rather than a limiting principle. The study follows a flow leading to ma-body-as-event. The study of 'ma' contributes to the phenomenal, cultural, and embodied knowledge production of Dance & Performance scholarship, and beyond, extending to fields of research mandating embodied inquiries. Having chosen to study a Japanese phenomenological concept through the practical framework (in some cases) of North American movement art practitioners, I come across issues of embodied translation and issues of movement approaches – or, stylistic codes and forms of ‘trans-action’. Aided by the artistic expressions of the lived body paradigm, this paper addresses the experience of movement: Shinto Zen rites, Nihon Buyo (Traditional Japanese Dance), Butoh practice, Somatic practice, dancing dream state, and Durational Performance Art. These forms call for movement awareness, which makes them ideal pilots for observation, description, analysis, and interpretation.

This self-study of ten dreams focuses on the topic of emergence of self and lifeworld from the vantage of imageless lucid dreaming. By engaging in the practice of phenomenology from within these dreams, I was provided an opportunity to account for conscious expectation, and explore the dreams’ spontaneous dimensions. The resulting dream texts are analyzed with a
modified phenomenological-heuristic method, producing a creative synthesis based on textual and structural descriptions of this researcher’s experience of spontaneous emergence. Heuristic levels of participation include paintings and drawings that augment the phenomenological analysis.

To date, there have been no published laboratory studies that look at imageless lucid dreams in particular, so we are still in the dark about the state’s physiological signatures. In fact, imageless lucid dreaming is in a similar place to where lucid dreaming was thirty years ago: experienced first-hand by many, and scolded by other non-believers that it is merely a “micro-awakening” between dreams. Until we have third-person validity, therefore, it’s important that we continue to document the phenomenology, or the first-hand experience, of this unique altered state. That’s why this paper includes a few of my paintings (acrylic on canvas) that attempt to depict some of the realms I am discussing, because words are not adequate to express these multi-dimensional spaces.

Network Functions Virtualization (NFV) has been
revolutionizing and improving the way networking services are
deployed but also requires the dynamic scaling of resources
during the lifecycle management of Virtual Network Functions
(VNFs) with increasing service demand. We propose an Integer
Linear Programming (ILP) approach and a Greedy heuristic to
address this NP-Hard scaling problem. Both horizontal (scale
out/in) and vertical (scale up/down) scaling are considered and
the scalability of the ILP is addressed by reducing the number
of candidate hosts in the search space. Extensive simulations
evaluate the performance of the algorithms in successful scalings
and VNF migrations and highlight the importance of using the
algorithms to tidy up the infrastructure to accept more users. The
results show that the ILP can outperform the Greedy heuristic
if appropriate actions are selected.

Transportation of a product from multi-source to multi-destination with minimal total transportation cost
plays an important role in logistics and supply chain management. Researchers have given considerable
attention in minimizing this cost with fixed supply and demand quantities. However, these quantities
may vary within a certain range in a period due to the variation of the global economy. So, the concerned
parties might be more interested in finding the lower and the upper bounds of the minimal total costs with
varying supplies and demands within their respective ranges for proper decision making. This type of transportation
problem has received attention of only one researcher, who formulated the problem and solved it
by LINGO. We demonstrate that this method fails to obtain the correct upper bound solution always. Then
we extend this model to include the inventory costs during transportation and at destinations, as they are
interrelated factors. The number of choices of supplies and demands within their respective ranges
increases enormously as the number of suppliers and buyers increases. In such a situation, although the
lower bound solution can be obtained methodologically, determination of the upper bound solution
becomes anNP hard problem. Herewecarry out theoretical analyses on developing the lower and the upper
bound heuristic solution techniques to the extended model. A comparative study on solutions of small size
numerical problems shows promising performance of the current upper bound technique. Another comparative
study on results of numerical problems demonstrates the effect of inclusion of the inventory costs.

This dissertation is comprised of a heuristic mixed-method study, employing a narrative inquiry approach to investigate poetry as a potential healing modality.  The study included self-selected participants as co-researchers (n=33) who were interested in learning more about their subtle energy systems.  A sonnet cycle, consisting of seven sonnets written by the researcher to encompass key characteristics of the seven main chakras in the ancient Vedic tradition, was the basis for the guided listening component of the study.  Qualitative data was collected through oral interviews, and a number of participants (n=16) also participated in an optional reflective writing exercise.  Primary themes, arising out of the thematic content analysis, were merged into a sonnet cycle as a means of creative synthesis.  Biofeedback incorporated electrophotonic imaging, and the Bio-Well device was utilized to obtain pre- and post-measurements prior to and following the guided listening exercise.  The participants’ personal observations centered on four elements of the multi-dimensional body.  Meaningful extracts, derived from self-reported emotional, physical, cognitive and spiritually-minded reflections, were considered within the context of the statistical findings.  Listening to a guided recording with poetry tested statistically significant in lowering the stress level parameters of the cohort.  Poetry written to explore the seven main chakras correlated with the movement of energy in the chakra energy centers explicitly commented upon by participants per the Bio-Well measurements of these chakras that were tested and correlated with participant qualitative data.  Participants also exhibited a highly significant change in their beliefs, regarding poetry as an energy healing modality as measured in the three-month follow-up survey.  Finally, this study supported the theory of a second reading of poetry as a means to embody a poem, originally proffered by John Fox, Founder of the Institute for Poetic Medicine.

This work presents algorithms to extend tenant
Virtualized Network Functions Forwarding Graphs (VNF-FG)
to embed new networking functions and introduce gradually
additional services into the already deployed tenant dedicated
slices. The related service graph extension problem is addressed
through an Integer Linear Programming (ILP) algorithm that
serves as a reference for performance comparisons with a
proposed heuristic algorithm. An eigendecomposition approach
is proposed, evaluated and compared.

ResumenLa proliferación de aplicaciones nativas o webapps y de la adaptación de las webs de los cibermedios a los dispositivos móviles es una tendencia imparable aunque desigual si distinguimos entre los grandes medios y los medios locales. Si bien existen formas estándar de evaluar la usabilidad para sitios y apps móviles, se echa en falta un sistema que permita aproximarse a evaluar la experiencia de usuario de este tipo de productos atendiendo a las cualidades específicas de la usabilidad de los medios informativos. Esto nos llevará a proponer un sistema de heurísticos enfocado a evaluar aspectos tan relevantes como los específicos de la información periodística y sus formatos, la arquitectura de información (estructura o no por secciones), la usabilidad básica, la ergonomía o el contexto de uso y la explotación de los sensores integrados en los smartphones.

In my eco-psychological critique of the culture of lucid dreaming, awareness and control are often conflated with one another due, in part, to a deep historical bias in which nature is viewed as a wilderness that is separate from, and at war with, humankind. I will present a phenomenological methodology for lucid dreaming that has helped me bridge this conflict within myself, centered on receptivity and connectivity.

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schema: (a) conceptual spaces and conceptual blending; (b) ars inveniendi and ars demonstrandi as two pillars of rational science; (c) two modes of analysis and synthesis – sequential and compositional; (d) taxonomies and typologies as two fundamental epistemic structures; (e) extended cognition, operative symbolism and model-based reasoning.

ATMOSPHERE 10 explores Fabrications. Fabrications implicate diverse artifacts and modes of making, together with the places, practices, contingencies and intentions that enable and contextualize making. In other words, this symposium will examine not simply what, how and why we make, but sites and situations of making. The aim is to explore how cultural and environmental circumstances become meaningful catalysts of design, building, teaching and research. This theme encompasses manifold concerns beyond the digital: complexities of urban and social fabrics; intricacies of environmental skins; potentials of building sites and workshops; as well as the stories and arguments through which we craft shared understandings of our fabricated world.

Abstracts due Nov 1, Symposium Feb 1-3, 2018 University of Manitoba, Winnipeg.

Keynote Speakers include: Brian MacKay-Lyons & Philip Beesley
http://umanitoba.ca/faculties/architecture/atmosphere/2018/brian-mackay-lyons.html
http://umanitoba.ca/faculties/architecture/atmosphere/2018/philip-beesley.html

1 Abstract—Power system reliability measures for residential distribution networks have gained a lot of attention in recent years. This is due to the introduction of smart grids where the quality of the delivered power becomes a crucial issue. In this paper, a new methodology to include cold load pickup (CLPU) events in the reliability assessment of power distribution systems is proposed. The developed methodology presents a platform to include CLPU events in the reliability assessment assuming an optimal systematic procedure is used to restore the affected load points. The methodology is applied on a test system using a state-of-the-art search technique named lightning search algorithm (LSA). The optimal plan takes into account electrical code protection system settings, system operation limits, and stochastic behavior of the load. The reliability indices for a base case without considering CLPU is compared with the case that considers CLPU assuming an optimal restoration. Both cases are compared further under fixed-restoration plans with different time intervals. The results demonstrate the effectiveness of the proposed methodology to improve the distribution network reliability by considering the CLPU events.

The way scientific discovery has been conceptualized has changed drastically in the last few decades: its relation to logic, inference, methods, and evolution has been deeply reloaded. The ‘philosophical matrix’ moulded by logical empiricism and analytical tradition has been challenged by the ‘friends of discovery’, who opened up the way to a rational investigation of discovery. This has produced not only new theories of discovery (like the deductive, cognitive, and evolutionary), but also new ways of practicing it in a rational and more systematic way. Ampliative rules, methods, heuristic procedures and even a logic of discovery have been investigated, extracted, reconstructed and refined. The outcome is a ‘scientific discovery revolution’: not only a new way of looking at discovery, but also a construction of tools that can guide us to discover something new. This is a very important contribution of philosophy of science to science, as it puts the former in a position not only to interpret what scientists do, but also to provide and improve tools that they can employ in their activity.

Despite deserving a place amongst the historic milestones of the philosophy of disciplines, the system of the sciences put forward by Whewell has so far received little interest. Yet his ideas had a significant impact on the researches subsequently carried out on the topic, exerting in particular a decisive influence on Peirce and Spencer. The present paper aims to display the innovatory nature of the philosophical foundations of the Whewellian classification of the sciences. In this respect, we will argue that the most striking feature of his disciplinary system lies in a heuristic categorization of the sciences according to their " methods of discovery ". This represents a double departure from both the Aristotelian and the Baconian disciplinary paradigms, which are instead underpinned by ontological and epistemological criteria, respectively. Next, we will explore the pivotal role of Whewell's classification of the sciences for his overall project of a philosophy of scientific discovery.

This thesis is concerned with developing and refining a collection of methods and tools which can be applied to the different steps of the Data Mining process. Data Mining is understood as the analysis of data using sophisticated tools and methods, which include aspects of data representation, data exploration, knowledge discovery, data modelling and data aggregation. Data Mining can be applied in real and complex domains, such as the domain of clinical prognosis, as well as with artificial test, or benchmark data. Medical informatics is a dynamic area where new approaches and techniques are constantly being developed, the objective being to improve current data representation, modelling and aggregation methods to achieve better diagnosis and prognosis. In this work we focus on two medical data domains: prognosis for ICU patients and diagnosis of Sleep Apnea cases, although it is proposed that the techniques have general use for any data domain. A key approach which is used for data processing and representation is that of fuzzy logic techniques. Existing techniques are benchmarked against the data, such as neural networks, tree induction and standard statistical analysis methods such as correlation, principal components and regression models.
We carry out a survey of existing techniques, authors and their approaches, in order to establish their strong and weak points, limitations, and opportunities where improvement may be achieved.
The first major area under consideration is data representation: how to define a unified scheme which encompasses different data types, such as numeric, continuous, ordered categorical, unordered categorical, binary and fuzzy; how to define membership functions; how to measure differences and similarities in the data. This is followed by a comprehensive benchmarking of existing AI and statistical algorithms on a real ICU medical dataset, comparing the ‘Data Mining’ results to methods proposed by the author.
We define  ‘fuzzy covariance’ as a  value which permits the measurement of relation between two fuzzy variables. Previous fuzzy covariance work was limited to the covariance of a fuzzy cluster to its fuzzy prototype [Gustafson79]. More recent authors [Nakamori97][Wangh95][Watada94] have created specialised fuzzy covariance calculations tailored for specific applications. In this work, a general fuzzy covariance algorithm, which measures the fuzzy covariance between two fuzzy variables, has been conceived, developed and tested. The initial work based the Hartigan joining algorithm and fuzzy covariances evolves into and is contrasted with the later work on data and attribute fusion using the WOWA aggregation operator .
‘Aggregation operators’ are considered as a method for modelling data for clinical diagnosis, and use ‘relevance’ and ‘reliability’ meta-data together with grades of membership to enhance the information which the aggregation operator receives in order to model the data. We also make enhancements to the WOWA operator, to enable it to process data with missing values and we develop a novel method for learning the weighting vectors.

Interdisciplinary psycho-spiritual research into workplace stress and self-care, is scant noting the fact that negative self-talk and harsh self-judgment stymie the search for inner meaning and self-care.  To address this, the paper uses an intuitive and reflection-oriented methodology to research self-care choices for the stressed and suffering worker. 
In particular, it breaks new ground because no workplace-based applied psycho-spiritual research uses bricolage, let alone the heuristic inquiry process which gives expression to it.  Bricolage is a tapestry of ideas, themes and possibilities cobbled together to produce creative outcomes.  It adapts and co-opts whatever information from whichever discipline that is necessary.  This approach appears well suited to the subjective, intuitive nature of workplace stress and suffering and especially where interdisciplinary approaches to self-care are warranted.
The heuristic inquiry process which is used for the first time for workplace self-care works intentionally with interior resources that may be unknown or fragmented and dialogues sensitively with inner ‘rules’ or patterns that may have become problematic. Incubation and reflective illumination produce tacit knowledge to augment healing intuition.  This process is illustrated by an example.  It is about a less intense focus that actively encourages tender, ‘standing apart’ from symptoms so as to allow perspectives to arise and the intuiting of transformative possibilities.  From this, self-compassion, humility and meaningful detachment are re-affirmed as ways to pay self-kindly attention and address self-criticism and self-blame. 
The contribution of the study is threefold.  First, it extends bricolage to workplace self-care by considering inner resistance and negative self-talk, both barriers to self-care.  Second, it affirms the heuristic inquiry process as an intuitive method for self-care research.  Third, and paradoxically, it shows that self-engagement, in a compassionate yet less intense way, can lead to self-care transformation.  Finally, limitations to the study and possibilities for future research are discussed.

This paper proposes a weighted double-heuristic search algorithm to find the shortest path between two points. It can be used in numerous fields such as graph theory, game theory, and network. This algorithm, called T*, uses a weighted and heuristic function as f(x) = α × t(x) + β × h1(x) + γ × h2(x). It selects the path which minimises f(x) where x is a current node on the path, t(x) is cost of the path from start to x, h1(x) is a heuristic to estimate the cost from x to the straight line passing through start and target, and h2(x) is a heuristic to estimate cost of the cheapest path from x to target. Furthermore, α, β, and γ indicate effective weights of each sub-function on f(x). T* algorithm is compared to the Greedy and A* algorithms in terms of hit rate and the number of processed nodes. Comparison results show that the proposed algorithm has a high efficiency compared to other algorithms.

In this paper I examine the heuristic view of mathematics focussing on an updated version of it. I discuss how the seminal work of Lakatos has been improved under several respects and I point at four issues that are particularly relevant for the philosophy of mathematics and mathematical practice from a heuristic point of view: 1. the quest for a method of discovery (§2); 2. the construction of heuristic procedures, that is rational and inferential ways of producing a hypothesis to solve a problem (§3); 3. the nature of mathematical objects (§4); 4. the relation between mathematics, evolution, and reality (§5).

Electricity is a significant power resource that is being hard to store physically. Energy policy aims to maintain continuous power supply to customers without shortage or waste of energy. To address this issue, this paper aims to provide a framework to forecast the future net electricity consumption of Turkey based on four factors (independent variables), namely, imports, exports, transmitted energy and gross generation, which have an impact on the net electricity consumption. The framework involves forecasting the independent variables using a nonlinear autoregressive-based neural network (NARANN) model. Afterward, an elastic net regression model is proposed to forecast the net electricity consumption of Turkey. Simulated annealing (SA) and evolutionary strategy (ES) were used to optimize the coefficients of the elastic net regression model. The results show that the proposed approach provides high accuracy for net electricity consumption forecasting.

En el presente trabajo se plantea una metodología de planeación de trayectorias para manipuladores seriales antropomórficos de seis grados de libertad y muñeca esférica enfocada en la minimización del consumo eléctrico y maximización de la manipulabilidad. Para lograr tal fin se expone un algoritmo de optimización el cual tiene como base el Algoritmo Heurístico de Kalman (AHK), cuya finalidad es encontrar la trayectoria óptima según la función multi-objetivo propuesta dentro de un espacio esférico simplificado propuesto. El algoritmo de optimización se evalúa mediante el análisis del comportamiento de dos trayectorias en el manipulador PUMA 560, simuladas en un programa desarrollado en la aplicación de Visual Basic perteneciente al software Autodesk Inventor.

Integration and adaptation of artificial intelligent designs with fuzzy inference techniques is an active area of research that can be used to meet the challenges of regeneration processes. Urban regeneration activities in built environment are complex and require a close collaboration between designers and planners in order to achieve a design plan that is environmentally robust and sustainable. Regeneration teamspsila inability to manually analyze complex maps for various regeneration choices induces human errors in the regeneration process. This often results in a prolonged impact on the economic, social and environmental wellbeing and sustainability of the region. This paper, presents the development of an urban regeneration fuzzy inference system (FIS) aimed at tackling the issue of regeneration simulation in built environment through the measurement of impact of certain socioeconomic parameters to the regeneration plan. The impact assessment logic is embedded in the form of an expertly guided rule-base of an FIS. The impact is calculated using the four core principles of urban smart growth (crime, accessibility, employment and health), with respect to a measure of Euclidean intra-regional distance based accessibility function between the regeneration area(s) and the surrounding built environment neighborhood. The FIS evaluates the suitability of various regeneration sub-areas in terms of the aforementioned four principles affecting the concept of a walk-able, sustainable and eco-friendly neighborhood.

In on-grid microgrids, electric vehicles (EVs) have to be efficiently scheduled for costeffective electricity consumption and network operation. The stochastic nature of the involved parameters along with their large number and correlations make such scheduling a challenging task. This paper aims at identifying pertinent innovative solutions for reducing the relevant total costs of the on-grid EVs within hybrid microgrids. To optimally scale the EVs, a heuristic greedy approach is considered. Unlike most existing scheduling methodologies in the literature, the proposed greedy scheduler is model-free, training-free, and yet efficient. The proposed approach considers different factors such as the electricity price, on-grid EVs state of arrival and departure, and the total revenue to meet the load demands. The greedy-based approach behaves satisfactorily in terms of fulfilling its objective for the hybrid microgrid system, which is established of photovoltaic, wind turbine, and a
local utility grid. Meanwhile, the on-grid EVs are being utilized as an energy storage exchange location. A real time hardware-in-the-loop experimentation is comprehensively conducted to maximize the earned profit. Through different uncertainty scenarios, the ability of the proposed greedy approach to obtain a global optimal solution is assessed. A data simulator was developed for the purposes of generating evaluation datasets, which captures uncertainties in the behaviors of the system’s parameters. The greedy-based strategy is considered applicable, scalable, and efficient in terms of total operating expenditures. Furthermore, as EVs penetration became more versatile, total expenses decreased significantly. Using simulated data of an effective operational duration of 500 years, the proposed approach succeeded in cutting down the energy consumption costs by about 50–85%, beating existing state-of-the-arts results. The proposed approach is proved to be tolerant to the large amounts of uncertainties that are involved in the system’s operational data.

En el área de la computación y las matemáticas, uno de los problemas abiertos vigentes es encontrar algoritmos eficientes y eficaces para resolver problemas teóricos del tipo NP; como son el problema de Bin Packing, el del Agente viajero y el de la Mochila, entre otros. Este tipo de problemas son considerados de alta complejidad computacional ya que a la fecha no se conocen algoritmos que los puedan resolver en un tiempo polinomial.

En particular, el Bin Packing Problem (BPP) es un problema NP-duro (es decir, NP y NP-hard) de optimización combinatoria en el cual, dado un conjunto de objetos de tamaño variable, se busca acomodarlos dentro de contenedores de tamaño fijo, buscando optimizar el número de contenedores a utilizar, es decir, usando el menor número de contendores para colocar el mayor número de objetos posible.

Para este problema existen diversas variantes tales como el bin packing unidimensional (1D-BPP), de 2 dimensiones (2D-BPP) o de 3 dimensiones (3D-BPP); en dichas variantes solo cambia el número de dimensiones tanto de los objetos como de los contenedores; no obstante, el presente trabajo se limita a estudiar el problema de bin packing de una dimensión uno.

Visto el nivel de importancia de este tipo de problemas, en particular del BPP, en el presente documento se estudia el modelo del Binpacking problem de una dimensión de manera que éste se implementa en Visual Studio y se resuelve con Cplex para 100 Instancias, además que se trabajan dos heurísticas (FF y FFD) y con ellas se resuelven las mismas Instancias y se comparan resultados.