A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hybrid Methods for Resource Allocation and Scheduling Problems in Deterministic and Stochastic Environments

This work presents exact, hybrid algorithms for mixed resource Allocation and Scheduling problems; in general terms, those consist into assigning over time finite capacity resources to a set of precedence connected activities. The proposed methods have broad applicability, but are mainly motivated by applications in the field of Embedded System Design. In particular, high-performance embedded computing recently witnessed the shift from single CPU platforms with application-specific accelerators to programmable Multi Processor Systems-on-Chip (MPSoCs). Those allow higher flexibility, real time performance and low energy consumption, but the programmer must be able to effectively exploit the platform parallelism. This raises interest in the development of algorithmic techniques to be embedded in CAD tools; in particular, given a specific application and platform, the objective if to perform optimal allocation of hardware resources and to compute an execution schedule. On this regard, since embedded systems tend to run the same set of applications for their entire lifetime, off-line, exact optimization approaches are particularly appealing. Quite surprisingly, the use of exact algorithms has not been well investigated so far; this is in part motivated by the complexity of integrated allocation and scheduling, setting tough challenges for ``pure'' combinatorial methods. The use of hybrid CP/OR approaches presents the opportunity to exploit mutual advantages of different methods, while compensating for their weaknesses. In this work, we consider in first instance an Allocation and Scheduling problem over the Cell BE processor by Sony, IBM and Toshiba; we propose three different solution methods, leveraging decomposition, cut generation and heuristic guided search. Next, we face Allocation and Scheduling of so-called Conditional Task Graphs, explicitly accounting for branches with outcome not known at design time; we extend the CP scheduling framework to effectively deal with the introduced stochastic elements. Finally, we address Allocation and Scheduling with uncertain, bounded execution times, via conflict based tree search; we introduce a simple and flexible time model to take into account duration variability and provide an efficient conflict detection method. The proposed approaches achieve good results on practical size problem, thus demonstrating the use of exact approaches for system design is feasible. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.

Demography in eusocial Hymenoptera

In my doctoral thesis I investigated the evolution of demographic traits within eusocial Hymenoptera. In the social bees, wasps and ants, eusociality has a unique effect on life span evolution as female larvae with the same genetic background can develop through phenotypic plasticity to a queen or a worker with vastly diverging life-history traits. Ant queens belong to the longest-lived insect species, while workers in most species live only a fraction of the queen’s life span. The average colony size of a species is positively correlated with social complexity, division of labor and diverging morphological female phenotypes all of which also affect life span. Therefore the demographic traits of interest in this thesis were life span and colony size. To understand the evolution of worker life span I applied a trade-off model that includes both hierarchical levels important in eusocial systems, namely the colony- and the individual-level. I showed that the evolution of worker life span may be an adaptive trait on the colony level to optimize resource allocation and therefore fitness in response to different levels of extrinsic mortality. A shorter worker life span as a result of reduced resource investments under high levels of extrinsic mortality increases colony fitness. In a further study I showed that Lasius niger colonies produce different aging phenotypes throughout colony development. Smaller colonies which apply a different foraging strategy than larger colonies produced smaller workers, which in turn have a longer life span as compared to larger workers produced in larger colonies. With the switch to cooperative foraging in growing colonies individual workers become less important for the colony caused by their increasing redundancy. Alternatively a trade of between growth and life span may lead to the results found in this study. A further comparative analysis to study the effect of colony size on life span showed a correlation between queen and worker life span when colony size is taken into account. While neither worker nor queen life span was associated with colony size, the differences between queen and worker life span increase with larger average colony sizes across all eusocial Hymenoptera. As colony size affects both queen and worker life span, I aimed to understand which factors lead to the small colony sizes displayed by some ant species. I therefore analyzed per-capita productivity at different colony sizes of eight cavity dwelling ant species. Most colonies of the study species grew larger than optimal productivity predicted. Larger colony size was shown to increase colony homeostasis, the predictability of future productivity and in turn the survival probability of the colony. I also showed that species that deploy an individual foraging mode may circumvent the density dependent decline in foraging success by splitting the colony to several nest sites.

Global Reuse and Optimal Waste Policy

Electronic waste generated from the consumption of durable goods in developed countries is often exported to underdeveloped countries for reuse, recycling and disposal with unfortunate environmental consequences. The lack of efficient disposal policies within developing nations coupled with global free trade agreements make it difficult for consumers to internalize these costs. This paper develops a two-country model, one economically developed and the other underdeveloped, to solve for optimal tax policies necessary to achieve the efficient allocation of economic resources in an economy with a durable good available for global reuse without policy measures in the underdeveloped country. A tax in the developed country on purchases of the new durable good combined with a waste tax set below the domestic external cost of disposal is sufficient for global efficiency. The implication of allowing free global trade in electronic waste is also examined, where optimal policy resembles a global deposit-refund system.

Predictors of optimal viral suppression in patients switched to abacavir, lamivudine, and zidovudine: the Swiss HIV Cohort Study

OBJECTIVE: To investigate predictors of continued HIV RNA viral load suppression in individuals switched to abacavir (ABC), lamivudine (3TC) and zidovudine (ZDV) after successful previous treatment with a protease inhibitor or non-nucleoside reverse transcriptase inhibitor-based combination antiretroviral therapy. DESIGN AND METHODS: An observational cohort study, which included individuals in the Swiss HIV Cohort Study switching to ABC/3TC/ZDV following successful suppression of viral load. The primary endpoint was time to treatment failure defined as the first of the following events: two consecutiveviral load measurements > 400 copies/ml under ABC/3TC/ZDV, one viral load measurement > 400 copies/ml and subsequent discontinuation of ABC/3TC/ZDV within 3 months, AIDS or death. RESULTS: We included 495 individuals; 47 experienced treatment failure in 1459 person-years of follow-up [rate = 3.22 events/100 person-years; 95% confidence interval (95% CI), 2.30-4.14]. Of all failures, 62% occurred in the first year after switching to ABC/3TC/ZDV. In a Cox regression analysis, treatment failure was independently associated with earlier exposure to nucleoside reverse transcriptase inhibitor (NRTI) mono or dual therapy [hazard ratio (HR), 8.02; 95% CI, 4.19-15.35) and low CD4 cell count at the time of the switch (HR, 0.66; 95% CI, 0.51-0.87 by +100 cells/microl up to 500 cells/microl). In patients without earlier exposure to mono or dual therapy, AIDS prior to switch to simplified maintenance therapy was an additional risk factor. CONCLUSIONS: The failure rate was low in patients with suppressed viral load and switch to ABC/3TC/ZDV treatment. Patients with earlier exposure to mono or dual NRTI therapy, low CD4 cell count at time of switch, or AIDS are at increased risk of treatment failure, limiting the use of ABC/3TC/ZDV in these patient groups.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Patient classification system: An integrated method for measuring nursing intensity and optimizing resource allocation

A patient classification system was developed integrating a patient acuity instrument with a computerized nursing distribution method based on a linear programming model. The system was designed for real-time measurement of patient acuity (workload) and allocation of nursing personnel to optimize the utilization of resources.^ The acuity instrument was a prototype tool with eight categories of patients defined by patient severity and nursing intensity parameters. From this tool, the demand for nursing care was defined in patient points with one point equal to one hour of RN time. Validity and reliability of the instrument was determined as follows: (1) Content validity by a panel of expert nurses; (2) predictive validity through a paired t-test analysis of preshift and postshift categorization of patients; (3) initial reliability by a one month pilot of the instrument in a practice setting; and (4) interrater reliability by the Kappa statistic.^ The nursing distribution system was a linear programming model using a branch and bound technique for obtaining integer solutions. The objective function was to minimize the total number of nursing personnel used by optimally assigning the staff to meet the acuity needs of the units. A penalty weight was used as a coefficient of the objective function variables to define priorities for allocation of staff.^ The demand constraints were requirements to meet the total acuity points needed for each unit and to have a minimum number of RNs on each unit. Supply constraints were: (1) total availability of each type of staff and the value of that staff member (value was determined relative to that type of staff's ability to perform the job function of an RN (i.e., value for eight hours RN = 8 points, LVN = 6 points); (2) number of personnel available for floating between units.^ The capability of the model to assign staff quantitatively and qualitatively equal to the manual method was established by a thirty day comparison. Sensitivity testing demonstrated appropriate adjustment of the optimal solution to changes in penalty coefficients in the objective function and to acuity totals in the demand constraints.^ Further investigation of the model documented: correct adjustment of assignments in response to staff value changes; and cost minimization by an addition of a dollar coefficient to the objective function. ^

Defence on demand: mechanisms behind optimal defence patterns

Background The optimal defence hypothesis (ODH) predicts that tissues that contribute most to a plant's fitness and have the highest probability of being attacked will be the parts best defended against biotic threats, including herbivores. In general, young sink tissues and reproductive structures show stronger induced defence responses after attack from pathogens and herbivores and contain higher basal levels of specialized defensive metabolites than other plant parts. However, the underlying physiological mechanisms responsible for these developmentally regulated defence patterns remain unknown. Scope This review summarizes current knowledge about optimal defence patterns in above- and below-ground plant tissues, including information on basal and induced defence metabolite accumulation, defensive structures and their regulation by jasmonic acid (JA). Physiological regulations underlying developmental differences of tissues with contrasting defence patterns are highlighted, with a special focus on the role of classical plant growth hormones, including auxins, cytokinins, gibberellins and brassinosteroids, and their interactions with the JA pathway. By synthesizing recent findings about the dual roles of these growth hormones in plant development and defence responses, this review aims to provide a framework for new discoveries on the molecular basis of patterns predicted by the ODH. Conclusions Almost four decades after its formulation, we are just beginning to understand the underlying molecular mechanisms responsible for the patterns of defence allocation predicted by the ODH. A requirement for future advances will be to understand how developmental and defence processes are integrated.

Blue Light and Abscisic Acid Independently Induce Heterophyllous Switch in Marsilea quadrifolia1

In natural habitats Marsilea quadrifolia L. produces different types of leaves above and below the water level. In aseptic cultures growth conditions can be manipulated so that leaves of the submerged type are produced continuously. Under such conditions the application of either blue light or an optimal concentration of abscisic acid (ABA) induced the development of aerial-type leaves. When fluridone, an inhibitor of ABA biosynthesis, was added to the culture medium it did not prevent blue light induction of aerial leaf development. During blue light treatment the endogenous ABA level in M. quadrifolia leaves remained unchanged. However, after the plants were transferred to an enriched medium, the ABA level gradually increased, corresponding to a transition in development from the submerged type of leaves to aerial leaves. These results indicate that the blue light signal is not mediated by ABA. Therefore, in the regulation of heterophyllous determination, discrete pathways exist in response to environmental signals.

Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Optimal production planning for PCB assembly

It is indisputable that printed circuit boards (PCBs) play a vital role in our daily lives. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB manufacturer’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly lines’ efficiency. This is done by: • integrating the component sequencing and the feeder arrangement problems together for both the pick-and-place machine and the chip shooter machine; • constructing mathematical models and developing an efficient and effective heuristic solution approach for the integrated problems for both types of placement machines, the line assignment problem, and the component allocation problem; and • developing a prototype of the PCB assembly planning system. The techniques proposed in Optimal Production Planning for PCB Assembly will enable process planners in the electronics manufacturing industry to improve the assembly line’s efficiency in their companies. Graduate students in operations research can familiarise themselves with the techniques and the applications of mathematical modeling after reading this advanced introduction to optimal production planning for PCB assembly.

Adaptive resource allocation for multicast orthogonal frequency division multiple access systems with guaranteed BER and rate

In this paper, we propose a resource allocation scheme to minimize transmit power for multicast orthogonal frequency division multiple access systems. The proposed scheme allows users to have different symbol error rate (SER) across subcarriers and guarantees an average bit error rate and transmission rate for all users. We first provide an algorithm to determine the optimal bits and target SER on subcarriers. Because the worst-case complexity of the optimal algorithm is exponential, we further propose a suboptimal algorithm that separately assigns bit and adjusts SER with a lower complexity. Numerical results show that the proposed algorithm can effectively improve the performance of multicast orthogonal frequency division multiple access systems and that the performance of the suboptimal algorithm is close to that of the optimal one. Copyright © 2012 John Wiley & Sons, Ltd. This paper proposes optimal and suboptimal algorithms for minimizing transmitting power of multicast orthogonal frequency division multiple access systems with guaranteed average bit error rate and data rate requirement. The proposed scheme allows users to have different symbol error rate across subcarriers and guarantees an average bit error rate and transmission rate for all users. Copyright © 2012 John Wiley & Sons, Ltd.

An Electromagnetism Metaheuristic for the Uncapacitated Multiple Allocation Hub Location Problem

In this article, the results achieved by applying an electromagnetism (EM) inspired metaheuristic to the uncapacitated multiple allocation hub location problem (UMAHLP) are discussed. An appropriate objective function which natively conform with the problem, 1-swap local search and scaling technique conduce to good overall performance.Computational tests demonstrate the reliability of this method, since the EM-inspired metaheuristic reaches all optimal/best known solutions for UMAHLP, except one, in a reasonable time.

Variable Neighborhood Search for Solving the Capacitated Single Allocation Hub Location Problem

In this paper a Variable Neighborhood Search (VNS) algorithm for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) is presented. CSAHLP consists of two subproblems; the first is choosing a set of hubs from all nodes in a network, while the other comprises finding the optimal allocation of non-hubs to hubs when a set of hubs is already known. The VNS algorithm was used for the first subproblem, while the CPLEX solver was used for the second. Computational results demonstrate that the proposed algorithm has reached optimal solutions on all 20 test instances for which optimal solutions are known, and this in short computational time.

Outage-optimal relay strategy under outdated channel state information in decode-and-forward cooperative communication systems

In this study, the authors investigate the outage-optimal relay strategy under outdated channel state information (CSI) in a decode-and-forward cooperative communication system. They first confirm mathematically that minimising the outage probability under outdated CSI is equivalent to minimising the conditional outage probability on the outdated CSI of all the decodable relays' links. They then propose a multiple-relay strategy with optimised transmitting power allocation (MRS-OTPA) that minimises the conditional outage probability. It is shown that this MRS is a generalised relay approach to achieve the outage optimality under outdated CSI. To reduce the complexity, they also propose a MRS with equal transmitting power allocation (MRS-ETPA) that achieves near-optimal outage performance. It is proved that full spatial diversity, which has been achieved under ideal CSI, can still be achieved under outdated CSI through MRS-OTPA and MRS-ETPA. Finally, the outage performance and diversity order of MRS-OTPA and MRS-ETPA are evaluated by simulation.