The nondominated set of a multiple objective discrete optimization problem is known to contain unsupported nondominated points, which outnumber the supported ones and are more difficult to obtain. We treat supported nondominated points as a representation and analyse their quality using different metrics beyond their sheer numbers. Under different data generation schemes on multiobjective knapsack and assignment problems, we observe that supported nondominated points almost always provide a good representation of the entire nondominated set.

We present a new approach to generate representations with a coverage error quality guarantee for multiobjective discrete optimization problems with any number of objectives. Our method is based on an earlier exact algorithm that finds the entire nondominated set using ε -constraint scalarizations. The representation adaptation requires the search to be conducted over a p-dimensional parameter space instead of the (p-1) -dimensional one of the exact version. The algorithm uses rectangles as search elements and for each rectangle, two-stage mathematical programs are solved to obtain efficient solutions. The representation algorithm implements a modified search procedure and is designed to eliminate a rectangle if it can be verified that it is not of interest given a particular coverage error requirement. Since computing the coverage error is a computationally demanding task, we propose a method to compute an upper bound on this quantity in polynomial time. The algorithm is tested on multiobjective knapsack and assignment problem instances with different error tolerance levels. We observe that our representation algorithm provides significant savings in computational effort even with relatively low levels of coverage error tolerance values for problems with three objective functions. Moreover, computational effort decreases almost linearly when coverage error tolerance increases. This makes it possible to obtain good quality representations for larger problem instances. An analysis of anytime performance on two selected problem instances demonstrates that the algorithm puts together a diverse representation starting from the early iterations.

IntroductionThe number of people diagnosed with dementia is increasing, creating significant economic burden globally. With the progression of the disease, patients need a caregiver whose wellbeing is important for continuous care. Providing respite as a service, through sharing the responsibility of caregiving or support for the caregiver, is a costly initiative. A peer-to-peer online support platform for dementia caregivers, motivated by the sharing economy, putting exchange of knowhow, resources, and services at its center, has the potential to balance cost concerns with a search for respite. The aim of this research is to assess caregivers' intention to engage in peer-to-peer exchange. MethodsA survey including sociodemographic, technology use, and caregiving variables, structured questionnaires (Zarit caregiver burden, WHO brief quality of life scale, ADCS-ADL and chronic stress scale) were administered, January 2018-May 2019, in the dementia outpatient clinic of a university hospital, to a convenience sample of n = 203 individuals identifying themselves as primary caregivers. A path analysis exploring the drivers of an intention to engage in peer-to-peer service exchange was conducted. ResultsIn the path model, caregivers experiencing higher caregiver burden showed higher intention to engage (0.079, p < 0.001). Disease stage had no effect while patient activities of daily living, chronic social role related stressors of the caregiver and general quality of life were significant for the effect on the caregiver burden. Existing household support decreased the caregiver burden, affecting the intention to engage. Caregivers who can share more know-how demonstrate a higher intention to engage (0.579, p = 0.021). Caregiver technology affinity (0.458, p = 0.004) and ability and openness to seek professional help for psychological diagnoses (1.595, p = 0.012) also increased intention to engage. ConclusionThe model shows caregiver burden to be a major driver, along with caregiver characteristics that reflect their technology affinity and openness to the idea of general reciprocity. Existing support for obtaining knowhow and exchanging empathy have a direct effect on the intention to engage. Given the scarcity of caregiver support in the formal care channels, the identified potential of enlarging informal support via a peer-to-peer exchange mechanism holds promise.

Alzheimer's Disease (AD) is believed to be the most common type of dementia. Even though screening for AD has been discussed widely, there is no screening program implemented as part of a policy in any country. Current medical research motivates focusing on the preclinical stages of the disease in a modeling initiative. We develop a partially observable Markov decision process model to determine optimal screening programs. The model contains disease free and preclinical AD partially observable states and the screening decision is taken while an individual is in one of those states. An observable diagnosed preclinical AD state is integrated along with observable mild cognitive impairment, AD and death states. Transition probabilities among states are estimated using data from Knight Alzheimer's Disease Research Center (KADRC) and relevant literature. With an objective of maximizing expected total quality-adjusted life years (QALYs), the output of the model is an optimal screening program that specifies at what points in time an individual over 50 years of age with a given risk of AD will be directed to undergo screening. The screening test used to diagnose preclinical AD has a positive disutility, is imperfect and its sensitivity and specificity are estimated using the KADRC data set. We study the impact of a potential intervention with a parameterized effectiveness and disutility on model outcomes for three different risk profiles (low, medium and high). When intervention effectiveness and disutility are at their best, the optimal screening policy is to screen every year between ages 50 and 95, with an overall QALY gain of 0.94, 1.9 and 2.9 for low, medium and high risk profiles, respectively. As intervention effectiveness diminishes and/or its disutility increases, the optimal policy changes to sporadic screening and then to never screening. Under several scenarios, some screening within the time horizon is optimal from a QALY perspective. Moreover, an in-depth analysis of costs reveals that implementing these policies are either cost-saving or cost-effective.

Alzheimer's disease (AD) constitutes a serious societal healthcare issue as the proportion of the aging population increases. There are ongoing discussions about the necessity of screening the population for AD. We investigate optimal population screening policies for AD using Markov Decision Processes (MDPs). The objective function combines quality-adjusted life years and costs. The disease states are identified according to Clinical Dementia Rating (CDR) scores. The screening test in the model is the Mini Mental State Examination (MMSE), a cognitive test that is widely used in clinical practice. A numerical implementation of the MDP model is presented based on data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and existing literature. In the baseline case, the optimal outcome is not to employ a population-wide screening program. We conduct extensive sensitivity analyses on several model parameters. Our study reveals that the optimal policy may be sensitive to changes in transition probability estimates. When we focus on transitions that are related to treatment effectiveness, we find that implementing a population screening policy becomes socially optimal when plans that lead to cognitive ability stabilization or improvement become available.

The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify a Decision Maker’s most preferred solution without generating the entire set of nondominated solutions. We propose a bilevel programming formulation that can be used to this end. The bilevel program is capable of delivering an efficient solution that maps into a given set, provided that one exits. If the Decision Maker’s preferences are known a priori, they can be used to specify the given set. Alternatively, we propose a method to obtain a representation of the nondominated set when the Decision Maker’s preferences are not available. This requires a thorough search of the outcome space. The search can be facilitated by a partitioning scheme similar to the ones used in global optimization. Since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none, a representation with a specified coverage error level can be found in a finite number of iterations. While building a discrete representation, the algorithm also generates an approximation of the nondominated set within the specified error factor. We illustrate the algorithm on the multiobjective linear programming problem.

The challenge in radiation treatment planning (RTP) is to ensure delivery of a prescription dose to the tumor while limiting the normal tissue toxicity. One way of dealing with this trade off is to use multiobjective optimization which no longer possesses a unique optimal objective function value. In multiobjective optimization, efficient solutions are used instead of the optimal solution which have the property that no improvement in any objective is possible without sacrificing in at least one other objective. In this study, we use achievement scalarization to obtain efficient solutions, i.e. treatment plans which are efficient, for the RTP. We adapt the parameters of the achievement scalarization to address a solution in a rectangle that is defined by the bounds on the objective functions. For a given set of bounds on each structure of the treatment volume, the formulation is able to attain a treatment plan that targets the bounds. We tested our approach on 10 locally advanced head-and-neck cancer cases. All of the cases include three tumor volumes, primary tumor, high-risk nodal volume, low-risk nodal volume, and five organs-at-risk (OAR), left and parotids, spinal cord, brain stem, oral cavity. We compare the proposed method with multiobjective solution algorithm from the literature and clinical plans. While satisfying the coverage of the target volumes, the proposed algorithm was able to improve the OAR sparing as much as 35%.

In practical situations, complex systems are often composed of subsystems or subproblems with single or multiple objectives. These subsystems focus on different aspects of the overall system, but they often have strong interactions with each other and they are usually not sequentially ordered or obviously decomposable. Thus, the individual solutions of subproblems do not generally induce a solution for the overall system. Here, we strive to identify “re-composition architectures” of such “interwoven” systems. Our intention is to connect the subsystems adequately, analyze the resulting performance, model/solve the overall system, and improve the overall solution instead of just solving each subsystem separately. We review recent developments in this field and discuss modeling and solution paradigms in a general and unified framework using the example of an interwoven system consisting of two interacting subsystems.

We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with \(p\) objective functions. The proposed algorithm is based on an exhaustive search of the \((p-2)\)-dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives.

Classification of imbalanced data sets in which negative instances outnumber the positive instances is a significant challenge. These data sets are commonly encountered in real-life problems. However, performance of well-known classifiers is limited in such cases. Various solution approaches have been proposed for the class imbalance problem using either data-level or algorithm-level modifications. Support Vector Machines (SVMs) that have a solid theoretical background also encounter a dramatic decrease in performance when the data distribution is imbalanced. In this study, we propose an L 1 -norm SVM approach that is based on a three objective optimization problem so as to incorporate into the formulation the error sums for the two classes independently. Motivated by the inherent multi objective nature of the SVMs, the solution approach utilizes a reduction into two criteria formulations and investigates the efficient frontier systematically. The results indicate that a comprehensive treatment of distinct positive and negative error levels may lead to performance improvements that have varying degrees of increased computational effort.

Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p - 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known epsilon-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved. (C) 2013 Elsevier B.V. All rights reserved.

Making (MCDM) which was held in Jyväskylä, Finland, in June 13-17, 2011.Biennial International Conferences on MCDM are the main events of the International Society on Multiple Criteria Decision Making for researchers and practitioners in the field.The conference in Jyväskylä was a particular success with 245 oral and 15 poster presentations organized into 68 sessions besides plenary and award sessions and attended by 311 registered participants.An excellent conference organization accompanied by the spectacular midnight sun led to memorable experiences for participants.The research content of the conference was very rich.Therefore, we believe the articles in this special issue constitute a fine representative sample of recent research achievements at the crossroad of global and multiobjective optimization.The articles you will find in this issue span a wide spectrum of traditionally difficult research areas in multiobjective optimization, including discrete, stochastic and parametric optimization.Application of stochastic optimization to multiobjective portfolio optimization, incorporation of data envelopment analysis into multiobjective evolutionary algorithms and introduction of innovization (innovation through optimization) are other topics covered in this special issue.In the article "Higher and Lower-level Knowledge Discovery from Pareto-optimal Sets," Sunith Bandaru and Kalyan Deb build on the concept of innovization, which refers to innovation through optimization by distinguishing between higher and lower level innovization.Their findings are promising for knowledge discovery in challenging engineering design problems.

We propose a one-norm support vector machine (SVM) formulation as an alternative to the well-known formulation that uses parameter C in order to balance the two inherent objective functions of the problem. Our formulation is motivated by the E-constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right-hand-side. Using dual variables we show equivalence of this formulation to the one with the trade-off parameter. We propose an algorithm that enumerates the entire efficient frontier by systematically changing the right-hand-side parameter. We discuss the results of a detailed computational analysis that portrays the structure of the efficient frontier as well as the computational burden associated with finding it. Our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size, and the benefit in terms of classifier performance is almost always substantial when compared to a single run of the corresponding SVM. In addition, both the run time and accuracy compare favorably to other methods that search part or all of the regularization path of SVM. (C) 2011 Elsevier B.V. All rights reserved.

When Microsoft and associates took down the Rustock botnet in March 2011, which organizations were affected? Were they the same ones that were affected during the Rustock spam slowdown of December 2010? Maybe they didn’t improve their information security (infosec) during those three months. This paper analyses this episode as an example of some types of drilldown using data underlying the frequent, regular, comprehensive organizational rankings by outbound spam volume, SpamRankings.net. Such rankings can provide reputational and economic incentives for the ranked organizations to improve their security, which has many policy implications. Just as a sneeze indicates disease, outbound spam indicates poor infosec.Organizations don’t want poor infosec to affect their reputation, so they don’t divulge that information. Fortunately, anti-spam blocklists collect outbound spam data for every organization on the Internet. Outbound spam indicates botnets, botnets indicate vulnerabilities, and vulnerabilities indicate susceptibility to other malware, including phishing, DDoS, and other malware. So we can compare outbound spam and botnets across organizations, and use them as a proxy for poor infosec. A proxy not just ISPs: for any Email Service Provider (ESP), organization that sends email. Nobody wants to do business with a bank, hospital, or university with poor infosec.We collect data daily from multiple anti-spam blocklists, and collate with netblocks and Autonomous System Numbers (ASNs) using tables from Team Cymru. The tables and graphs here derive from the CBL blocklist, including custom spam volume (message count per spamming IP address) and botnet assignments per address.We selected two similar incidents for the same botnet (Rustock) a few months apart. We searched for ASNs with the most spam coming from that botnet. We compared those ASNs spamming between the incidents, and further compared the botnets for certain of those ASNs, as well as another ASN. This Rustock case study is novel in examining ASNs affected by a particular botnet, and botnets infesting particular ASNs, both at specific times, and over a longer timeframe, showing what happens when a botnet slows down or is taken down.Also novel are the ongoing Internet-wide comparisons publicly visible in the frequent, regular, and comprehensive rankings of SpamRankings.net. The project’s model combining peer influence and commons theory for economic governance of the Internet indicates that such rankings motivate ESPs to improve their infosec in order to improve their reputation; and can also help them improve by benchmarking their output with similar ESPs. We are using incremental rollout of SpamRankings.net in natural field experiments on the Internet to determine the effectiveness of the rankings.Policy implications of such rankings and drilldowns include: improving Internet security without additional laws or governmental policies; determining which national policies have the most effect; determining the effectiveness of specific infosec against specific botnets or vulnerabilities; incentives to integrate disparate infosec information; improved national competitiveness through less vulnerability to cybercrime and industrial espionage; and improved national security through less vulnerability to cyberwarfare.

Network security problems are deteriorating worldwide, and can potentially undermine the growth of the digital economy and imperil the multitude of innovations that have been a significant driver of economic growth as well as providing in- creased services to individuals, businesses, and governments. The emergence of botnets as a powerful force undermining security has raised new and important issues. In particu- lar, the difficulty of detection, elimination and prevention of botnets or spam caused thereof on an absolute scale us- ing computing technologies alone have focused attention on studying behavior patterns of botnets and spammers, to help devise better countermeasures. This paper has two ob- jectives; first to introduce a theoretical modeling approach to spammer behavior and derivation of the model, and sec- ond, to compare some of the derivations with data that has been collected from blocklist organizations. By making in- ferences about the blocklist rules, the spammer can strate- gize to maximize the amount of spam sent, and we find evidence of spammers using multiple strategies. The block- list can achieve reduction of spam by investigating longer history of a node's behavior instead of focusing on detection alone. While some of the derivations seem consistent with the data there is considerable room for modification and ex- tension of the modeling approach. The paper concludes with suggestion for the extension of the model.

We propose a one-norm support vector machine (SVM) formulation as an alternative to the well-known formulation that uses parameter C in order to balance the two inherent objective functions of the problem. Our formulation is motivated by the ǫ-constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right-hand-side. Using dual variables we show equivalence of this formulation to the one with the trade-off parameter. We propose an algorithm that enumerates the entire efficient frontier by systematically changing the right-hand-side parameter. We discuss the results of a detailed computational analysis that portrays the computational burden as well as the potential benefits of obtaining the efficient frontier. Our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size, and the benefit in terms of classifier performance is almost always substantial.