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When faced with important decisions, we tend to base our decision-making on a rational framework, which often includes multiple decision criteria. Spatial decision problems have been characterized as a set of geographically defined decision alternatives (locations) with associated criterion values (e.g., Malczewski 1999). Within Geographic Information Systems (GIS), multi-criteria decision analyses (MCDA) tools have been used for decision support in environmental, transportation, and urban/regional planning, in waste management, as well as in hydrology, agriculture, and forestry, to name but a few areas of application (Malczewski 2006). Often, MCDA tools are only loosely coupled with GIS software (e.g., calculations completed in a spreadsheet) or take the form of custom implementations in a GIS scripting/programming environment. Few GIS vendors have integrated generic MCDA functionality in their products, with the notable exceptions of Idrisi’s Multi-Criteria Evaluation module and ArcGIS’ Overlay Toolset. Both of these operate on raster data layers using map algebra operations to combine cell values into an evaluation score for each candidate location (raster cell). In this technical note, we present “MCDA4ArcMap”, an open-source tool for MCDA and geovisualization of vector data in Arc-Map. The analytical functionality of the tool includes three MCDA methods: weighted linear combination (WLC), ordered weighted averaging (OWA), and a local variant of WLC (LWLC). WLC corre-sponds to the weighted overlay tool that readers may know from ArcGIS. As an extension of the criterion importance weighting in WLC, the OWA method allows the decision-maker to specify a de-gree of risk in their approach to decision-making. OWA has been implemented previously in Idrisi (Jiang & Eastman 2000). The recently proposed LWLC (Malczewski 2011) adjusts criterion impor-tance weights with regards to the local range of criterion values. Criterion weights are increased in a neighbourhood, if their local range is large relative to their global range in the study area, or decreased if the local range is relatively small. This approach ad-heres to the range-sensitivity principle that stipulates that criterion weights should depend on the ranges of criterion values occurring in a specific decision problem.

This paper proposes an energy management (EM) model for residences in an inclining block rate (IBR) tariff environment. Given a cluster, i.e., a group of appliances which satisfies certain requirements, the proposed scheme is primarily driven by two layers of clustered priorities. The first layer of clusters comprises various services of the residences and governs it with shareable z1 priorities, and the second layer of clusters binds the major power-consuming appliances under each substation and regulates it with dynamically changing z2 priorities. Integer linear programming is used to solve the multi-criteria decision problem crafted to address both grid-connected and isolated modes of operations. The model is tested on MATLAB using the IEEE 123-bus system with modified Pecan Street Dataset. Various results reveal that the proposed model is effective in providing a reliable power supply to the critical loads in all the scenarios while keeping the price within the preference limit with minimum comfort-loss for end-users, even in presence of non-responsive IBR environment

Best-worst method (BWM) has attracted increasing attention. It has been generalized to different fuzzy environments and applied to various real-life decision problems. This paper develops a new intuitionistic fuzzy (IF) best-worst method (IFBWM) for multi-criteria decision-making (MCDM). When a decision maker (DM) makes comparisons, there may be some hesitancies. Thus, the reference comparisons are represented as intuitionistic fuzzy values (IFVs), the Best-to-Others vector and the Others-to-Worst vector are IF vectors. According to the multiplicative consistency of intuitionistic fuzzy preference relation, this paper gives the consistency equations and views them as IF equations. The derivation of optimal IF weights of criteria is formulated as an IF decision-making problem. Thereby, a mathematical programming model is constructed to assure that the derived optimal IF weights of criteria is a normalized IF weight vector. Depending on the risk preference of DM, four linear programming models are presented to obtain the optimal IF weights based on the constructed mathematical programming model for the optimistic DM, the pessimistic DM and the neutral DM, respectively. Furthermore, this paper investigates the process of improving the consistency. Several examples are demonstrated to show the application and effectiveness of the proposed IF BWM.

Machine Learning has emerged in the last years as the main solution to many of nowadays’ data-based decision problems. However, while new and more powerful algorithms and the increasing availability of computational resources contributed to a widespread use of Machine Learning, significant challenges still remain. Two of the most significant nowadays are the need to explain a model’s predictions, and the significant costs of training and re-training models, especially with large datasets or in streaming scenarios. In this paper we address both issues by proposing an approach we deem predictive and user-centric. It is predictive in the sense that it estimates the benefit of re-training a model with new data, and it is user-centric in the sense that it implements an explainable interface that produces interpretable explanations that accompany predictions. The former allows to reduce necessary resources (e.g. time, costs) spent on retraining models when no improvements are expected, while the latter allows for human users to have additional information to support decision-making. We validate the proposed approach with a group of public datasets and present a real application scenario.

The notion of zig-zag number was introduced as an attempt to provide a unified algorithmic framework for directed graphs. Nevertheless, little was known about the complexity of computing this directed graph invariant. We prove that deciding whether a directed graph has zig-zag number at most k is in NP for each fixed k ≥ 0 . Although for most of the natural decision problems this is an almost trivial result, settling k - zig-zag number in NP is surprisingly difficult. In addition, we prove that 2- zig-zag number is already an NP -hard problem.

Nowadays, a large number of intelligent devices involved in the Industrial Internet of Things (IIoT) environment lead to unprecedented challenges in security. Due to limited resources with weak security protection, the IIoT devices can be easily compromised to launch Distributed Denial-of-Service (DDoS) attacks, resulting in catastrophic results. Although there are many DDoS mitigations of traditional static schemes, the proactive defense method to resist attacks has not been well studied. Furthermore, existing proactive schemes ignored the delay-sensitive characteristic of applications under the IIoT environments. To address these issues, we first adopt two kinds of Moving Target Defense (MTD) techniques that dynamically control the admission of devices and migrate service replicas to isolate attackers on limited edge clouds and mitigate DDoS attacks early near its source. Then, we formulate a multi-stage optimization problem of MTD mechanisms deployment and model it as Constrained Markov Decision Processes (CMDP) in order to maximize the available resources of the system under the limitations of the IIoT environments. Besides, we present an MTD Optimal Strategy (MOS) algorithm to solve decision problems in a cost-effective manner. The proposed algorithm can achieve an optimal admission allocation by means of attackers gathering within the same service where the service migration decisions are assisted by means of value iteration. The experimental results verify that the proposed algorithm, compared with existing strategies, can effectively mitigate DDoS attacks with acceptable degradation of the quality of service (QoS).

Cloud-edge heterogeneous network is an emerging technique built on edge infrastructure, which is based on the core of cloud computing technology and edge computing capabilities. The joint problem of computation offloading, cache decision, and resource allocation for cloud-edge heterogeneous network system is a challenging issue. In this paper, we investigate the joint problem of computation offloading, cache decision, transmission power allocation, and CPU frequency allocation for cloud-edge heterogeneous network system with multiple independent tasks. The goal is to minimize the weighted sum cost of the execution delay and energy consumption while guaranteeing the transmission power and CPU frequency constraint of the tasks. The constraint of computing resource and cache capacity of each Access Point (AP) are considered as well. The formulated problem is a mixed integer non-linear optimization problem. In order to solve the formulated problem, we propose a two-level alternation method framework based on Reinforcement Learning (RL) and Sequential Quadratic Programming (SQP). In the upper level, given the allocated transmission power and CPU frequency, the task offloading decision and cache decision problem is solved using Deep Q-Network method. In the lower level, the optimal transmission power and CPU frequency allocation with the offloading decision and cache decision is obtained by using SQP technique. Simulation results demonstrate that the proposed scheme achieves significant reduction on the sum cost compared to other baselines.

The freemium pricing model has become mainstream in the software industry. A large user base can induce positive network effects while expanding security risks associated with unpatched users. This study explores a two-stage decision problem faced by software vendors that involves a freemium versioning strategy and a subsequent security-patching strategy when taking both the positive network externality and negative security externality into consideration. It is noteworthy that a joint effect of the two externalities on the vendor’s management decisions exists. First, we analytically derive three patching strategies for the vendor: P S 1 (rebates all users), P S 2 (rebates only freeware users), and P S 3 (rebates no users). Our results indicate that, if the strength of the positive network externality is relatively low, the optimal security-patching strategy will be significantly affected by the negative security externality. Specifically, when the intensity of the negative security externality is low, the vendor’s optimal patching strategy will be P S 1 . However, with the increase in the negative security externality, the optimal patching strategy changes to P S 2 and then to P S 3 , whereas the strategy spaces of P S 1 and P S 2 decrease in the positive network externality to zero. Nevertheless, if the strength of the positive network externality is relatively high, the vendor is better off selecting P S 1 when the negative security externality is low. However, when the negative security externality is high, P S 3 is optimal. Furthermore, based on optimal patching strategies, we reveal the optimal conditions required for the vendor to adopt the freemium model compared with commercial only. Of interest, we find that the vendor adopting the freemium version is also influenced by the interaction of the two externalities. Finally, through numerical experiments, we find that the vendor and social planner’s interests can be aligned under certain conditions. However, this is not always the case.

The Nash equilibrium is an important concept in game theory. It describes the least exploitability of one player from any opponents. We combine game theory, dynamic programming, and recent deep reinforcement learning (DRL) techniques to online learn the Nash equilibrium policy for two-player zero-sum Markov games (TZMGs). The problem is first formulated as a Bellman minimax equation, and generalized policy iteration (GPI) provides a double-loop iterative way to find the equilibrium. Then, neural networks are introduced to approximate Q functions for large-scale problems. An online minimax Q network learning algorithm is proposed to train the network with observations. Experience replay, dueling network, and double Q-learning are applied to improve the learning process. The contributions are twofold: 1) DRL techniques are combined with GPI to find the TZMG Nash equilibrium for the first time and 2) the convergence of the online learning algorithm with a lookup table and experience replay is proven, whose proof is not only useful for TZMGs but also instructive for single-agent Markov decision problems. Experiments on different examples validate the effectiveness of the proposed algorithm on TZMG problems.

Buildings are exposed to risks from environmental hazards such as earthquakes, windstorms and floods. Substantial uncertainties from various sources are inevitably involved in the risk estimation and decision-making for activities such as design and disaster risk mitigation for buildings. Decision makers seek to achieve economic efficiency while ensure building safety by managing the extreme tail risk that is typically a concern when facing low-probability, high-consequence events. Thus, risk preferences and tolerances play an important role in the decision process, which often vary among different decision makers. The conventionally used minimum expected life-cycle cost criterion (MELC) fails to adequately cope with large uncertainty and risk preferences. To this end, this paper presents the application of a set of decision models beyond the MELC to support decision-making under uncertainty for buildings exposed to environmental hazards. The objective is to provide risk-informed decision support for decision-makers with a wide range of risk appetites while taking into account uncertainties involved in the life-cycle cost. The features, strengths and weaknesses of these decision models are discussed from a practical point of view. The application and selection of the decision models are demonstrated by two practical decision problems: (i) seismic design of a high-rise commercial building, and (ii) wind hazard mitigation for a low-rise residential building. These examples illustrate how the decisions for choosing seismic design levels and wind mitigation measures vary when different decision models and model settings are applied.

We study a general class of dynamic multi-agent decision problems with asymmetric information and non-strategic agents, which includes dynamic teams as a special case. When agents are non-strategic, an agent's strategy is known to the other agents. Nevertheless, the agents strategy choices and beliefs are interdependent over times, a phenomenon known as signaling. We introduce the notion of sufficient information that effectively compresses the agents information in a mutually consistent manner. Accordingly, we propose an information state for each agent that is sufficient for decision making purposes. We present instances where we can determine an information state with a time-invariant domain for each agent. We present a generalization of the policy-independence property of belief in Partially Observed Markov Decision Processes to dynamic multi-agent decision problems. Furthermore, we propose a sequential decomposition that decouples the interdependence between the agents strategies and beliefs over time, and enables us to formulate a dynamic program to determine a globally optimal policy in dynamic teams via backward induction.

Energy harvesting (EH) enabled cellular internet of things (IoT) is a promising solution to handle the charging and accessing of massive IoT nodes. However, limited by the high frequency band of future 5G, the radius of the small base station (SBS) is reduced, hence greatly increasing the cost of the network operators (NOs). In this paper, we consider the joint cell association, cell sleeping, and incentive decision problem for EH aided cellular IoT with full duplex (FD) self-backhauls. We formulate a Stackelberg game to investigate the coordination between the utilities of NO and energy transmitters (ETs), where both the features of FD self-backhauls and cell sleeping are introduced to reduce the expense of NO. We then propose an alternative direction algorithm to solve the equilibrium of the game efficiently, where the relationship of the formulated constraints and variables are utilized to transform the original problem into two sub-problems. We propose a two-level Lagrangian relaxation to solve the first sub-problem, while the other is proved to be convex and solve by an efficient iteration. Simulation results demonstrate the benefits of our algorithm in utility improvement and expense reduction. Moveover, it shows that our algorithm can obtain high efficiency by adjusting the tradeoff between the number of active SBS and transmitting power of ETs according to the network deployment.

The theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems. The discrete Choquet and Sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies. We address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through evolutionary algorithms. We discuss two efficient methods suitable for k-interactive capacities. The results are supported by the extensive numerical evidence and provide a useful tool for large scale simulations.

In recent years, increasing resource consumption worldwide has alarmed experts. This problem contributes to the need for more ecological solutions and processes including the use of renewable energies, which reduces organizations’ environmental impact. To find ways to improve new green solutions and process integration, researchers need to study and measure these innovation effects, especially on small- and medium-sized enterprises (SMEs). However, evaluating renewable energy impacts on SMEs is not as easy as would first appear. This challenge can be addressed by developing an analysis model to mitigate the limitations of recent studies and, concurrently, deal with this complex subjective issue. In this article, the combined use of cognitive mapping and the decision-making trial and evaluation laboratory (DEMATEL) technique facilitated the generation of a complete, transparent, and informed model that can help managers make better decisions in this context. Specifically, grounded in intensive group work sessions with renewable energy specialists, the results address some of the limitations of more generic models and include a multicriteria analysis system that provides guidelines for renewable energy management practices, with the potential to improve SME performance. To enable a fuller interpretation of the decision problem in question, the most important indicators were identified and the cause-and-effect relationships between these criteria were analyzed. The findings were validated by the panel members and a member of the Portuguese Renewable Energy Association. The advantages and limitations of the proposed model are also discussed.

In this paper, we study a multi-agent project staffing problem involving a single project, which has to be scheduled under resource constraints. We consider a functional organisational structure where a team leader and a project manager are together responsible for the operational execution of a project. The team leader, which has the formal authority over the resources, is standing at the top of the hierarchy and determines the number and mix of (additional) employees and tries to level the workload over the planning period in order to avoid idle resource times. The project manager is responsible for the scheduling of the project activities and his/her objective is to minimise the project duration. The interaction between both agents in the decision-making process is, on the one hand, hierarchical, i.e. the team leader imposes his/her decision on the project manager. On the other hand, the decision taken by the team leader should comply to the objective of the project manager such that the staffing plan and project schedule is agreed by both parties. We propose a bilevel optimisation model that embeds a nested inner optimisation problem, i.e. the project manager decision problem, as a constraint in the outer optimisation problem, i.e. the decision problem of the team leader. The algorithm is a mathematical programming method thriving on the generation of additional lazy constraints via feasibility callbacks so that the team leader problem has to respect the requirements formulated in the project manager problem. In the computational experiments, we compare this solution approach to alternative classical optimisation approaches and we validate the design choices related to the proposed speed-up mechanisms and parameter settings.

Three-way decision provides a new perspective for dealing with uncertainty and complexity in decision-making problems. However, behaviors of decision-makers may be influenced by different risk attitudes in reality. To address this problem, we construct a regret-based three-way decision model under interval type-2 fuzzy environment. Basically, regret theory and interval type-2 fuzzy set are utilized to improve three-way decision in coping with the risk and uncertainty. Two core issues focus on the determination of decision rules and estimation of conditional probabilities for different decision-makers under interval type-2 fuzzy environment. The maximum-utility decision rules are derived based on regret theory. An interval type-2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method is utilized to estimate the conditional probability. The results of the illustrative example show that the proposed model can effectively solve uncertain decision problems. The comparative analysis and experimental evaluations are utilized to elaborate on the performance of the regret-based three-way decision model.

Consider a multiobjective decision problem with uncertainty in the objective functions, given as a set of scenarios. In the single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. A well-known alternative method in the single-objective case is to compare possible decisions under uncertainty with the optimal decision with the benefit of hindsight, i.e. to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this contribution, we extend the concept of regret from the single-objective case to the multiobjective setting and introduce a proper definition of multivariate (robust) (relative) regret. In contrast to the few existing ideas that mix scalarization and optimization, we clearly separate the modelling of multiobjective (robust) regret from its numerical solution. Moreover, our approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases. We illustrate all approaches based on a biobjective shortest path problem under uncertainty.

This paper aims to provide a scientific approach that indicates the need to focus on renewable energy potential to meet energy needs in Turkey. Turkey began to take advantage of renewable energy technologies a few years ago. Accordingly, the issue of determining the best renewable resources for the country has been brought to the agenda in recent years. The issue was considered to be a limited multi-objective optimization problem allowing us to achieve a reliable result. However, the parameter of each resource was considered as a range value, rather than traditionally expressed as an exact value, and a multi-objective decision problem was developed with an interval coefficient. This method allows us to obtain more accurate and reliable results without the need to resort to normalization methods used to eliminate unit differences. According to the results of this study, the most convenient alternatives for Turkey are hydro, wind, and solar power. The findings also support decision policies aimed at reaching targets for the electricity sector in 2023, as put forth by the Ministry of Energy and Natural Resources (MENR).

In this letter, we establish the convergence of fitted value iteration and fitted Q-value iteration for continuous-state continuous-action Markov decision problems (MDPs) with state-dependent action sets. We further extend the algorithm and the convergence result to the case of monotone MDPs.

This paper treats the Piggyback Transportation Problem: A large vehicle moves successive batches of small vehicles from a depot to a single launching point. Here, the small vehicles depart toward assigned customers, supply shipments, and return to the depot. Once the large vehicle has returned and another batch of small vehicles has been loaded at the depot, the process repeats until all customers are serviced. With autonomous driving on the verge of practical application, this general setting occurs whenever small autonomous delivery vehicles with limited operating range, e.g., unmanned aerial vehicles (drones) or delivery robots, need to be brought in the proximity of the customers by a larger vehicle, e.g., a truck. We aim at the most elementary decision problem in this context, which is inspired by Amazon’s novel last-mile concept, the flying warehouse. According to this concept, drones are launched from a flying warehouse and – after their return to an earthbound depot – are resupplied to the flying warehouse by an air shuttle. We formulate the Piggyback Transportation Problem, investigate its computational complexity, and derive suited solution procedures. From a theoretical perspective, we prove different important structural problem properties. From a practical point of view, we explore the impact of the two main cost drivers, the capacity of the large vehicle and the fleet size of small vehicles, on service quality.

Judging an act’s causal efficacy plays a crucial role in causal decision theory. A recent development appeals to the causal modeling framework with an emphasis on the analysis of intervention based on the causal Bayes net for clarifying what causally depends on our acts. However, few writers have focused on exploring the usefulness of extending structural causal models to decision problems that are not ideal for intervention analysis. I found that it is structural models, rather than intervention analysis, serves as a valuable formal tool for a range of realistic decision problems that involve mixed causal mechanisms. The thesis concludes that structural models provide a more general framework for rational decision-makers.

Online reputation (reflected in consumer ratings) has become a key marketing-mix variable in the digital world. We consider a market consisting of competing firms that participate in a platform such as Expedia or Yelp. Each firm exerts effort to improve its ratings, but in doing so, also influences the mean market rating. The sales of a firm are influenced by its own ratings and the mean rating of the firms in the market. An equilibrium analysis of the mean market rating reveals several insights. A more heterogeneous market (one where the parameters of the firms are very different) leads to a lower mean market rating and higher total profit of the firms in the market. Our results can inform platforms to target certain firms to join: Growing the middle of the market (firms with average ratings) is the best option considering the goals of the platform (increase total profit of the firms) and the other stakeholders, namely, incumbents and consumers. For firms, we find that a firm's profit can increase from an adverse event (such as, a reduction in sales margin, or an increase in the cost of control) depending on how other firms in the market are affected by the event. Our findings are particularly significant for platform owners who could benefit from growing the platform in a strategic manner. We model each firm's decision problem as a stochastic control problem where the objective is to maximize discounted profit over a planning horizon. These control problems are connected through a common market belief that represents the mean rating of the firms in the market. The joint actions of the firms generate a mean market equilibrium. We prove that such an equilibrium exists, is unique, and use a simple algorithm to compute its value.