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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 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.

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 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.

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 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.

The Networks of Genetic Processors (NGPs) are non-conventional models of computation based on genetic operations over strings, namely mutation and crossover operations as it was established in genetic algorithms. Initially, they have been proposed as acceptor machines which are decision problem solvers. In that case, it has been shown that they are universal computing models equivalent to Turing machines. In this work, we propose NGPs as enumeration devices and we analyze their computational power. First, we define the model and we propose its definition as parallel genetic algorithms. Once the correspondence between the two formalisms has been established, we carry out a study of the generation capacity of the NGPs under the research framework of the theory of formal languages. We investigate the relationships between the number of processors of the model and its generative power. Our results show that the number of processors is important to increase the generative capability of the model up to an upper bound, and that NGPs are universal models of computation if they are formulated as generation devices. This allows us to affirm that parallel genetic algorithms working under certain restrictions can be considered equivalent to Turing machines and, therefore, they are universal models of computation.

The capacities and the Choquet integral are powerful tools to represent decision problems with dependencies and aggregate correlated decision criteria. Random generation of suitable capacities is a vital and challenging task in this decision model because of an exponential number of the involved parameters as well as the associated monotonicity restrictions. In this paper we present various approaches to representing decision makers’ preferences on aggregation through linear constraints , random generation of capacities from the selected polytope , testing the uniformity of the resulting distribution, and constructing the dominance relations between the alternatives, which are subsequently used to get the most credible ranking of the alternatives.

This paper investigates the joint problem of access point (AP) assignment and power allocation (PA) in a three-tier hybrid radio frequency/visible light communication (VLC) heterogeneous network (HetNet). The main goal is to maximize the HetNet’s sum-rate under practical constraints such as APs’ power budgets and users’ quality-of-service (QoS) requirements, while maintaining an acceptable level of illumination in the VLC system. When this design problem is formulated mathematically, it turns out to be a combinatorial decision problem that involves non-linear constraints, and hence is NP hard. To efficiently obtain good quality solutions for the formulated problem, a reformulation into the college admission model is first performed. Then, a distributed and low-complexity algorithm based on matching theory and an efficient heuristic PA scheme are proposed to obtain a good quality suboptimal solution for the joint problem. Simulation results highlight the robustness of the proposed solution and its significant gain in network sum-rate as compared to different benchmark schemes. The effect of various system parameters such as the minimum QoS and maximum illumination requirements on the performance of the proposed solution is studied. Finally, the theoretical analysis of convergence, stability, and complexity of the proposed technique is performed.

Multi-access edge computing (MEC) has already shown great potential in enabling mobile devices to bear the computation-intensive applications by offloading some computing jobs to a nearby access point (AP) integrated with a MEC server (MES). However, due to the varying network conditions and limited computational resources of the MES, the offloading decisions taken by a mobile device and the computational resources allocated by the MES can be formulated as a mixed-integer nonlinear programming (MINLP) problem, which may not be optimized with the lowest cost. In this paper, we propose a novel offloading framework for the multi-server MEC network where each AP is equipped with an MES assisting mobile users (MUs) in executing computation-intensive jobs via offloading. Specifically, we formulate the offloading decision problem as a multiclass classification problem and formulate the MES computational resource allocation problem as a regression problem. Then a multi-task learning based feedforward neural network (MTFNN) model is designed and trained to jointly optimize the offloading decision and computational resource allocation. Numerical results show that the proposed MTFNN outperforms the conventional optimization method in terms of inference accuracy and computational complexity.

Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, i.e., contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently. This work is under consideration for acceptance in TPLP., Comment: Paper presented at the 37th International Conference on Logic Programming (ICLP 2021), 16 pages

This paper deals with the theoretical analysis of the spatial concentration and localization of firms and employees over a set of regions. In particular, it provides a simple site-selection theoretical model to describe the probabilistic framework of the location patterns. The adopted quantitative tool is the stochastic theory of urns. The model moves from the empirical evidence of the deviation of the spatial location of companies from the uniform distribution and of employees from the distribution of firms. Factors leading to such deviations are taken into consideration. Specifically, we formalize a decision problem grounded on the economic attributes of the regions and also on the distribution of the existing firms and employees in the territory. To our purpose, the site-selection model is presented as a stepwise process.

In most modern energy markets, electricity is traded in pay-as-clear auctions. Usually, multiple sequential markets with daily auctions, in which each hourly product is traded separately, coexist. In each market and for each traded hour, each power producer and consumer submits multiple price and volume combinations, called bids. After all bids are submitted by the market participants, the market-clearing price for each hour is published, and the market participants must fulfill their accepted commitments. The corresponding decision problem is particularly difficult to solve for market participants with stochastic supply or demand. We formulate the energy trading problem as a dynamic program and derive the optimal bidding functions analytically via backward recursion. We demonstrate that, for each hour and market, the optimal bidding function is completely defined by two bids. While we focus on power producers with stochastic supply (e.g., wind or solar), our model is applicable to power consumers with stochastic demand, as well. The optimal policy is applicable in most liberalized energy markets, virtually independent of the structure of the underlying electricity price process.

Many supply chain stakeholders rely on the cross-docking concept, according to which products delivered in specific transportation management units to the cross-docking terminal (CDT) undergo decomposition, sorting based on the end customer preferences, consolidation, and then transported to the final destinations. Scheduling of the inbound and outbound trucks for service at the CDT doors is considered as one of the convoluted decision problems faced by the CDT operators. This study proposes a new Adaptive Polyploid Memetic Algorithm (APMA) for the problem of scheduling CDT trucks that can assist with proper CDT operations planning. APMA directly relies on the polyploidy concept, where copies of the parent chromosomes (i.e., solutions) are stored before performing the crossover operations and producing the offspring chromosomes. The number of chromosome copies is controlled through the adaptive polyploid mechanism based on the objective function improvements achieved and computational time changes. Moreover, a number of problem-specific hybridization techniques are used within the algorithm to facilitate the search process. Computational experiments show that the application of adaptive polyploidy alone may not be sufficient for the considered decision problem. Hybridization techniques that directly consider problem-specific properties are required in order to improve solution quality at convergence. Furthermore, the APMA algorithm developed in this article substantially outperforms some of the well-known state of the art metaheuristics with regards to solution quality and returns truck schedules that have lower total truck service cost.

We study the dynamic programming approach to revenue management in the context of attended home delivery. We draw on results from dynamic programming theory for Markov decision problems to show that the underlying Bellman operator has a unique fixed point. We then provide a closed-form expression for the resulting fixed point and show that it admits a natural interpretation. Moreover, we also show that – under certain technical assumptions – the value function, which has a discrete domain and a continuous codomain, admits a continuous extension, which is a finite-valued, concave function of its state variables, at every time step. Furthermore, we derive results on the monotonicity of prices with respect to the number of orders placed in our setting. These results open the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate dynamic programming context. We illustrate our findings on a low-dimensional and an industry-sized numerical example using real-world data, for which we derive an approximately optimal pricing policy based on our theoretical results.

The open shop is a classical scheduling problem known since 1976, which can be described as follows. A number of jobs have to be processed by a given set of machines, each machine should perform an operation on every job, and the processing times of all the operations are given. One has to construct a schedule to perform all the operations to minimize finish time also known as the makespan. The open shop problem is known to be NP-hard for three and more machines, while is polynomially solvable in the case of two machines. We consider the routing open shop problem, being a generalization of both the open shop problem and the metric traveling salesman problem. In this setting, jobs are located at nodes of a transportation network and have to be processed by mobile machines, initially located at a predefined depot. Machines have to process all the jobs and return to the depot to minimize makespan. A feasible schedule is referred to as normal if its makespan coincides with the standard lower bound. We introduce the Irreducible Bin Packing decision problem, use it to describe new sufficient conditions of normality for the two machine problem, and discuss the possibility to extend these results on the problem with three and more machines. To that end, we present two new computer-aided optima localization results.

Multi-attribute decision making (MADM) refers to a decision problem of choosing the best alternative or carrying out the ranking of alternatives under multiple attributes, and it is a key component of modern decision sciences. Three-way decisions (3WD) can effectively address MADM problems by reducing decision risks compared with traditional two-way decisions (2WD), and a decision model based on probabilistic dominance relations is presented in this paper. Particularly, we put forward a kind of 3WD-based MADM (3WD-MADM) with probabilistic dominance relations, where the two state sets are developed by virtue of probabilistic dominance classes. Afterwards, the independent innovation ability of high-tech enterprises is evaluated by using the proposed new method. At last, the newly proposed 3WD-MADM model in this paper is verified from different perspectives by comparative and experimental analyses.

As a class of batch-mode reinforcement learning (RL) methods for Markov decision problems with large or continuous state spaces, approximate policy iteration (API) has received increasing attention in the past decades. One open problem in the design of API algorithms is how to construct the basis functions or features for value function approximation (VFA). In this paper, we propose a novel batch-mode RL approach with randomly projected features for VFA. The proposed approach can be viewed as an extension of extreme learning machines (ELMs) to RL problems so it can be called ELM-API. The ELMs have been popularly studied in supervised learning problems, but there is not much work on the extension of ELMs to learning control problems. The proposed approach has advantages over the previous API algorithms in that the features for VFA can be quickly generated without complex parameter selection and the performance will be adaptive to different sample sets in batch-mode RL. In particular, the ELM-API approach can realize fast and efficient feature reconstruction when training sample sets are relatively small. Comprehensive simulation studies on two benchmark learning control problems were carried out to test the performance of API algorithms with different feature construction methods. It is shown that the ELM-API algorithm can obtain comparable or better performance than the previous API approaches. To further show the effectiveness of ELM-API in real-world applications, the simulation results on a more challenging high-dimensional lane-changing decision problem in dynamic traffic environment are also reported, which show the capability of the ELM-API algorithm in learning satisfactory lane-changing policies with high data efficiency.

The alternative assessment and decision-making are often complicated and involve enormous decision makers (DMs), which leads to a large group decision making (LGDM) problem, and usually requires to reach consensus within a limited time. As a powerful technique in representing linguistic evaluations, the probabilistic linguistic term set is popular to express the opinions of DMs. Under this scenario, DMs who support the same linguistic term are naturally clustered into one subgroup, whereas the distance formulas are inappropriate because whether the DM supports a linguistic term is a dichotomous variable; therefore, Tanimoto coefficient is introduced to calculate the group consensus level. Additionally, an efficient consensus model is proposed to bridge the gap between the subgroup and group opinions. In particular, a weight adjustment function is proposed to process the minority opinions. A novel method including minor and major adjustment manner is proposed to manage the noncooperative behaviors. DMs are allowed to recluster into another subgroup for major adjustment manner; on the contrary, the adjustment direction and quantities are provided for minor adjustment manner. A case study of forest fire emergency decision-making is explored and a simulation is conducted to verify the proposed consensus model in the LGDM problem. The proposed consensus model is suitable for situations where the subgroup and group decision matrices are subject to preference selections and can be applied in other decision problems.

The paper aims to present an integrated approach to solve the decision-making problem under the probabilistic hesitant fuzzy information (PHFI) features, which is an extension of the hesitant fuzzy set. The considered PHFI not only allows multiple opinions, but also associates occurrence probability to each opinion, which increases the reliability of the information. Motivated by these features of PHFI, an approach is presented to solve the decision problem with partial known information about the attribute and expert weights. In addition, an algorithm for finding some missing values in the preference information is presented and stated their properties. Afterward, the Hamy mean operator has been used to aggregate the different collective information into a single one. Also, we presented a COPRAS method to the PHFI for ranking the given alternatives. The presented algorithm has been demonstrated through a case study of cloud vendor selection and its validity has been revealed by comparing the approach results with the several existing algorithm results.

The similarity measures have been extensively used as an efficient tool to analyze the degree of similarity between two sets of objects. The linguistic q-rung orthopair fuzzy set provides a flexible model to represent uncertain qualitative information more precisely. This paper defines some new generalized trigonometric similarity measures between two linguistic q-rung orthopair fuzzy sets. We use the linguistic scaling function to accommodate the different semantic levels of the linguistic terms during the similarity measuring process. Several basic and advanced mathematical properties are proved in detail. Next, we present a generalized hybrid trigonometric similarity measure between two linguistic q-rung orthopair fuzzy sets. The weighted version of the developed similarity measures is also defined and extends them to a continuous domain. It is worth mentioning that all the proposed similarity measures are reduced into the similarity measures between linguistic intuitionistic fuzzy sets and the linguistic Pythagorean fuzzy sets when we take $$q=1$$ and $$q=2$$ , respectively. A new decision-making method based on developed generalized hybrid trigonometric similarity measure is formulated to solve multiple attribute decision-making problems under the linguistic q-rung orthopair fuzzy environment. Finally, a numerical example is given to illustrate the flexibility and effectiveness of the developed method in solving real-world decision problems.

The paper aims to introduce the novel concept of q-connection number (q-CN) for interval-valued q-rung orthopair fuzzy set (IVq-ROFSs) and thus to develop a method for solving the multiple-attribute group decision making (MAGDM) problem. The IVq-ROFS is a tool to represent the uncertain information with an integer parameter $$q\ge 1$$ , while the connection number (CN) processes the uncertainties and certainties into a single system with three degrees, namely “identity”, “contrary” and “discrepancy”. Driven by these required properties, this paper introduces a q-CN for IVq-ROFSs to represent the information in a more concise way. To this end, we divide the paper into three aspects. First, we define q-CN and a scoring function to evaluate the numbers. Second, we give some new q-exponential operation laws (q-EOLs) and operators over q-CNs in which bases are real numbers and exponents are q-CNs. Moreover, we define an operator based on these laws and derive their properties. Third, a novel MAGDM method for solving decision problems with IVq-ROFS information is illustrated with several examples. The advantages and superiority analysis of the proposed framework are also given to assert the results.

This paper puts forward a new hybrid Grey Additive-Veto Model (GAVM) for selecting suppliers, which optimizes the choice by the decision-maker’s (DM) preference. This study uses a Multi-Criteria Decision Making (MCDM) approach. The model proposed incorporates the uncertainty of real-world decision problems, through the Grey Numbers. Given the DM’s compensatory rationality, the method reflects tradeoffs amongst different criteria. However, a compensatory model may not represent the DM faithfully and realistically. For this is proposed a performance veto condition. Additionally, the DM may consider that suppliers with a high uncertainty are not desirable or even that they are not acceptable. For this is also proposed width performance veto condition. Given practical implications, the need for an enriched analysis of the ranking is perceived because during the ranking process, there are some situations in which the DM is undecided (mistrust, hesitation) about the statement that a given supplier is better ranked than another supplier. This hesitation is mainly caused by uncertainty arising from the grey numbers, and from attitudes, functions and characteristics of vetoes that the DM has defined. As findings, this paper shows that GAVM is suited to dealing with multicriteria decisions with uncertain information, veto conditions and its potential applicability is illustrated by a numerical supplier selection example. In addition, the numerical example shows that the enriched analysis of the ranking proposed can be conducted to direct the DM’s efforts to further enriching the insights for more assertive and coherent decision-making.

Modern business judgment is mostly faced with complex, unclear nature, and not fully confirmed research objects and needs a lot of relevant data investigation, inherent contradiction retrieval, and the discovery and extraction of potential laws. Formulation of rules and evaluation of system uncertainty: Appropriate decisions can be made based on this. Rough set theory is a new mathematical tool to deal with uncertain knowledge. Therefore, the theory of rough set is helpful for decision-makers to solve the decision problems of complex systems. The simplification of knowledge of information systems and incomplete information systems and the theoretical and methodological study of rule acquisition are the central issues of rough set theory and applied research. A variety of simplified theories and methods have been proposed from a variety of viewpoints. However, there are still many theoretical problems that need to be investigated and solved in these aspects. In addition, the investment environment is a complex organic system that includes economic environment, social environment, resource environment, infrastructure, and other factors. There are a variety of data to measure these factors, which are mutually restrictive and interdependent. At present, domestic and foreign scholars have basically formed a series of assessment methods and models of investment environment assessment, but most of these assessment methods are affected by the differences in the degree of subjective factors of evaluators and the establishment of index weights in the assessment process. In most cases, more reliance is placed on subjective, artificial assignments and scoring loops. Therefore, it is an appropriate and reasonable method to evaluate the investment environment through data to evaluate all the factors affecting the investment environment and reach a comprehensive evaluation conclusion, which can effectively avoid human subjective factors to a certain extent.

Disaster response operations typically involve multiple decision-makers, and each decision-maker needs to make its decisions given only incomplete information on the current situation. To account for these characteristics – decision making by multiple decision-makers with partial observations to achieve a shared objective –, we formulate the decision problem as a decentralized-partially observable Markov decision process (dec-POMDP) model. To tackle a well-known difficulty of optimally solving a dec-POMDP model, multi-agent reinforcement learning (MARL) has been used as a solution technique. However, typical MARL algorithms are not always effective to solve dec-POMDP models. Motivated by evidence in single-agent RL cases, we propose a MARL algorithm augmented by pretraining. Specifically, we use behavioral cloning (BC) as a means to pretrain a neural network. We verify the effectiveness of the proposed method by solving a dec-POMDP model for a decentralized selective patient admission problem. Experimental results of three disaster scenarios show that the proposed method is a viable solution approach to solving dec-POMDP problems and that augmenting MARL with BC for its pretraining seems to offer advantages over plain MARL in terms of solution quality and computation time.

We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability. © 2021 IEEE, IEEE Transactions on Power Systems, 36 (3), ISSN:0885-8950, ISSN:1558-0679

In this paper, we propose decision analysis methods for determining the optimal number of agents of a service system where the system rates (arrival, service, and abandonment) are modeled as dependent random variables. In doing so, we take the Bayesian point of view of inference and obtain joint posterior distributions of the system rates. We solve the proposed stochastic staffing decision problem with augmented probability simulation based optimization methods. The novelty of our approach stems from the use of dependent system rates to determine optimal staffing in a constrained optimization setting for stochastic service systems. We demonstrate the implications of ignoring dependence and uncertainty in system rates on simulated data for general service systems, and illustrate the application of the proposed methodology on call center operations.

A two-dimensional automaton has a read-only input head that moves in four directions on a finite array of cells labeled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward. We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is NP -complete, and is in P for general-alphabet two-way nondeterministic two-dimensional automata. We also show that the language equivalence and inclusion problems for two-way deterministic two-dimensional automata are decidable, while the language universality, equivalence, and inclusion problems for two-way nondeterministic two-dimensional automata are undecidable. The deterministic case is the first known positive decidability result for a language equivalence problem on two-dimensional automata over a general alphabet. Finally, we discuss the notion of row and column projection languages. We show that the row projection language of a unary three-way nondeterministic two-dimensional automaton is always regular, and that there exists a unary three-way deterministic two-dimensional automaton with a nonregular column projection language. For two-way nondeterministic two-dimensional automata, on the other hand, both the row and column projection languages are always regular.

The model of coherent lower and upper conditional previsions, based on Hausdorff inner and outer measures, is proposed to represent the preference orderings and the equivalences, respectively assigned by the conscious and unconscious thought in human decision making under uncertainty. Complexity of partial information is represented by the Hausdorff dimension of the conditioning event. When the events, that describe the decision problem, are measurable is represented to the s-dimensional Hausdorff outer measure, where s is the Hausdorff dimension of the conditioning event, an optimal decision can be reached. The model is applied and discussed in Linda’s Problem and the conjunction fallacy is resolved.

In the study of two-sided matching decision problems, preference ordinal information is a key factor. However, in real life, it is often difficult to ascertain complete preference ordinal informati...

Linguistic information processing exists in multi-criteria decision making, and linguistic truth-valued lattice implication algebra (LTV-LIA) has definite advantages in handling comparable and incomparable linguistic values. To deal with the preference relations with linguistic evaluation information, we establish a novel approach for solving fuzzy multi-criteria decision problem under linguistic information based on LTV-LIA. In this paper, we propose linguistic lattice-valued preference relation (LLVPR). LLVPR positive and negative matrixes are introduced to evaluate the advantages and disadvantages of alternatives respectively. In order to get a reasonable result, we introduce a new algorithm to check and repair the consistency of a LLVPR. A linguistic lattice-valued 2-tuple representation model (LLV2-tuple) and some new aggregation operations are presented to get the comprehensive linguistic information without information loss. Considering different decision makers have different preferences, a multiple preferences implication operation of LLV2-tuple is introduced. Finally, we propose a novel linguistic analytic hierarchy process embedded in aggregation layer and implication layer, introducing algorithm and numerical examples. A comparative analysis is adopted to illustrate the rationality.

Recently, crowdsensing revolutionizes sensing paradigm in Internet of Things (IoTs). However, a practical incentive mechanism which works for time-varying scenario and fairly incentivizes users to participate in crowdsensing is less studied. In this paper, we propose an incentive mechanism for crowdsensing under continuous and time-varying scenario using three-stage Stackelberg game. In such a scenario, different requesters generate sensing tasks with payments to the platform at each time slot. The platform makes pricing decision to determine rewards for tasks without complete information, and then notifies task-price pairs to online users in Stage I. In Stage II, users select optimal tasks as their interests under certain constraints and report back to the platform. The platform fairly selects users as workers in order to ensure users’ long-term participation in Stage III. We use Lyapunov optimization to address online decision problems for the platform in Stage I and III where there are no prior knowledge and future information available. We propose an FPTAS for users to derive their interests of tasks based on their mobile devices’ computing capabilities in Stage II. Numerical results in simulations validate the significance and superiority of our proposed incentive mechanism.

In this paper, we introduce a method for resolving decision problems concerning multiple criteria in relation to a finite set of decision alternatives. This approach makes use of paraconsistent logic, Pavelka style fuzzy logic and many-valued similarity. To demonstrate the robustness of the method, two data sets, one on the performance of five mobile phone operators in Ghana and the other, a numerical example have been analysed and the rankings compared correspondingly with those of three existing dominant Multi-Attribute Decision Making (MADM) approaches, namely Elimination and Choice Translating Reality II (ELECTRE II); Preference Ranking Organisation MeTHod for Enrichment Evaluation (PROMETHEE I and II) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Apart from providing a ranking that is similar to these three famous outranking methods, the novel approach has the edge over them due to its ability to relatively handle large size decision problems - decision problems with numerous criteria and alternatives - without much difficulty.

Testing provides essential information for managing infectious disease outbreaks, such as the COVID‐19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease‐positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false‐negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data‐driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID‐19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID‐19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.

The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of probability measures with finite support. In this paper, we show that finding a barycenter of sparse support is hard, even in dimension 2 and for only 3 measures. We prove this claim by showing that a special case of an intimately related decision problem SCMP—does there exist a measure with a non-mass-splitting transport cost and support size below prescribed bounds? Is NP-hard for all rational data. Our proof is based on a reduction from planar 3-dimensional matching and follows a strategy laid out by Spieksma and Woeginger (Eur J Oper Res 91:611–618, 1996) for a reduction to planar, minimum circumference 3-dimensional matching. While we closely mirror the actual steps of their proof, the arguments themselves differ fundamentally due to the complex nature of the discrete barycenter problem. Containment of SCMP in NP will remain open. We prove that, for a given measure, sparsity and cost of an optimal transport to a set of measures can be verified in polynomial time in the size of a bit encoding of the measure. However, the encoding size of a barycenter may be exponential in the encoding size of the underlying measures.

In recent history, reinforcement learning (RL) proved its capability by solving complex decision problems by mastering several games. Increased computational power and the advances in approximation with neural networks (NN) paved the path to RL’s successful applications. Even though RL can tackle more complex problems nowadays, it still relies on computational power and runtime. Quantum computing promises to solve these issues by its capability to encode information and the potential quadratic speedup in runtime. We compare tabular Q-learning and Q-learning using either a quantum or a classical approximation architecture on the frozen lake problem. Furthermore, the three algorithms are analyzed in terms of iterations until convergence to the optimal behavior, memory usage, and runtime. Within the paper, NNs are utilized for approximation in the classical domain, while in the quantum domain variational quantum circuits, as a quantum hybrid approximation method, have been used. Our simulations show that a quantum approximator is beneficial in terms of memory usage and provides a better sample complexity than NNs; however, it still lacks the computational speed to be competitive.

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of an authentic COVID-19 laboratory. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

Integrating fog computing with vehicular networks led to the rapidly growing demands of vehicle applications regarding computation-intensive and low response time with meeting the request deadline. The limited resources of the fog node have made it unable to meet the demands of such applications. Offloading the requests to other Off-Load Destination (OLD) is a suitable solution for the fog node to deal with these demands. Nonetheless, this simultaneously faces two challenges. The first challenge is the offloading to a nearby fog node which stills not the fully efficient choice when this nearby fog node is busy. The second challenge is the selection decision of the optimal OLD where the fog node incurs additional burden through getting status information of all neighboring fog nodes, affecting the selection decision, which is why it may not fulfill the request deadline. To solve the first challenge, a new hybrid offloading architecture has been proposed, where the underutilized resources of Vehicular Fog Computing (VFC) are joined with the cloud to be an OLD, thus increase the processing chance of the offloaded requests. The second challenge has been solved by optimizing the selection decision of the fog node via taking the global network resources benefit of Software Defined Network (SDN) in the proposed offloading architecture to design an SDN-based offloading policy. The selection decision problem is formulated as a Binary-Linear Programming and solved by CPLEX software. The simulation results show that our proposed improves the performance of the fog node by providing less response time and significantly outperforming other offloading policies.

Yager has proposed the decision making under measure-based granular uncertainty, which can make decision with the aid of Choquet integral, measure and representative payoffs. The decision making under measure-based granular uncertainty is an effective tool to deal with uncertain issues. The intuitionistic fuzzy environment is the more real environment. Since the decision making under measure-based granular uncertainty is not based on intuitionistic fuzzy environment, it cannot effectively solve the decision issues in the intuitionistic fuzzy environment. Then, when the issues of decision making are under intuitionistic fuzzy environment, what is the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets is still an open issue. To deal with this kind of issues, this paper proposes the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can effectively solve the decision making issues in the intuitionistic fuzzy environment, in other words, it can extend the decision making under measure-based granular uncertainty to the intuitionistic fuzzy environment. Numerical examples are applied to verify the validity of the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The experimental results demonstrate that the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can represent the objects successfully and make decision effectively. In addition, a practical application of applied intelligence is used to compare the performance between the proposed model and the decision making under measure-based granular uncertainty. The experimental results show that the proposed model can solve some decision problems that the decision making under measure-based granular uncertainty cannot solve.

This paper first discusses the establishment of multi-attribute decision problem model and the determination of weights. Then this paper points out a situation that the method of updating weights using the fixed weight vector cannot effectively describe the weights’ variation when the state vector is continuously changing. To get rid of this problem, an iterative weight updating method is proposed. Finally, based on the existing optimistic coefficient method, the influence of high-order terms is discussed: updating weights with the fixed weight vector and updating weights with iteration. Experiments show that the higher-order terms in the state variable weight vector have a negative effect on the decision result.

We discuss the solution of complex multistage decision problems using methods that are based on the idea of policy iteration (PI), i.e., start from some base policy and generate an improved policy. Rollout is the simplest method of this type, where just one improved policy is generated. We can view PI as repeated application of rollout, where the rollout policy at each iteration serves as the base policy for the next iteration. In contrast with PI, rollout has a robustness property: it can be applied on-line and is suitable for on-line replanning. Moreover, rollout can use as base policy one of the policies produced by PI, thereby improving on that policy. This is the type of scheme underlying the prominently successful AlphaZero chess program. In this paper we focus on rollout and PI-like methods for problems where the control consists of multiple components each selected (conceptually) by a separate agent. This is the class of multiagent problems where the agents have a shared objective function, and a shared and perfect state information. Based on a problem reformulation that trades off control space complexity with state space complexity, we develop an approach, whereby at every stage, the agents sequentially (one-at-a-time) execute a local rollout algorithm that uses a base policy, together with some coordinating information from the other agents. The amount of total computation required at every stage grows linearly with the number of agents. By contrast, in the standard rollout algorithm, the amount of total computation grows exponentially with the number of agents. Despite the dramatic reduction in required computation, we show that our multiagent rollout algorithm has the fundamental cost improvement property of standard rollout: it guarantees an improved performance relative to the base policy. We also discuss autonomous multiagent rollout schemes that allow the agents to make decisions autonomously through the use of precomputed signaling information, which is sufficient to maintain the cost improvement property, without any on-line coordination of control selection between the agents. For discounted and other infinite horizon problems, we also consider exact and approximate PI algorithms involving a new type of one-agent-at-a-time policy improvement operation. For one of our PI algorithms, we prove convergence to an agent-by-agent optimal policy, thus establishing a connection with the theory of teams. For another PI algorithm, which is executed over a more complex state space, we prove convergence to an optimal policy. Approximate forms of these algorithms are also given, based on the use of policy and value neural networks. These PI algorithms, in both their exact and their approximate form are strictly off-line methods, but they can be used to provide a base policy for use in an on-line multiagent rollout scheme.

Product portfolio optimization is a typical multiobjective problem. The multichoice goal programming method becomes a popular means of resolving multiobjective decision problems. However, the classic multichoice goal programming method treats the product portfolio optimization in isolation and does not consider the mutual influence between portfolio products. Researchers should consider the interaction between products in portfolio optimization so that they can be adjusted to “real world” problems. The interaction between products can be explained by population dynamics. Logistic model is a classical method to analyze the population interaction. The equilibrium point of logistic model can show the ideal state of product population coordinated development. The combination of logistic and multichoice goal programming method is an effective approach to analyze the interaction of product portfolio. This paper therefore proposes a new alternative method to formulate the multiobjective problem and also uses an illustrative example to demonstrate the usefulness of the proposed method. The comparative analysis of model optimization results shows that logistic multichoice goal programming model can take into account resource constraints, product collaboration, and output maximization. Logistic multichoice goal programming model shows good performance in the aspects of operation complexity, operation time, sensitivity analysis, and collaborative entropy evaluation.

We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many agents, which are taken independently by solving convex optimization problems that depend on the price configuration and on realizations of future states of the economy. One traditional way of solving this problem is via a mixed complementarity formulation. However, this approach can become impractical when the numbers of agents and/or scenarios become large. This work concerns agent-wise and scenario-wise decomposition algorithms to solve the equilibrium problems in question, assuming that the solutions of the agents’ problems are unique, which is natural in many applications (when solutions are not unique, the approximating problems are still well-defined, but the convergence properties of the algorithm are not established). The algorithm is based on a previous work of the authors, where a suitable regularization of solution mappings of fully parameterized convex problems is developed. Here, we show one specific strategy to manage the regularization parameter, extend some theoretical results to the current setting, and prove that the smooth approximations of the market coordinator’s problem converge epigraphically to the original problem. Numerical experiments and some comparisons with the complementarity solver PATH are shown for the two-stage stochastic Walrasian equilibrium problem.

Multiple decision support methods have been developed to support multi-criteria problems, offering a structured approach. One such method is FITradeoff, which is based on tradeoff, and has a strong axiomatic structure. Implemented in a Decision Support System, FITradeoff offers an experience with low cognitive effort and time demanded by the decision maker. Despite its advantages, some issues remain unclear. In this study, we sought to perform an analysis about the cognitive aspects during the elicitation process using FITradeoff in which the subjects solved decision problems developed by themselves. Two neuroscience tools, Eye-Tracker and a 14-channel EEG were used for neurological and psychophysiological data collection. From the results obtained, analyzes and considerations were made about the elicitation process with FITradeoff and the impact of different types of criteria on the performance of the decision maker. With these findings, it is expected to create direction for improvements in the Decision Support System.

Warehouses are an inevitable component in any supply chain and a vividly investigated object of research. Much attention, however, is absorbed by warehousing systems dedicated to the special needs of online retailers in the business-to-consumer segment. Due to the ever increasing sales volumes of e-commerce this focus seems self-evident, but a much larger fraction of retail sales are still realized by traditional brick-and-mortar stores. The special needs of warehouses servicing these stores are focused in this paper. While e-commerce warehouses face low-volume-high-mix picking orders, because private households tend to order just a few pieces per order from a large assortment, distribution centers of retail chains rather have to process high-volume-low-mix orders. We elaborate the basic requirements within both business segments and identify suited warehousing systems for brick-and-mortar stores (e.g., fully-automated case picking). The setup of each identified warehousing system is described, elementary decision problems are discussed, and the existing literature is surveyed. Furthermore, we identify future research needs.

This paper develops a new cooperative dynamic time consistent model for studying regional air pollution management issues in a cooperative game framework for formulating pollution control policies and dynamically consistent compensation mechanisms. As air pollution is a transboundary issue, unilateral response on the part of one region is generally ineffective. Regional cooperation is essential to resolve serious environmental problems. In addition, the long-term environmental impacts are closely related to the building up existing air pollution stocks in Sulfur Dioxide (SO2), Nitrogen Dioxide (NO2), Respirable suspended particulates (RSP) and Ozone (O3). A cooperative dynamic game with different types of pollutants is developed. We characterize the non-cooperative outcomes, and examine the cooperative arrangements, group optimal actions, and individually rational imputations. In particular, an air pollution levy consisting of four components involving damage charges on emissions of sulfur dioxide, nitrogen dioxide, respirable suspended particulates and ozone depletion materials. Cooperative games offer the possibility of socially optimal and group efficient solutions to the lack of cooperation among different regions involving decision problems among strategic actors. This paper makes a valuable contribution to the literature as this is the first cooperative dynamic time consistent model for regional management of different types of air pollutants.

Hub covering location problem focuses on the construction of the hub network. The importance of this problem has been addressed in many fields including freight transportation and telecommunication network. As a long-term strategic decision problem, the construction of the hub network has large scale environmental influences especially the emissions of greenhouse gas. In the meanwhile, the precise information of the parameters cannot be obtained. Therefore, this work investigates the sustainable hub covering location problem with uncertain parameters. The purpose is to minimize the overall cost and impose restrictions on the total CO2 emissions, simultaneously. The travel times are depicted by uncertain variables to portray inherent indeterminacy within this problem. The incomplete network is adopted to decrease the total investment cost considerably. Accordingly, two uncertain programming models are constructed and transformed into their equivalent forms. A modified genetic algorithm is proposed to solve the proposed models. Several experiments are performed to interpret the efficiency of the proposed algorithm and the validity of the proposed models. The experimental results show that accounting for the emission restriction and the adoption of incomplete hub network will significantly affect the overall investment cost and the construction of the hub network.

AV subnetworks is a way to deal with automated traffic and its technological need that will likely increase during the AVs deployment period. This strategy carries many benefits, yet some inconveniences are worth to mention. One of them relies on the fact that the design of AV subnetworks is often in practice focused on mitigating congestion in the peak-hours. However, designing for the most congested hour can be quite delicate when such a strategy is fixed throughout the day. The remaining part of the day involves different mobility patterns and shifting trips patterns throughout the day, i.e., different Origin-Destination pairs. When such O-D pairs are inside these AV subnetworks, CV owners cannot drive, and therefore a new mode of transport is necessary. This paper focuses on the lower-level decision problem, i.e., the traffic distribution during the transition period while AVs are being deployed in urban areas and AV subnetworks are expanding. A nonlinear mathematical programming model is presented to perform the trip distribution, where walking appears as an alternative. The main objective of this paper is to study the impacts of AV subnetworks from a CV owners’ perspective. A novel formulation guarantees that CV trips starting inside AV subnetworks throughout the day aren’t ignored – this means an alternative mode of transport, in this case, walking. This paper evaluates throughout the day when such situations would likely occur in a case study of the city of Delft, in the Netherlands, in two scenarios with AV subnetworks. The experiments revealed that walking is somehow inevitable when AVs reach 75% of the vehicle fleet – increasing travel costs up to 26.0% and 43.8%.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. This paper provides a brief tour through the main fuzzy and linguistic decision-making trends, studies, methodologies and models developed in the last 50 years. Fuzzy and linguistic decision-making approaches allow to address complex real-world decision problems where humans exhibit vagueness, imprecision and/or use natural language to assess decision alternatives, criteria, etc. The aim of this paper is threefold. Firstly, the main fuzzy set theory and computing with words based representation paradigms of decision information, with their different levels of expressive richness and complexity, are reviewed. Secondly, three core decision-making frameworks are examined: (1) multi-criteria decision-making, (2) group consensus-driven decision-making, and (3) multi-person multi-criteria decision making. Thirdly, the paper discusses new complex decision making frameworks that have emerged in recent years, where decisions are guided by the “wisdom of the crowd”: their associated challenges are highlighted and considerations on much needed key guidelines for future research in the field are provided.

In robotic mobile fulfillment systems, human pickers don’t go to the inventory area to search for and pick the ordered items. Instead, robots carry shelves (called “pods”) containing ordered items from the inventory area to picking stations. At the picking stations, pickers put ordered items into totes; then these items are transported to the packing stations. This type of warehousing system relieves the human pickers and improves the picking process. In this paper, we concentrate on decisions about the assignment of pods to stations and orders to stations to fulfill picking for each incoming customer’s order. In previous research for an RMFS with multiple picking stations, these decisions are made sequentially with heuristics. Instead, we present a new MIP-model to integrate both decision problems. To improve the system performance even more, we extend our model by splitting orders. This means parts of an order are allowed to be picked at different stations. To the best of the authors’ knowledge, this is the first publication on split orders in an RMFS. And we prove the computational complexity of our models. We analyze different performance metrics, such as pile-on, pod-station visits, robot moving distance and throughput. We compare the results of our models in different instances with the sequential method in our open-source simulation framework RAWSim-O. The integration of the decisions brings better performances, and allowing split orders further improves the performances (for example: increasing throughput by 46%). In order to reduce the computational time for a real-world application, we have proposed a heuristic.