Explore the vast range of titles available.

For modeling decentralized decision-making problems with uncertain random parameters, an uncertain random multilevel programming is proposed. For some special case, an equivalent crisp mathematical programming to the established uncertain random programming is presented. A searching method by integrating uncertain random simulations, neural network, and genetic algorithm is produced to search the quasi-optimal solution under some decision-making criterion. Finally, the proposed uncertain random multilevel programming is applied to a production control problem.

In this paper, we consider an uncertain project scheduling problem, in which activity durations, with no historical data generally, are estimated by belief degrees and assumed to be uncertain variables. To achieve different management goals, we build three uncertain chance-constrained programming models for project scheduling problem, in which the chance constraint must reach a predetermined confidence level. Moreover, these models can all be transformed to their crisp forms, and an intelligent algorithm is designed to search the optimal schedule. Finally, a numerical example is presented to illustrate the usefulness of the proposed model.

Goal programming provides an efficient technique to deal with decision making problems with multiple conflicting objectives. This paper joins the streams of research on goal programming by providing a so-called uncertain random goal programming to model the multi-objective optimization problem involving uncertain random variables. Several equivalent deterministic forms are derived on the condition that the set of parameters consists of uncertain variables and random variables. Finally, an example is given to illustrate the application of the approach.

Uncertainty theory, founded in 2007, has become a branch of mathematics to model uncertainty rather than randomness. As an indispensable part of uncertainty theory, uncertain graph and uncertain network optimization has received the wide attention of many scholars. Naturally, a series of original research achievements have been obtained on uncertain graph and uncertain network optimization. This paper aims to present a state-of-the-art review on the recent advance in uncertain graph and uncertain network optimization. Furthermore, it hopes to predict the possible future research directions. Based on Web of Science database, this paper retrieves 144 related papers from 2011 to 2021 to analyze the features of published articles. More precisely, we analyze the annual number of publications, key topics and sub-fields, journals, and most-cited articles. In addition, the main results and models for uncertain graph and uncertain network optimization are summarized. Furthermore, the limitations of existing literature and the possible development trend are discussed.

In this research paper, using uncertainty theory we introduced and developed entropy-based uncertain four-dimensional transportation problem with fixed charges, discounted costs, and vehicle costs. In this transportation system, we considered a discount policy on the transportation cost which depends on the basis of the transported amount. Here, the discounted costs are in the form of all unit discounts (AlUD), incremental quantity discounts (InQD), and the combination of these two. The main objective is to minimize the total transportation cost via maximum entropy which ensures the number of items to be transported from some source to some destinations by some conveyances through some routes. For optimizing the proposed model, using uncertain programming techniques, we have developed two different models such as expected value programming model and expected constrained programming model. Then, Using minimizing distance method and linear weighted method we formulated and solved the equivalent deterministic transformation of these two constructed models. Finally, to show the application of the proposed models and methods we presented a numerical example with optimal results.

Enhanced index tracking (EIT) problem is concerned with selecting a tracking portfolio to beat the benchmark on return while having the minimum tracking error. This paper addresses the EIT problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. Under the framework of uncertainty theory, the paper proposes a new uncertain EIT model where the higher-order moment of the downside is used as the tracking error measure, as higher-order moment makes the model more widely applicable and the downside risk is in line with investors’ perception of risk. Besides, some realistic constraints are considered in the new uncertain EIT model. Then, the properties of the proposed model are discussed. To solve the model, we proposed, which is a nonlinear integer programming problem, a meta-heuristic algorithm presented. The efficiency of the algorithm and the applications of the proposed model are illustrated through numerical experiments.

In this paper, an uncertain Multi-objective Multi-item Solid Transportation Problem (MMSTP) based on uncertainty theory is presented. In the model, transportation costs, supplies, demands and conveyances parameters are taken to be uncertain parameters. There are restrictions on some items and conveyances of the model. Therefore, some particular items cannot be transported by some exceptional conveyances. Using the advantage of uncertainty theory, the MMSTP is first converted into an equivalent deterministic MMSTP. By applying convex combination method and minimizing distance function method, the deterministic MMSTP is reduced into single objective programming problems. Thus, both single objective programming problems are solved using Maple 18.02 optimization toolbox. Finally, a numerical example is given to illustrate the performance of the models.

This paper discusses the oil project optimal portfolio selection under uncertain environment where cash flows of the projects are mostly determined by experts’ estimations due to the lack of historical investment data. The oil project investment is usually distinguished by its high input, high risk and highly fluctuating ROI sensitive to the economic, political and technology uncertainties. Besides, in most of the cases, it is quite difficult to find reliable referential historical data for a specific project. All these peculiarities make actual oil project investment decision under high uncertainties. In this paper, we use normal uncertain variables to describe the cash flows and estimate the uncertainty distribution of the cash flows by experts’ experimental data. Then, under the constraint of controlling for bankruptcy, we give uncertain programming models to construct portfolios that maximize the expected returns and minimize the sine cross-entropy of the actual return from a prior return. Finally, we provide some numerical examples that fit different risk preference assumptions to further illustrate the feasibility and effectiveness of the models.

In this paper, we discuss the formulation of the oilfield development plan in case of significant nondeterminacy in oilfield development. And the plan needs to ensure production and achieve minimum cost and maximum new recoverable reserves. The uncertain factors in oilfield development are analyzed in this paper, and we consider the uncertain nature of the stimulation effect of measures and new recoverable reserves per well and quantify them. On this basis, an uncertain multi-objective optimal model of oilfield development planning is constructed. The model aims to minimize the expectation of development cost and maximize the expectation of new recoverable reserves, and optimizes the workload of each measure under the constraints including the oil production and the resources limitation. Based on uncertainty theory, the model is transformed into a deterministic model. And a nondominated sorting genetic algorithm with elite strategy is developed to solve the model and get the Pareto solution set. Then the multi-attribute decision-making is applied to select the multiple development plans, which provides the basis for the decision-making of the oilfield development plan. Finally, a numerical example is given to verify the effectiveness of the model and algorithm, and their practical application values under the background of oilfield development planning.

This paper addresses the multi-objective optimization of water–rail–road (WRR) intermodal transport system under uncertainty by explicitly capturing intermodal hub operation activities. Through the use of hub-and-spoke-type network, we formulate an uncertain multi-objective programming model for the WRR intermodal transportation network design problem, in which the cost, time and reliability objectives are simultaneously considered. Subsequently, we turn the original model into a deterministic equivalent multi-objective programming model under mild assumptions. Eventually, we utilize the ε -constraint method to reformulate the crisp multi-objective programming model to a modified mono objective one, which has proven to be NP-hard. Hence, we develop a memetic algorithm (MA) by combining a genetic algorithm and local intensification to solve the proposed problem. When designing the MA, we propose a combination encoding scheme to represent the location of intermodal hubs, the allocation of the demand nodes and the assignment of transportation modes. Moreover, we provide two local intensification operators to enhance exploitation ability. Finally, we implement a series of numerical experiments based on the Turkish network data set to verify the practicability of the proposed model and effectiveness of the solution approach developed in the paper.