Polynomial algorithms for some scheduling problems with one nonrenewable resource

This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability of a resource is depleted and replenished at the occurrence times of a set of events. The decision problem of ERCPSP consists of determining whether an instance has a feasible schedule or not. When there is only one nonrenewable resource, this problem is equivalent to find a feasible schedule that minimizes the number of resource units initially required. It generalizes the maximum cumulative cost problem and the two-machine maximum completion time flow-shop problem. In this paper, we consider this problem with some specific precedence constraints: parallel chains, series-parallel and interval order precedence constraints. For the first two cases, polynomial algorithms based on a linear decomposition of chains are proposed. For the third case, a polynomial algorithm is introduced to solve it. The priority between events is defined using the properties of interval orders.

Robust optimization of EMU brake module based on interval analysis

PurposeThis study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.Design/methodology/approachA robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.FindingsCompared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.Originality/valueThis study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

An Interval Optimization-Based Approach for Electric–Heat–Gas Coupled Energy System Planning Considering the Correlation between Uncertainties

In this paper, a novel methodological framework for energy hub (EH) planning, considering the correlation between renewable energy source (RES) and demand response (DR) uncertainties, is proposed. Unlike other existing works, our study explicitly considers the potential correlation between the uncertainty of integrated energy system operations (i.e., wind speed, light intensity, and demand response). Firstly, an EH single-objective interval optimization model is established, which aims at minimizing investment and operation costs. The model fully considers the correlation between various uncertain parameters. Secondly, the correlation between uncertainties is dealt with by the interval models of multidimensional parallelism and affine coordinate transformation, which are transformed into a deterministic optimization problem by the interval order relationship and probability algorithm, and then solved by a genetic algorithm. Finally, an experimental case is analyzed, and the results show that the research method in this paper has good engineering practicability. At the same time, different correlations among uncertainties have different influences on integrated energy system planning. Correlation and influence are positively correlated.

A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.

Erratum to " Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

This note corrects an error in our paper RAIRO-Operations Research /doi.org/10.1051/ro/2020066 as we should drop the expression ”with at least one strict inequality” in the definition of interval order in Section 2. Instead of proposing this short amendment, the authors of RAIRO-Operations Research doi.org/10.1051/ro/2020107 gave a proposition that requires an additional condition on the constraint functions. However, we claim that all the results of our paper are correct once the modification above is done.

Algebraic Structure of Step Traces and Interval Traces

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

Legislators’ roll-call voting behavior increasingly corresponds to intervals in the political spectrum

Scaling techniques such as the well known NOMINATE position political actors in a low dimensional space to represent the similarity or dissimilarity of their political orientation based on roll-call voting patterns. Starting from the same kind of data we propose an alternative, discrete, representation that replaces positions (points and distances) with niches (boxes and overlap). In the one-dimensional case, this corresponds to replacing the left-to-right ordering of points on the real line with an interval order. As it turns out, this seemingly simplistic one-dimensional model is sufficient to represent the similarity of roll-call votes by U.S. senators in recent years. In a historic context, however, low dimensionality represents the exception which stands in contrast to what is suggested by scaling techniques.

Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders

We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order is nested.

Algebraic Structure of Step Traces and Interval Traces

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

Firing patterns of gonadotropin-releasing hormone neurons are sculpted by their biologic state

Gonadotropin-releasing hormone (GnRH) neurons form the final pathway for the central neuronal control of fertility. GnRH is released in pulses that vary in frequency in females, helping drive hormonal changes of the reproductive cycle. In the common fertility disorder polycystic ovary syndrome (PCOS), persistent high-frequency hormone release is associated with disrupted cycles. We investigated long- and short-term action potential patterns of GnRH neurons in brain slices before and after puberty in female control and prenatally androgenized (PNA) mice, which mimic aspects of PCOS. A Monte Carlo (MC) approach was used to randomize action potential interval order. Dataset distributions were analysed to assess (i) if organization persists in GnRH neuron activity in vitro , and (ii) to determine if any organization changes with development and/or PNA treatment. GnRH neurons in adult control, but not PNA, mice produce long-term patterns different from MC distributions. Short-term patterns differ from MC distributions before puberty but become absorbed into the distributions with maturation, and the distributions narrow. These maturational changes are blunted by PNA treatment. Firing patterns of GnRH neurons in brain slices thus maintain organization dictated at least in part by the biologic status of the source and are disrupted in models of disease.