Study on multi-objective nonlinear programming problem with rough parameters

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

Necessary optimality condition for the minimal time crisis relaxing transverse condition via regularization

We derive necessary optimality conditions for the time of crisis problem under a more general hypothesis than the usual one encountered in the hybrid setting, which requires that any optimal solution should cross the boundary of the constraint set transversely. Doing so, we apply the Pontryagin Maximum Principle to a sequence of regular optimal control problems whose integral cost approximates the time of crisis. Optimality conditions are derived by passing to the limit in the Hamiltonian system (without the use of the hybrid maximum principle). This convergence result essentially relies on the boundedness of the sequence of adjoint vectors in L∞. Our main contribution is to relate this property to the boundedness in L1 of a suitable sequence which allows to avoid the use of the transverse hypothesis on optimal paths. An example with non-transverse trajectories for which necessary conditions are derived highlights the use of this new condition.

Visual Market equilibrium model for power seller multi-microgrid based on a graphic game

Microgrids (MGs) have characteristics of flexibility and intelligence. These grids provide potential for integrating renewable energy sources. Hybrid Microgrids make possible to manage complementary between sources and storage schemes, enabling exploration of stronger commercial impact of these energy producing stations. This paper proposes a new market model of equilibrium operation for MGs in local energy markets. MGs remotely located in the grid are virtually associated to compete with other MGs better located. The model meets the interests of the MGs by remuneration of the delivered power and the other stakeholders via loss reduction. A deterministic method based on reduction of the constraint set size and application of Karush-Kuhn-Tucker (KKT) conditions process visually the Nash equilibrium (NE) and the Pareto efficiency (PE). The non-cooperative static game has the ability to encourage the participation of small agents in the grid.

Compatibility of state constraints and dynamics for multiagent control systems

This study concerns the problem of compatibility of state constraints with a multiagent control system. Such a system deals with a number of agents so large that only a statistical description is available. For this reason, the state variable is described by a probability measure on $${\mathbb {R}}^d$$ R d representing the density of the agents and evolving according to the so-called continuity equation which is an equation stated in the Wasserstein space of probability measures. The aim of the paper is to provide a necessary and sufficient condition for a given constraint (a closed subset of the Wasserstein space) to be compatible with the controlled continuity equation. This new condition is characterized in a viscosity sense as follows: the distance function to the constraint set is a viscosity supersolution of a suitable Hamilton–Jacobi–Bellman equation stated on the Wasserstein space. As a byproduct and key ingredient of our approach, we obtain a new comparison theorem for evolutionary Hamilton–Jacobi equations in the Wasserstein space.

Syntax Prosody in Optimality Theory (SPOT) app tutorial

SPOT (Syntax Prosody in Optimality Theory app; http://spot.sites.ucsc.edu) automates candidate generation and evaluation for work on the syntax-prosody interface. SPOT is intended to facilitate the creation and comparison of multiple versions of an analysis, in service of refining constraint definitions and theory development. The codebase is available at https://github.com/syntax-prosody-ot. This paper briefly explains the motivation for the SPOT app, then walks through the process of creating an analysis in SPOT. We show how to create input syntactic trees, either manually or automatically; how to select a constraint set; and how to generate tableaux with candidates, constraints, and violation counts. Finally, we show how to use the output of SPOT to calculate rankings and typologies using an OT application.

Jupiter's envelope is not homogeneous

<p>The amount and distribution of heavy elements in Jupiter’s interior is crucial to understand how the planet was formed and evolved. The results provided by the Juno mission in the last years have fundamentally changed our view of the interior of Jupiter. The remarkably accurate gravity data, including odd gravity harmonics, have allowed us to put constrains on the zonal flows, the extent of differential rotation and lead us to find that Jupiter has most likely a dilute core. In this study we do interior structure calculations using a Bayesian statistical approach and fitting all observational constrains, to show that a non-homogenous envelope is also a constraint set up by the Juno measurements, which is helping us to get closer to unveiling Jupiter’s deep secrets. </p>

On the asymptotic behavior of the Douglas–Rachford and proximal-point algorithms for convex optimization

Banjac et al. (J Optim Theory Appl 183(2):490–519, 2019) recently showed that the Douglas–Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive iterates generated by the algorithm converges to certificates of primal and dual strong infeasibility. Their result was shown in a finite-dimensional Euclidean setting and for a particular structure of the constraint set. In this paper, we extend the result to real Hilbert spaces and a general nonempty closed convex set. Moreover, we show that the proximal-point algorithm applied to the set of optimality conditions of the problem generates similar infeasibility certificates.

Comparisons of VRP Optimization Algorithmic Methods for the Optimal Routing of Multiple Delivery Vehicles with Time Constraint

Transportation costs account for a large portion of business expense in any logistics firm; thus, achieving proper solutions that manage those transportation activities well and reduce such expense should be the number one priority for the business. Essentially, such logistics management involves the routing plans for company vehicles that perform delivery/pick up and also the number of vehicles utilized. This study investigated and compared the optimization performances of routing algorithms using simulated geographic data based in Chiang Rai, Thailand, emulating the post office operation which had 1 post office, 4 delivery vehicles and 2 delivery zones (2 vehicles per zone): 65 customer locations for zone A and 74 for zone B. The major objective of this particular routing problem, called Vehicle Routing Problem (VRP), was that the total delivery distance of those 4 delivery vehicles combined should be minimized; moreover, those vehicles mush finish their delivery operation within a time constraint, set at 2 hours. The optimization algorithms, employed for the routing procedures, were Large Neighborhood Search (LNS), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Ant Colony Optimization (ACO), combined into 3 hybrid algorithms (LNS|PSO, LNS|DE and LNS|ACO). Those hybrid algorithms including pure ones (DE, PSO and ACO) were compared for their optimization performances; and the results showed that LNS|ACO hybrid algorithm was superior than the other two hybrid ones and also far better than pure DE, PSO and ACO algorithms at various parameter variants. Additionally, most algorithms (hybrid and pure ones) finished the delivery routing within the time constraint of 2 hours except only for the pure algorithms at minimum parameter variant.

An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment

This paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of α-cut, the F-MOMCF problem is transformed into the α-MOMCF problem. The α-MOMCF problem can be solved using an interactive approach combined with the weighting Tchebycheff problem. The advantages of this method are that it elicits information from the decision maker (DM) to modify the given constraint set, it gives the optimum penalty, and the effort required for obtaining the solution is reduced. The stability set of the first kind related to the α-best compromise solution is determined. A numerical example is given for illustration and to check the validity of the approach.

Water strider females use individual experience to adjust jumping behaviour to their weight within physical constraints of water surface tension

Different species of water striders match leg speeds to their body sizes to maximize their jump take off velocity without breaking the water surface, which might have aided evolution of leg structures optimized for exploitation of the water surface tension. It is not understood how water striders achieve this match. Can individuals modify their leg movements based on their body mass and locomotor experience? Here we tested if water striders, Gerris latiabdominis, adjust jumping behaviour based on their personal experience and how an experimentally added body weight affects this process. Females, but not males, modified their jumping behaviour in weight-dependent manner, but only when they experienced frequent jumping. They did so within the environmental constraint set by the physics of water surface tension. Females’ ability to adjust jumping may represent their adaptation to frequent increases or decreases of the weight that they support as mating bouts, during which males ride on top of females, start or end, respectively. This suggests that natural selection for optimized biomechanics combined with sexual selection for mating adaptations shapes this ability to optimally exploit water surface tension, which might have aided adaptive radiation of Gerromorpha into a diversity of semiaquatic niches.