This paper studies the category theoretic aspects of ε-approach nearness spaces and ε-approach merotopic spaces, respectively, ε ∈ (0,∞], which are useful in measuring the degree of nearness (resemblance) of objects. Such structures measure the almost nearness of two collections of subsets of a nonempty set. The categories εANear and εAMer are shown to be full supercategories of various well-kn...

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monoto...

Continuing the work of Hiriart-Urruty and Phelps, we discuss (in both locally convex spaces and Banach spaces) the formulas for the conjugates and subdifferentials of the precomposition of a convex function by a continuous linear mapping and the marginal function of a convex function by a continuous linear mapping. We exhibit a certain (incomplete) duality between the operations of precompositi...

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, MAXIMUM ACYCLIC SUBGRAPH and MAXIMUM BETWEENNESS, we prove NP-hard approximation factors of 14 15 + ε and 1 2 + ε . When it is hard to approximate an OCSP by a constant better than taking a uniformly-at-random ordering, then the OCSP is said to be approximation r...

A highly competitive micro evolutionary algorithm to solve unconstrained optimization problems called μJADE (micro adaptive differential evolution), is adapted to deal with constrained search spaces. Two constraint-handling techniques (the feasibility rules and the ε-constrained method) are tested in μJADE and their performance is analyzed. The most competitive version is then compared against ...

The oil and gas networks are overlapped because of the inclusion associated in crude oil. This necessitates integration planning supply chain together. In recent years, hydrocarbon market has experienced high fluctuation demands prices which leads to considerable economic disruptions. Therefore, chain, considering uncertainty is a significant area research. this regard, study develops multi-obj...

Consider the problem of deciding whether a graph is 3-colorable. This problem is NP-complete. The optimization version of this problem is, given a 3-colorable graph G, color it using as few colors as possible. In the regime of polynomial time approximation algorithms, this problem has been studied extensively [Wig82, Blu94, KMS98, ACC06, Chl07]. The current best known approximation factor is ac...