A temporal constraint language Γ is a set of relations with first-order definitions in (Q;<). Let CSP(Γ) denote the set of constraint satisfaction problem instances with relations from Γ. CSP(Γ) admits robust approximation if, for any ε ≥ 0, given a (1 − ε)-satisfiable instance of CSP(Γ), we can compute an assignment that satisfies at least a (1−f(ε))-fraction of constraints in polynomial time....

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the -constraint method, the Benson method, the hybrid method and the elastic -constrai...

We present a novel constraint-partitioning approach for solving continuous nonlinear optimization based on augmented Lagrange method. In contrast to previous work, our approach is based on a new constraint partitioning theory and can handle global constraints. We employ a hyper-graph partitioning method to recognize the problem structure. We prove global convergence under assumptions that are m...

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dua...

The risks associated with wind power forecast (WF) deviations are of paramount importance to many system participants (PSPs). However, traditional sampling approaches computationally prohibitive model these deviations. Additionally, setting a risk level for satisfying different PSPs receives little attention. This paper constructs risk-adjustable stochastic day-ahead scheduling (RSDS) balance t...

An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least (1 − g(ε))-fraction of the constraints given a (1 − ε)-satisfiable instance, where g(ε) → 0 as ε → 0. Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction problem admits an efficient robust algorithm. This pa...

The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the ε constrained differential evolution εDE, which is the combination of the ε constrained...

In cities where the urban rail transit (URT) systems do not provide 24-h services, passengers may be able to reach their destinations if last train services have closed by time they arrive at transfer stations. This paper aims seek a well-coordinated timetable that can transport as many possible (referred reachable passengers) and also those who cannot unreachable stations close destinations. A...

The thermo-hydraulic behavior of the air flow over a two dimensional ribbed channel wasnumerically investigated in various rib-width ratio configurations (B/H=0.5-1.75) atdifferent Reynolds numbers, ranging from 6000 to 18000. The capability of differentturbulence models, including standard k-ε, RNG k-ε, standard k-ω, and SST k-ω, inpredicting the heat transfer rate was compared with the experi...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...