Reducing the size of a logic circuit through lattice identities is an important and well-studied discrete optimization problem. In this paper, we consider a related problem of integrating several circuits into a single hypercircuit using the recently-developed concept of lattice hyperterms. We give a combinatorial algorithm for integrating k-out-of-n symmetrical diagrams which play important ro...

We consider a problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, which generate the appropriate annihilating acoustic signal (antisound). A general solution for the control sources has been obtained previously in both continuous ...

This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably mor...

this paper investigates a discrete-time impatient customer queue with bernoulli-schedule vacation interruption. the  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. we obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. cost an...

After deriving the particle swarm equations from basic physics, this paper shows by contradiction that NFL Theorem 1, and consequently Theorems 2 and 3, are irrelevant to continuous optimization. As the discrete nature of matter at its most fundamental level is generally irrelevant from the broader classical perspective, so to is the discrete nature of an optimization problem at its most fundam...

In this study, we set the average taxi time of flight as the objective of the gate and runway assignment problem. We present a gate and runway combinatorial optimization model with several restrictions such as restrictions of gate and runway time, type of aircraft and service. We design a Discrete Particle Swarm Optimization (DPSO) algorithm to solve this problem. Inspired by the genetic algori...

Learning short binary codes is challenged by the inherent discrete nature of the problem. The graph cuts algorithm is a well-studied discrete label assignment solution in computer vision, but has not yet been applied to solve the binary coding problems. This is partially because it was unclear how to use it to learn the encoding (hashing) functions for out-of-sample generalization. In this pape...

From the review, it is studied that the min cut k – partitioning problem is a fundamental partitioning problem and is NP hard also. Most of the existing partitioning algorithms are heuristic in nature and they try to find a reasonably good solution. These algorithms falls in move – based category in which solution is generated iteratively from an initial solution applying move to the recent sol...

Abstract. This paper discusses the symbol of the Hessian of a shape optimization problem in a viscid, incompressible flow. The symbol of the Hessian for the Stokes shape optimization problem is analytically approximated by tracking a Fourier mode through the operators involved. We propose a discrete method for finding the symbol and confirm the correctness by comparison with the analytical data...

Analytic and discrete optimization approaches for routing an aircraft in hostile air spaces have been developed. Using these approaches, an aircraft’s optimal risk path (where the risk is being detected by enemy radars) with constraints on aircraft speed, altitude and turn capability, mission range, mission time, fuel, etc. is computed. In the discrete optimization approach, we use different me...