Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Discrete binary cat swarm optimization algorithm

Abstract: In this paper, we present a new algorithm binary discrete optimization method based on cat swarm optimization (CSO). BCSO is a binary version of CSO generated by observing the behaviors of cats. As in CSO, BCSO consists of two modes of operation: tracing mode and seeking mode. The BCSO presented in this paper is implemented on a number of benchmark optimization problems and zero-one knapsack problem. The obtained results are compared with a number of different optimization problems including genetic algorithm and different versions of binary discrete particle swarm optimization. It is shown that the proposed method greatly improves the results obtained by other binary discrete optimization problems.

An Overview of Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems

Abstract: This paper reviews several peak-to-average power ratio (PAR) reduction techniques and the related optimization problems. Chipping-based PAR reduction techniques are related to convex optimization problems and the global optimum solutions are relatively easy to find. Probabilistic techniques result in discrete optimization. Although finding its global optima is difficult, moderate suboptimal solutions can be achieved with low computational cost. Coding is promising because of its inherit error-correcting property. However, its extremely low coding rate in cases of large number of subcarriers prevents its application. Many criteria involve in the selection of a PAR reduction technique, e.g., PAR reduction capacity, power increase, bit error rate increase, complexity, and throughput. A main consideration is that the cost of extra complexity for PAR reduction is lower than the cost of power inefficiency. Low complexity PAR reduction techniques may find application in mobile communications

On the Automatic Verification of Systems with Continuous Variables and Unbounded Discrete Data Structures

Abstract: We address the verification problem of invariance properties for hybrid systems. We consider as general models of hybrid systems finite automata, supplied with (unbounded) discrete data structures and continuous variables. We focus on the case of systems manipulating discrete counters and one pushdown stack, and on the other hand, constant slope continuous variables. The use of unbounded discrete data sturcture allows to consider systems with a powerful control, and to reason about important notions as the number of occurrences of events in some computation. The use of constant slope continuous variables allows to reason for instance about the time separating events and the durations of phases within some computation interval. We present decidability results for several subclasses of such models of hybrid systems; this provides automatic verification procedures for these systems.

Algorithm for the instantaneous frequency estimation using time-frequency distributions with adaptive window width

Abstract: A method for minimization of the mean square error (MSE) of the instantaneous frequency estimation using time-frequency distributions, in the case of a discrete optimization parameter, is presented. It does not require a knowledge of the estimation bias. The method is illustrated on adaptive window width determination in the Wigner distribution.

Minimizing Convergence Error in Multi-Agent Systems Via Leader Selection: A Supermodular Optimization Approach

Abstract: In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degree-based leader selection methods in a numerical study.