We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

Voltage stability has become an important issue in planning and operation of many power systems. Contingencies such as unexpected line outages in a stressed system may often result in voltage instability, which may lead to voltage collapse. This paper presents evolutionary algorithm techniques like Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA II) approach for solv...

This chapter presents the application of a comprehensive statistical analysis for both algorithmic performance comparison and optimal parameter estimation on a multi-objective digital signal processing problem. The problem of designing optimum digital finite impulse response (FIR) filters with the simultaneous approximation of the filter magnitude and phase is posed as a multiobjective optimiza...

In this paper we propose two novel approaches for solving constrained multi-objective optimization problems using steady state GAs. These methods are intended for solving real-world application problems that have many constraints and very small feasible regions. One method called Objective Exchange Genetic Algorithm for Design Optimization (OEGADO) runs several GAs concurrently with each GA opt...

Multi-objective optimization (MO) is a highly demanding research topic because many realworld optimization problems consist of contradictory criteria or objectives. Considering these competing objectives concurrently, a multi-objective optimization problem (MOP) can be formulated as finding the best possible solutions that satisfy these objectives under different tradeoff situations. A family o...

Abstract The flexible job-shop scheduling problem (FJSP) is a critical model in manufacturing systems that assigns operations from different jobs to various machines. However, optimizing multiple targets during the production process always necessary. While non-dominated sorting genetic algorithm (NSGA-II) an effective method solve multi-objective FJSP, it can have main drawbacks of converging ...

Many real world problems require careful balancing of fiscal, technical, and social objectives. Informed negotiation and balancing of objectives can be greatly aided through the use of evolutionary multiobjective optimization (EMO) algorithms, which can evolve entire tradeoff (or Pareto) surfaces within a single run. The primary difficulty in using these methods lies in the large number of para...

Planning and scheduling are as decision making processes which they have important roles in production systems and industries. According that, job shop scheduling is one of NPhard problems to solve multi-objective decision making approaches. So, the problem is known as uncertain with many variables in optimal solution view. Finding optimal solutions are essential task in scheduling of jobs betw...

In this paper we propose a novel approach for solving constrained multi-objective optimization problems using a steady state GA and reduced models. Our method called Objective Exchange Genetic Algorithm for Design optimization (OEGADO) is intended for solving real-world application problems that have many constraints and very small feasible regions. OEGADO runs several GAs concurrently with eac...