The ordinary genetic algorithm may be thought of as conducting a single market in which solutions compete for success, as measured by the fitness funtion. We introduce a two-market genetic algorithm, consisting of two phases, each of which is an ordinary single-market genetic algorithm. The twomarket genetic algorithm has a natural interpretation as a method of solving constrained optimization problems. Phase 1 is optimality improvement; it works on the problem without regard to constraints. Phase 2 is feasibility improvement; it works on the existing population of solutions and drives it towards feasibility. We tested this concept on 14 standard knapsack test problems for genetic algorithms, with excellent results. The paper concludes with discussions of why the twomarket genetic algorithm is successful and of how this work can be extended.

Abstract- Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use penalty functions. In this paper, we present these penalty-based methods and discuss their strengths and weaknesses.

Abstract. In a two-market genetic algorithm applied to a constrained optimization problem, two ‘markets ’ are maintained. One market establishes fitness in terms of the objective function only; the other market measures fitness in terms of the problem constraints only. Previous work on knapsack problems has shown promise for the two-market approach. In this paper we: (1) extend the investigation of two-market GAs to nonlinear optimization, (2) introduce a new, two-population variant on the two-market idea, and (3) report on experiments with the two-population, two-market GA that help explain how and why it works. 1

A two-population Genetic Algorithm for constrained optimization is exercised and analyzed. One population consists of feasible candidate solutions evolving toward optimality. Their infeasible but promising offspring are transferred to a second, infeasible population. Four striking

We explore data-driven methods for gaining insight into the dynamics of a two population genetic algorithm (GA), which has been effective for constrained optimization problems. We track and compare one population of feasible solutions and another population of infeasible solutions. Feasible solutions are selected and bred to improve their objective function values. Infeasible solutions are selected and bred to reduce their constraint violations. Interbreeding between populations is completely indirect, that is, only through their offspring that happen to migrate to the other population. We introduce an empirical measure of distances between individuals and population centroids to monitor the progress of evolution. We find that the centroids of the two populations approach each other and stabilize. This is a valuable characterization of convergence. We find the infeasible population influences, and sometimes dominates the genetic material of the optimum solution. Since the infeasible population is not evaluated by the objective function, it is free to explore boundary regions, where the optimum may be found. This is a blackbox algorithm. Roughly speaking, the No Free Lunch theorems for optimization show that all blackbox algorithms (such as Genetic Algorithms) have the same average performance over the set of all problems. As such, our algorithm would, on average, be no better than random search or any other blackbox search method. However, we provide two general theorems that give conditions that render null the No Free Lunch results. The approach taken here thereby escapes the No Free Lunch implications.

Abstract. Many challenges remain in the development of tactical planning systems that will enable automated, cooperative replanning of routes and mission assignments for multiple unmanned ground vehicles (UGVs) under changing environmental and tactical conditions. We have developed such a planning system that uses an evolutionary algorithm to assign waypoints and mission goals to multiple UGVs so that they jointly achieve a set of mission goals. Our evolutionary system applies domain-specific genetic operators, termed tactical advocates because they capture specific tactical behaviors, to make targeted improvements to plans. The plans are evaluated using a set of tactical critics that together comprise a multiobjective fitness function. Each critic evaluates a plan against criteria such as avoiding an enemy or meeting mission goals. Experimental results show that this approach produces highquality plans with the potential for real-time dynamic replanning. 1

In this paper we demonstrate the applicability of evolutionary algorithms (EAs) to the optimization of circuit designs. We examine the design of a full-adder cell, and show the capability of design of experiments (DOE) methods to improve the parameter-settings of EAs.

Abstract: This paper presents a meta-heuristic optimization algorithm, Tabu Search (TS), and describes how it can be used to solve a wide variety of chemical engineering problems. Modifications to the original algorithm and constraint handling techniques are described and integrated to extend its applicability. All components of TS are described in detail. Initial values for each key parameter of TS are provided. In addition, guidelines for adjusting these parameters are provided to relieve a significant amount of time-consuming trial-and-error experiments that are typically required with stochastic optimization. Several small NLP and MINLP test cases and three small- to middle- scale chemical process synthesis problems demonstrate the feasibility and effectiveness of the techniques with recommended parameters. 1.

Abstract. We investigate the performance of the recently proposed Unified Particle Swarm Optimization method on constrained engineering optimization problems. For this purpose, a penalty function approach is employed and the algorithm is modified to preserve feasibility of the encountered solutions. The algorithm is illustrated on four well–known engineering problems with promising results. Comparisons with the standard local and global variant of Particle Swarm Optimization are reported and discussed. 1

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