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As an intelligent search optimization technique, genetic algorithm (GA) is an important approach for non-deterministic polynomial (NP-hard) and complex nature optimization problems. GA has some internal weakness such as premature convergence and low computation efficiency, etc. Improving the performance of GA is a vital topic for complex nature optimization problems. The selection operator is a crucial strategy in GA, because it has a vital role in exploring the new areas of the search space and converges the algorithm, as well. The fitness proportional selection scheme has essence exploitation and the linear rank selection is influenced by exploration. In this article, we proposed a new selection scheme which is the optimal combination of exploration and exploitation. This eliminates the fitness scaling issue and adjusts the selection pressure throughout the selection phase. The $$\chi ^2$$ goodness-of-fit test is used to measure the average accuracy, i.e., mean difference between the actual and expected number of offspring. A comparison of the performance of the proposed scheme along with some conventional selection procedures was made using TSPLIB instances. The application of this new operator gives much more effective results regarding the average and standard deviation values. In addition, a two-tailed t test is established and its values showed the significantly improved performance by the proposed scheme. Thus, the new operator is suitable and comparable to established selection for the problems related to traveling salesman problem using GA.

In this study, we developed a model which elaborates relationship among efficiency of an estimator and survey cost. This model is based on a multiobjective optimization programming structure. Survey cost and efficiency of related estimator(s) lie in different directions, i.e., if one increases, the other decreases. The model presented in this study computes cost for a desired level of efficiency on various characteristics (goals). The calibrated model minimizes the cost for the compromise optimal sample selection from different strata when characteristic j is subject to achieve at least 1−αj level of efficiency of its estimator. In the first step, the proposed model minimizes the variance for a fixed cost, and it then finds the rise in cost for an αj percent rise in efficiency of any characteristic j. The resultant model is a multiobjective compromise allocation goal programming model.

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon.

We consider the problem of multivariate multi-objective allocation where no or limited information is available within the stratum variance. Results show that a game theoretic approach (based on weighted goal programming) can be applied to sample size allocation problems. We use simulation technique to determine payoff matrix and to solve a minimax game.