Algorithms inspired from natural phenomena are seem to be efficient to solve various optimization problems.This paper investigates a new technique inspiring from the animal group living behavior to solve traveling salesman problem (TSP), the most popular combinatorial optimization problem.The proposed producer-scrounger method (PSM) models roles and interactions of three types of animal group members: producer, scrounger and dispersed.PSM considers a producer having the best tour, few dispersed members having worse tours and scroungers.In each iteration, the producer scans for better tour, scroungers explore new tours while moving toward producer's tour; and dispersed members randomly checks new tours.For producer's scanning, PSM randomly selects a city from the producer's tour and rearranges its connection with several near cities for better tours.Swap operator and swap sequence based operation is employed in PSM to update a scrounger towards the producer.The proposed PSM has been tested on a large number of benchmark TSPs and outcomes compared to genetic algorithm and ant colony optimization.Experimental results revealed that proposed PSM is a good technique to solve TSP providing the best tours in most of the TSPs.

Analytic Hierarchy Process (AHP) has been widely used in varieties of decision making processes among several alternatives, where data on pair-wise comparisons are aggregated and the degree of importance of each alternative is quantified. The process of assigning importance or priorities against the alternatives has inherent limitations, which lead to higher possibility of inconsistency. This paper focuses on two basic limitations of the AHP, first one is its inconsistency generated from huge comparisons in judgment matrix and the second one is the use of ‘ranking weightages’ given by AHP. To eliminate these limitations, this research paper recommends to calculate relative importance among alternatives from the ratings assigned from “Likert scale” to form a “suggestion matrix” with zero percent CR before judgment matrix which gives privilege to decision makers to change relative importance within the range of CR. This process intensifies the effectiveness of AHP by reducing time consumption through optimizing inconsistency.

The goal of Traveling Salesman Problem (TSP) is to find the shortest circular tour visiting every city exactly once. TSP has many real world applications and a number of methods have been investigated to solve TSP. Recently, nature inspired algorithms are also attracted to solve it. Here we studied Group Search Optimizer(GSO), the recently proposed nature inspired algorithm, to solve TSP. GSO is a population based optimization technique on the metaphor of producer-scrounger based social behavior of animals where producer searches for finding foods and scrounger searches for joining opportunities. GSO has found as an efficient method for solving function optimization problems for which it modeled. In this study we employ the concept of Swap Operator (SO) and Swap Sequence (SS) to modify GSO for TSP. The modified GSO (mGSO) was tested on a number of benchmark TSPs and results compared with some existing approaches. mGSO has shown best results (best tour cost) for some problems and competitive performance in other cases.

Based on capture-mark-recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L greater than or equal to 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.