A CGS-MSM PGA Based on Multi-Agent and its Application in Solving 0-1 Knapsack Problem

This study presents a comprehensive analysis of recent studies that explore the application of genetic algorithms (GAs) for optimizing solutions to the 0/1 Knapsack Problem (KP). The 0/1 Knapsack Problem, a classic combinatorial optimization challenge, involves selecting a subset of items with given weights and values to maximize the total value without exceeding a specified weight limit. Genetic algorithms, inspired by the principles of natural selection and genetics, have emerged as a powerful heuristic for tackling this NP-hard problem. Our review synthesizes findings from contemporary research, highlighting the effectiveness of various GA approaches, including standard GAs, hybrid models, and enhanced techniques incorporating local search and other optimization strategies. We evaluate the performance metrics, computational efficiency, and solution quality achieved by these methods. Additionally, we discuss the strengths and limitations of GAs in addressing the 0/1 Knapsack Problem, providing insights into their practical applications and potential improvements. The paper concludes with recommendations for future research directions, aiming to advance the state-of-the-art in genetic algorithm-based optimization for the 0/1 Knapsack Problem.

This is a research project on using Genetic Algorithm to solve 0-1 Knapsack Problem. Knapsack problem is a combinational optimization problem. Given a set of items, each with a weight & value, it determine the number of each item to include in a collection so that the total weight is less than a given limit & the total value is as large as possible. The paper consists of three parts. In the first section we give brief description of Genetic Algorithms and some of its basic elements. Next, we describe the Knapsack Problem and Implementation of Knapsack problem using Genetic Algorithm. The main purpose of this paper is to implement Knapsack problem by an algorithm that is based on Genetic Algorithm. In this paper I have used Roulette-Wheel, Tournament Selection and Stochastic selection as a selection function and the succeeding populations are analyzed for the fitness value with hope to achieve the correct solution and expected results were observed.

The knapsack problem is problem that is still often found in everyday life, one of which is the problem of selecting goods to be transported into containers for delivery of goods. This knapsack problem can be solved by using various optimization algorithms, one of which is the genetic algorithm. This study aims to design a genetic algorithm model to solve the 2-dimensional knapsack problem. 2-dimensional knapsack problem is a knapsack problem that has 2 constraints and in this study, the constraints used were weight and volume.. The evaluation results of the genetic algorithm will be compared with dynamic programming. From the evaluation results that have been carried out, it can be concluded that genetic algorithms can produce near-optimal results with faster computational times than dynamic programming.

Adaptive parameter control in evolutionary computation is achieved by a method of computational resource allocation, both spatially and temporally. Spatially it is achieved for the parallel genetic algorithm by the partitioning of the search space into many subspaces. Search for solution is performed in each subspace by a genetic algorithm which domain of chromosomes is restricted inside that particular subspace. This spatial allocation of computational resource takes the advantage of exhaustive search which avoids duplicate effort, and combine it with the parallel nature of the search for solution in disjoint subspaces by genetic algorithm. In each subspace, temporal resource allocation is also made for different competing evolutionary algorithms, so that more CPU time is allocated to those algorithms which showed better performance in the past. This general idea is implemented in a new adaptive genetic algorithm using the formalism of mutation matrix, where the need for setting a survival probability is removed. The temporal resource allocation is introduced and implemented in a single computer using the quasi-parallel time sharing algorithm for the solution of the zero/one knapsack problem. The mutation matrix M(t) is constructed using the locus statistics and the fitness distribution in a population At with N rows and L columns, where N is the size of the population and L is the length of the encoded chromosomes. The mutation matrix is parameter free and adaptive as it is time dependent and captures the accumulated information in the past generation. Two competing strategies of evolution, mutation by row (chromosome), and mutation by column (locus) are used for the competition of CPU time. Time sharing experiment on these two strategies is performed on a single computer in solving the knapsack problem. Based on the investment frontier of time allocation, the optimal configuration in solving the knapsack problem is found.

This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.

How to allocate workflow resources with cost constraint to optimize workflow time performance was studied. The average throughput time of workflow instances is used to measure the workflow time performance. A method based on queuing theory was proposed to calculate the average throughput time of workflow instances. Since the problem can be come down to an unbounded knapsack problem (UKP), an improved GA (Genetic Algorithm) suitable to solve the UKP was proposed to solve the problem. Examples were given to illustrate the feasibility and validity of the method. The results show that the algorithm has good evolution performance and can achieve or approach the optimal solutions. And compared with other allocation methods, our method performs best.

A comparative study on the performance of dissortative mating and immigrants-based strategies for evolutionary dynamic optimization

There are a lot of typical statistical problems in discrete combination optimization, including integer linear programming, covering problem, knapsack problem, graph theory, network flow and dispatching. As for the NPC (Non-deterministic Polynomial complete) problems, many algorithms have been developed for the discrete optimization where the heuristic algorithm is one kind of the important and effective methods. In this paper, a new swarm intelligent algorithm is proposed, combined with BPSO (Binary Particle Swarm Optimization), GA (Genetic Algorithm) and maximum difference calculation, to solve the TSP and Knapsack two typical discrete combination optimal problems. The proposed algorithm can search the historical memory and differentiated search strategy is introduced to keep the diversity of the group so as to select the elite gene features as the candidates. Experiments are designed and performed to analyze the convergence of the algorithm and the solutions are obtained in high-dimensional searching space. As for the binary combination problem, results demonstrate that the developed algorithm has faster convergence speed and higher quality compared to the traditional swarm intelligent algorithms.

This paper investigates solving the imprecise weight coefficients knapsack problem by genetic algorithms. We investigate the possibility of using genetic algorithms solving the fuzzy knapsack problem without defining membership functions for each imprecise weight coefficient. The proposed approach simulates a fuzzy number by distributing it into some partition points. We use genetic algorithms to evolve the values in each partition point so that the final values represent the membership grade of a fuzzy number. The fuzzy concept of the genetic algorithms approach is different, but gives better results than the traditional fuzzy approach.

A lot of uncertainties and complexities exist in real life problem. Unfortunately, the world approaches such intricate realistic life problems using traditional methods which has failed to offer robust solutions. In recent times, researchers look beyond classical techniques. There is a model shift from the use of classical techniques to the use of standardized intelligent biological systems or evolutionary biology. Genetic Algorithm (GA) has been recognized as a prospective technique capable of handling uncertainties and providing optimized solutions in diverse area, especially in homes, offices, stores and industrial operations. This research is focused on the appraisal of GA and its application in real life problem. The scenario considered is the application of GA in 0-1 knapsack problem. From the solution of the GA model, it was observed that there is no combination that would give the exact weight or capacity the 35kg bag can carry but the possible range from the solution model is 34kg and 36kg. Since the weight of the bag is 35kg, the feasible or near optimal solution weight of items the bag can carry would be 34kg at benefit of 16. Additional load beyond 34kg could lead to warping of the bag.

In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.

Though Knapsack Problem appears to be simple, it is a NP-hard problem that is not solved in polynomial time as combinational optimization problems. To solve this problem, GA(Genetic Algorithms) was used in the past. However, there were difficulties in real experiments because the conventional method didn`t reflect the precise characteristics of DNA. In this paper we proposed ACO (Algorithm for Code Optimization) that applies DNA coding method to DNA computing to solve problems of Knapsack Problem. ACO was applied to (0,1) Knapsack Problem; as a result, it reduced experimental errors as compared with conventional methods, and found accurate solutions more rapidly.

This paper researches on the problem of searching for the reliable path for transportation networks. The reliable path finding problem is concerned with searching for the path with the maximum value of connectivity reliability. In view of the literature on travel time variations, the relationship between the mean travel time and its connectivity reliability is adopted in the proposed model. In order to simplify the difficulties of the solution, this paper takes the travel time and its connectivity reliability equal to a 0–1 knapsack problem, then defines a new conception of greedy transform which is given an efficient algorithm, after combining the new greedy transform method with Genetic Algorithm, obtains Hybrid Genetic Algorithm (HGA). This algorithm (HGA) can be considered as an efficient algorithm to solve the reliable path finding problem and some other knapsack problems. Numerical results are presented to demonstrate the applications of the proposed algorithm.

The shifting balance genetic algorithm (SBGA) is an extension of the genetic algorithm (GA) that was created to promote guided diversity to improve performance in highly multimodal environments. Based on a new behavioral model for the SBGA, various modifications are proposed: these include a mechanism for managing dynamic population sizes with population restarts, and communication among the colonies. The enhanced SBGA is compared against the original SBGA system and other multipopulational GA systems on a complex mathematical function (F8F2) and on the NP-complete 0/1 knapsack problem. In all cases, the enhanced SBGA outperformed all other systems, and on the 0/1 knapsack problem, it was the only one to find the global optimum.

Taming the 0/1 knapsack problem with monogamous pairs genetic algorithm