An Order Based Memetic Evolutionary Algorithm for Set Partitioning Problems

Travelling Salesman Problem with profits (TSPP) is a special case of the general Travelling Salesman Problem, all nodes must not be visited, but profit is collected from visited nodes. It is a well-known NP-hard combinatorial optimization problem in the literature. Because of the problem's complexity, exact methods cannot find the global optimum solution to this problem, so many heuristic and metaheuristic solution techniques are studied to find a feasible solution in a reasonable time. In this research, two different metaheuristic algorithms, Simulated Annealing with Many-moves and Variable Neighborhood Search, are proposed to solve the TSPP. Proposed algorithms are tested with three different problem instances and compared in terms of the efficiency of algorithms.

The traveling salesman problem (TSP) is an NP-hard problem being studied by many researchers. Metaheuristic algorithms generally depend on nature-inspired phenomena successfully applied to combinatorial optimization, such as routing, scheduling, assignment problems, engineering, optimization, genetics, robotics, nanotechnology, and various fields. In this paper, new versions of physarum-energy optimization algorithms (PEOs) which are population-based optimization algorithms were applied to the symmetric traveling salesman problems. PEOs use multiple solutions (population), multiple conductivities (dij) for the stochastic disturbance model and appropriate parameter strategies to update the solutions in each generation. To measure the effectiveness of the PEOs and the hybrids, the algorithms have been evaluated on several benchmark problems compared to the recent metaheuristics. The computational results show that the PEOs and their hybrids (k-NN, 2-opt, 3-opt, k-opt) can find high-quality results compared to the original physarum-energy optimization algorithm (PEO), ant colony optimization (ACO), black hole algorithm (BH), tabu search (TS), and other hybrid algorithms such as whale optimization algorithm + 4-opt heuristic (WOA + 4-opt), camel algorithm + 4-opt heuristic (CA + 4-opt), genetic algorithm + 2-opt heuristic (GA + 2-opt), and the k-NN, 2-opt, 3-opt, k-opt algorithms. Moreover, the population-based PEOs and their derived forms solve the optimization problem quite competitively in CPU time compared to other test algorithms.

The loss minimization problem is one of the most important problems to save the operational cost in distribution systems. Therefore, more efficient approaches are required to handle such a combinatorial problem. This paper presents an efficient meta-heuristic method for reconfiguration of distribution systems. A Tabu Search (TS) algorithm is used to reconfigure distribution systems so that active power losses are globally minimized with turning on / off sectionalizing switches. TS algorithm is introduced with some modifications such as using a tabu list with variable size according to the system size; this should lead to robust algorithm, and prevent cycling. Also, a random multiplicative move is used in the search process to diversify the search toward unexplored regions. A new method to check the radial topology of the system is presented. The proposed method is applied to 32-node and 69-node distribution systems. The obtained results using the proposed TS approach are compared with results obtained using Simulated Annealing (SA) approach and Parallel Tabu Search (PTS) approach in the previous work to examine the performance.

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard combinatorial optimization problems, widely studied due to its numerous industrial applications in logistics, supply chain management, and resource planning. Over the years, various metaheuristic algorithms have been developed to provide near-optimal solutions within a reasonable computational time. While traditional methods such as Genetic Algorithms (GA) and Simulated Annealing (SA) have been applied widely to the TSP, recent developments in metaheuristics have introduced new methods that can ensure improved performance. In this study, we compare three new metaheuristics: Arctic Puffin Optimization (APO), Human Evolutionary Optimization (HEO), and Ship Rescue Optimization (SRO). These methods, inspired by puffin's behavior, human evolutions, and naval rescue, respectively, have demonstrated high optimization capability in various areas. However, these have not been extensively tried on solving the TSP yet. This research seeks to establish the performance of these algorithms by comparing their convergence rate, solution quality, and computational efficiency with well-established metaheuristics. The results of the experiment expose the strengths and weaknesses of such innovative approaches, showing their potential as competitive alternatives to solve complex combinatorial optimization problems

The shortest route finding problem is a significant topic in graph theory and combinatorial optimization, with wide applications in logistics, transportation, and scheduling. This research aims to improve the quality of the solution and time efficiency in solving the Traveling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algorithm using the application of the Tabu Search algorithm. The CIH algorithm constructs an initial solution by inserting points based on minimum weight. At the same time, the Tabu Search algorithm is applied to enhance the solution by avoiding local optima using a tabu list mechanism. The research data, consisting of the distances between parking retribution collection points by the Malang City Transportation Agency in Sukun Sub-district, were obtained from Google Maps. The algorithm performance evaluation is done by comparing the total mileage before and after optimization, and statistically analyzed using the Wilcoxon signed-rank test because the data does not follow a normal distribution. The results showed that optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted in routes with shorter travel distances than using the CIH algorithm alone. This finding proves that optimizing the CIH algorithm with Tabu Search increases the effectiveness of finding the shortest route.The shortest route finding problem is a significant topic in graph theory and combinato-rial optimization, with wide applications in logistics, transportation, and scheduling. Thisresearch aims to improve the quality of the solution and time efficiency in solving the Trav-eling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algo-rithm using the application of the Tabu Search algorithm. The CIH algorithm constructs aninitial solution by inserting points based on minimum weight. At the same time, the TabuSearch algorithm is applied to enhance the solution by avoiding local optima using a tabulist mechanism. The research data, consisting of the distances between parking retributioncollection points by the Malang City Transportation Agency in Sukun Sub-district, were ob-tained from Google Maps. The algorithm performance evaluation is done by comparing thetotal mileage before and after optimization, and statistically analyzed using the Wilcoxonsigned-rank test because the data does not follow a normal distribution. The results showedthat optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted inroutes with shorter travel distances than using the CIH algorithm alone. This finding provesthat optimizing the CIH algorithm with Tabu Search increases the effectiveness of findingthe shortest route.

2차원 저장소 적재는 NP-hard 문제로서 그 문제의 정확한 해를 구하는 것이 어려운 것으로 알려져 있으며, 이의 더 좋은 해를 얻기 위해 유전자(genetic) 알고리즘, 시뮬레이티드 어닐링(simulated annealing), 타부서치(tabu search)등과 같은 근사적 접근법이 제안되어 왔다. 하지만 분지한계(branch-and-bound)나 타부서치 기법들을 이용한 기존의 대표적인 근사 알고리즘들은 휴리스틱 알고리즘의 해에 기반을 둠으로 효율성이 낮고 반복수행에 의한 계산시간이 길다. 따라서 본 논문에서는 이러한 근사 알고리즘의 복잡성을 간소화하고, 알고리즘의 효율성을 높이기 위해 적재가능성을 판단하는 적합성 함수(fitness function)를 정의하고 이를 이용하여 어떤 특정 개체의 적재영역을 판단하는데 영향을 주는 적재영역의 수를 계산한다. 또한, 이들을 이용한 새로운 휴리스틱 알고리즘을 제안하였다. 끝으로 기존의 휴리스틱 또는 메타휴리스틱 기법과의 비교실험을 통해 기존의 휴리스틱 알고리즘인 FFF와 FBS에 비해 97%의 결과가 같거나 우수하였으며, 타부서치 알고리즘에 비해 86%의 결과가 같거나 우수한 것으로 나타났다. The two-dimensional bin packing problem(2D-BPP) has been known to be NP-hard, and it is difficult to solve the problem exactly. Many approximation methods, such as genetic algorithm, simulated annealing and tabu search etc, have been also proposed to gain better solutions. However, the existing approximation algorithms, such as branch-and-bound and tabu search, have shown the low efficiency and the long execution time due to a large of iterations. To solve these problems, we first define the fitness function to simplify and increase the utility of algorithm. The function decides whether an item is packed into a given area, and as an important information for a packing strategy, the number of subarea that can accommodate a given item is obtained from the variant of the fitness function. Then we present a heuristic algorithm BF for 2D bin packing, constructed by the fitness function and subarea. Finally, the effectiveness of the proposed algorithm will be expressed by the comparison experiments with the heuristic and the metaheuristic of the literatures. As comparing with existing heuristic algorithms and metaheuristic algorithms, it has been found that the packing rate of algorithm BP is the same as 97% as existing heuristic algorithms, FFF and FBS, or better than them. Also, it has been shown the same as 86% as tabu search algorithm or better.

<p><strong>Context and relevance.</strong>The traveling salesman problem (TSP) is one of the key NP-hard combinatorial optimization problems with wide applications in logistics, transportation planning, and other fields. Exact methods for solving TSP become inefficient as the problem dimension increases, making the use of metaheuristic methods such as simulated annealing (SA), ant colony optimization (ACO), and particle swarm optimization (PSO) relevant. <strong>Objective. </strong>To conduct a comparative analysis of the effectiveness of SA, ACO and PSO for solving the traveling salesman problem with 100 points, to evaluate their convergence and to identify the optimal parameters. <strong>Hypothesis. </strong>The ant algorithm, due to the pheromone trail mechanism, will provide higher accuracy of solutions compared to SA and PSO, but will require more computational resources. <strong>Methods and materials. </strong>The study conducted computational experiments with varying parameters of each algorithm. For SA, the initial temperature and cooling coefficient were analyzed, for ACO, the influence of pheromones and distances, for PSO, the cognitive and social coefficients. <strong>Results. </strong>ACO showed the best results, finding a route with a length of 9.23, demonstrating high efficiency for medium-sized problems. PSO took an intermediate position with a route length of 32.64, making it suitable for moderately complex problems. SA was the least effective, with a route length of 45.2, which limits its use for complex routing networks. <strong>Conclusions. </strong>The ant algorithm demonstrated the greatest efficiency due to the balance between exploring the solution space and exploiting the found routes, which is especially important for maritime Arctic logistics, where sustainable route optimization is required under high uncertainty. PSO showed good convergence, but it is inferior to ACO in terms of accuracy. SA, despite its simplicity, is less effective for high-dimensional problems. The obtained results are of particular practical value for route optimization in the Arctic region, where traditional methods often prove to be ineffective.</p>

When the project is scheduled with a given set of resources, it is difficult to find the optimal solution. Resourceconstrained scheduling problems (RCPSP) are generally NP-hard. In this paper, a high level heuristic procedure “Tabu Search Algorithm (TSA)” is proposed to provide good solutions to resource-constrained, deterministic activity duration project scheduling problems. We present the application results of the computational tabu search and OPL-CPLEX algorithm and compare them with that of earlier applicable researches along with a discussion about further research. Our computational results are presented, which establish the superiority of tabu search over the existing heuristic algorithms. Two different solution strategies are also discussed, namely tabu search and OPLCPLEX exact algorithm approach which can be used with the proposed model. Due to the execution time, we have shown that OPL-CPLEX's algorithm is a valid method with medium scale RCPSPs. For the considered deterministic problems, a good agreement has been obtained between theoretical and experimental results.

In view of Traveling Salesman Problem (TSP) is a NP hard problem, Lion Swarm Optimization (LSO) Algorithm is a new swarm intelligence optimization algorithm. Therefore, in this paper, it uses improved hybrid LSO algorithm to solve TSP. Because the basic LSO algorithm is mainly used to solve the continuous problem, and the TSP is a discrete combinatorial optimization problem, this paper improves the LSO algorithm, introduces the greedy strategy, and combines with the Population Competitive Search (PCS) algorithm in the later stage of the search. As a result, the convergence speed is accelerated and the search efficiency is improved. The classic TSP example is tested, and the simulation results show that the algorithm proposed in this paper has strong stability and is an effective method for solving TSP.

Nowadays, the development of systems based on Networks-on-Chip (NoCs) brings big challenges to the designers due to problems of scalability, such as efficient Mapping and Placement, which are NP-hard problems. Several solutions have been proposed to solve this type of problem that is a variation of Quadratic Assignment Problems (QAP), being Tabu Search (TS) algorithms the ones showing most promising results. In NoC-based dynamically reconfigurable systems (NoC-DRSs), both mapping and placement problems present several layers of complexity due the reconfigurable scenarios. A previous work has adopted TS algorithm variations, but the best solution is not achieved with the wished high frequency. This paper introduces the original Forced Inversion (FI) Heuristic over Tabu Search algorithms for 2D-Mesh FPGA NoC-DRSs, in order to avoid local minima. Results with a series of benchmarks are presented and the performances of different approaches are quantitatively and qualitatively compared.

: Over the last 10 to 20 years, heuristic search in the Operations Research and Artificial Intelligence communities has focused on developing high level general purpose algorithms, such as Tabu Search and Genetic Algorithms. However, understanding of when and why these algorithms perform well still lags. Our project extended the theory of certain combinatorial optimization problems to develop analytical characterizations of portions of search spaces and as the basis for creating new algorithms for two well known problems. We focused attention on two specific subclasses of NP-Hard problems: elementary landscapes, which include Traveling Salesman Problem (TSP) and embedded landscapes, which include Maximum Satisfiability (MAXSAT). Our analysis supports calculating exactly the statistical moments of the distributions of values in regions of MAXSAT search spaces and explains why true plateaus are rare. Our new algorithm for TSP is competitive with the state of the art, while being much simpler and easier to understand.

Tabu search with simulated annealing for solving a location–protection–disruption in hub network

Travelling Salesman Problem (TSP) is a NP-Hard combinatorial optimization problem and many real life problems are constrained replica of it which possesses exponential time complexity and requires heavy combination capability. In this work a new nature inspired meta-heuristics called Egyptian Vulture Optimization Algorithm (EVOA) is being introduced and presented for the first time and illustrated with examples how it can be utilized for the constrained graph based problems and is utilized to solve the various dimensional datasets of the traditional travelling salesman problem. There are not many discrete optimization bio-inspired algorithms available in the literature and in that respect it is a novel one which can readily utilized for the graph based and assignment based problems. This EVOA is inspired by the natural and skilled phenomenal habits, unique perceptions and intelligence of the Egyptian Vulture bird for carry out the livelihood and acquisition of food which is inevitable for any kind of organisms. The Egyptian Vulture bird is one of the few birds who are known for showing dexterous capability when it comes to its confrontation with tough challenges and usage of tools with combinations of force and weakness finding ability. The results show that the Egyptian Vulture Optimization meta-heuristics has potential for deriving solutions for the TSP combinatorial problem and it is found that the quality and perfection of the solutions for the datasets depend mainly on the number of dimensions when considerable for the same number of iterations.Keywordsegyptian vulture optimization algorithmdiscrete domain problemscombinatorial optimizationgraph based constrained problemsnature inspired heuristicstravelling salesman problem

Job shop scheduling problem (JSP) is an attractive field for researchers and production managers since it is a famous problem in many industries and a complex problem for researchers. Due to NP-hardness property of this problem, many meta-heuristics are developed to solve it. Solution representation (solution seed) is an important element for any meta-heuristic algorithm. Therefore, many researchers try to present different encodings to solve this problem. Fattahi et al., and Gen & Cheng suggested two solutions for this problem that both have advantages and weaknesses in searching solution space to reach an acceptable solution. In the current paper, a cyclic algorithm based on tabu search algorithm was proposed to improve the exploration and exploitation powers of these encodings. Also, several problems of different sizes are solved by it and the obtained results were compared. Results showed the applicability and effectiveness of the proposed solution representation in comparison with the existing ones