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Register a new userA weighted-sum method for solving the bi-objective traveling thief problem
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Added by
Jonatas Chagas
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal solution for the other components. This can be a challenge for single-objective formulations, where the respective influence that each component has on the overall solution quality can vary from instance to instance. In this paper, we study a bi-objective formulation of the traveling thief problem, which has as components the traveling salesperson problem and the knapsack problem. We present a weighted-sum method that makes use of randomiz
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The subset sum problem is a typical NP-complete problem that is hard to solve efficiently in time due to the intrinsic superpolynomial-scaling property. Increasing the problem size results in a vast amount of time consuming in conventionally available computers. Photons possess the unique features of extremely high propagation speed, weak interaction with environment and low detectable energy level, therefore can be a promising candidate to meet the challenge by constructing an a photonic computer computer. However, most of optical computing schemes, like Fourier transformation, require very high operation precision and are hard to scale up. Here, we present a chip built-in photonic computer to efficiently solve the subset sum problem. We successfully map the problem into a waveguide network in three dimensions by using femtosecond laser direct writing technique. We show that the photons are able to sufficiently dissipate into the networks and search all the possible paths for solutions in parallel. In the case of successive primes the proposed approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize a complicated computational function that is intractable with conventional computers, and suggest the subset sum problem as a good benchmarking platform for the race between photonic and conventional computers on the way towards photonic supremacy.
The main feature of large-scale multi-objective optimization problems (LSMOP) is to optimize multiple conflicting objectives while considering thousands of decision variables at the same time. An efficient LSMOP algorithm should have the ability to escape the local optimal solution from the huge search space and find the global optimal. Most of the current researches focus on how to deal with decision variables. However, due to the large number of decision variables, it is easy to lead to high computational cost. Maintaining the diversity of the population is one of the effective ways to improve search efficiency. In this paper, we propose a probabilistic prediction model based on trend prediction model and generating-filtering strategy, called LT-PPM, to tackle the LSMOP. The proposed method enhances the diversity of the population through importance sampling. At the same time, due to the adoption of an individual-based evolution mechanism, the computational cost of the proposed method is independent of the number of decision variables, thus avoiding the problem of exponential growth of the search space. We compared the proposed algorithm with several state-of-the-art algorithms for different benchmark functions. The experimental results and complexity analysis have demonstrated that the proposed algorithm has significant improvement in terms of its performance and computational efficiency in large-scale multi-objective optimization.
The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained Pareto optimal set (POS) to train prediction models via machine learning approaches. In this paper, we train an Incremental Support Vector Machine (ISVM) classifier with the past POS, and then the solutions of the DMOP we want to solve at the next moment are filtered through the trained ISVM classifier. A high-quality initial population will be generated by the ISVM classifier, and a variety of different types of population-based dynamic multi-objective optimization algorithms can benefit from the population. To verify this idea, we incorporate the proposed approach into three evolutionary algorithms, the multi-objective particle swarm optimization(MOPSO), Nondominated Sorting Genetic Algorithm II (NSGA-II), and the Regularity Model-based multi-objective estimation of distribution algorithm(RE-MEDA). We employ experiments to test these algorithms, and experimental results show the effectiveness.
The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem (KP). Increasingly algorithms have been proposed for solving this novel problem that combines two interdependent sub-problems. In this paper, TTP is investigated theoretically and empirically. An algorithm based on the score value calculated by our proposed formulation in picking items and sorting items in the reverse order in the light of the scoring value is proposed to solve the problem. Different approaches for solving the TTP are compared and analyzed; the experimental investigations suggest that our proposed approach is very efficient in meeting or beating current state-of-the-art heuristic solutions on a comprehensive set of benchmark TTP instances.
The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. cite{CGR}, replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.
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