VLSs: A Local Search Algorithm for Distributed Constraint Optimization Problems

Local search algorithms are widely applied in solving large-scale distributed constraint optimization problem (DCOP). Distributed stochastic algorithm (DSA) is a typical local search algorithm to solve DCOP. However, DSA has some drawbacks including easily falling into local optima and the unfairness of assignment choice. This paper presents a novel local search algorithm named VLSs to solve the issues. In VLSs, sampling according to the probability corresponding to assignment is introduced to enable each agent to choose other promising values. Besides, each agent alternately performs a greedy choice among multiple parallel solutions to reduce the chance of falling into local optima and a variance adjustment mechanism to guide the search into a relatively good initial solution in a periodic manner. We give the proof of variance adjustment mechanism rationality and theoretical explanation of impact of greed among multiple parallel solutions. The experimental results show the superiority of VLSs over state-of-the-art DCOP algorithms.

Heuristics for Finding Sparse Solutions of Linear Inequalities

In this paper, we consider the problem of finding a sparse solution, with a minimal number of nonzero components, for a set of linear inequalities. This optimization problem is combinatorial and arises in various fields such as machine learning and compressed sensing. We present three new heuristics for the problem. The first two are greedy algorithms minimizing the sum of infeasibilities in the primal and dual spaces with different selection rules. The third heuristic is a combination of the greedy heuristic in the dual space and a local search algorithm. In numerical experiments, our proposed heuristics are compared with the weighted-[Formula: see text] algorithm and DCA programming with three different non-convex approximations of the zero norm. The computational results demonstrate the efficiency of our methods.

Optimal Path Planning using Informed Probabilistic Road Map Algorithm

This study aims to propose a new path planning algorithm that can guarantee the optimal path solution. The method used is to hybridize the Probabilistic Road Map (PRM) algorithm with the Information Search Algorithm. This hybridization algorithm is called the Informed-PRM algorithm. There are two informed search methods used. The first method is the informed sampling through an ellipsoid subset whose eccentricity is dependent on the length of the shortest current solution that is successfully planned in that iteration. The second method is to use a local search algorithm. The basic PRM algorithm will be run in the first iteration. Since the second iteration, the generation of sample points in the PRM algorithm will be carried out based on information. The informed sampling method will be used to generate 50% of the sampling points. Meanwhile, the remaining number of sample points will be generated using a local search algorithm. Using several benchmark cases, we compared the performance of the Informed-PRM algorithm with the Rapidly Exploring Random Tree* (RRT*) and informed RRT* algorithm. The test results show that the Informed-PRM algorithm successfully constructs the nearly optimal path for all given cases. In producing the path, the time and path cost of the Informed-PRM algorithm is better than the RRT* and Informed RRT* algorithm. The Friedman test was then performed to check for the significant difference in performance between Informed-PRM with RRT* and Informed RRT*. Thus, the Informed-PRM algorithm can be implemented in various systems that require an optimal path planning algorithm, such as in the case of medical robotic surgery or autonomous vehicle systems.

A Local Search Algorithm for Train Unit Shunting with Service Scheduling

In this paper we consider the train unit shunting problem extended with service task scheduling. This problem originates from Dutch Railways, which is the main railway operator in the Netherlands. Its urgency stems from the upcoming expansion of the rolling stock fleet needed to handle the ever-increasing number of passengers. The problem consists of matching train units arriving on a shunting yard to departing trains, scheduling service tasks such as cleaning and maintenance on the available resources, and parking the trains on the available tracks such that the shunting yard can operate conflict-free. These different aspects lead to a computationally extremely difficult problem, which combines several well-known NP-hard problems. In this paper, we present the first solution method covering all aspects of the shunting and scheduling problem. We describe a partial order schedule representation that captures the full problem, and we present a local search algorithm that utilizes the partial ordering. The proposed solution method is compared with an existing mixed integer linear program in a computational study on realistic instances provided by Dutch Railways. We show that our local search algorithm is the first method to solve real-world problem instances of the complete shunting and scheduling problem. It even outperforms current algorithms when the train unit shunting problem is considered in isolation, that is, without service tasks. Although our method was developed for the case of the Dutch Railways, it is applicable to any shunting yard or service location, irrespective of its layout, that uses self-propelling train units and that does not have to handle passing trains.

A Restart Local Search for Solving Diversified Top-k Weight Clique Search Problem

Diversified top-k weight clique (DTKWC) search problem is an important generalization of the diversified top-k clique (DTKC) search problem with practical applications. The diversified top-k weight clique search problem aims to search k maximal cliques that can cover the maximum weight in a vertex weighted graph. In this work, we propose a novel local search algorithm called TOPKWCLQ for the DTKWC search problem which mainly includes two strategies. First, a restart strategy is adopted, which repeated the construction and updating processes of the maximal weight clique set. Second, a scoring heuristic is designed by giving different priorities for maximal weight cliques in candidate set. Meanwhile, a constraint model of the DTKWC search problem is constructed such that the research concerns can be evaluated. Experimental results show that the proposed algorithm TOPKWCLQ outperforms than the comparison algorithm on large-scale real-world graphs.

Optimization of local search algorithm parameters for generating nonlinear substitutions

Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography algorithms. They complicate symmetric transformations and introduce nonlinearity into the input-output relationship, which ensures the stability of the algorithms against some cryptanalysis methods. Generation of S-boxes can be done in different ways. However, heuristic techniques are the most promising ones. On the one hand, the generated S-boxes are in the form of random substitutions, which complicates algebraic cryptanalysis. On the other hand, heuristic search allows one to achieve high rates of nonlinearity and δ-uniformity, which complicates linear and differential cryptanalysis. This article studies the simplest local search algorithm for generating S-boxes. To assess the efficiency of the algorithm, the concept of a track of a cost function is introduced in the article. Numerous experiments are carried out, in particular, the influence of the number of internal and external loops of local search on the complexity of generating the target S-box is investigated. The optimal (from the point of view of minimum time consumption) parameters of the local search algorithm for generating S-blocks with a target nonlinearity of 104 and the number of parallel computing threads 30 are substantiated. It is shown that with the selected (optimal) parameters it is possible to reliably form S-blocks with a nonlinearity of 104.

Multi-objective Aggregate Production Planning for Multiple Products: A Local Search-Based Genetic Algorithm Optimization Approach

The diversity of products and fierce competition make the stability and production cost of manufacturing industry more important. So, the purpose of this paper is to deal with the multi-product aggregate production planning (APP) problem considering stability in the workforce and total production costs, and propose an efficient algorithm. Taking into account the relationship of raw materials, inventory cost and product demand, a multi-objective programming model for multi-product APP problem is established to minimize total production costs and instability in the work force. To improve the efficiency of the algorithm, the feasible region of the planned production and the number of workers in each period are determined and a local search algorithm is used to improve the search ability. Based on the analysis of the feasible range, a genetic algorithm is designed to solve the model combined with the local search algorithm. For analyzing the effect of this algorithm, the information entropy strategy, NSGA-II strategy and multi-population strategy are compared and analyzed with examples, and the simulation results show that the model is feasible, and the NSGA-II algorithm based on the local search has a better performance in the multi-objective APP problem.