A Modified ACO with K-OPT for Restricted Covering Salesman Problems in Different Environments

In this study, the ant colony optimization (ACO) algorithm is modified with the K-opt operation to solve the covering salesman problem(CSP) under one restriction in crisp and imprecise (fuzzy, rough) environments. A CSP involves two phases- the division of cities into groups with the selection of the visiting cities and searching of the Hamiltonian circuit through the visiting cities. But, none of the studies in the literature is made following the direct approach. Also, none of the studies in the literature gives attention to reduce the total travel distance of the unvisited cities from the visited city of a group. Moreover, there is no algorithm in the literature which provides the solution of a CSP with the specified coverage range $r$. Also, none has introduced any algorithm to solve CSPs in imprecise environments. Though algorithms are available to solve the Traveling Salesman Problems in the imprecise environments, the approach cannot deal with the problems involving fuzzy data with non-linear membership functions or the problems involving rough data where the rough estimation can not be done using Lebesgue measure. The well establish algorithm for any routing problem is the ACO, but not much attention has been paid to solve the CSP using ACOs. To overcome these limitations on the studies of the ACO on the CSPs, here, an algorithm is proposed for the division of groups of the set of cities depending upon the maximum number of cities in a group and the total number of groups. Then ACO is used to find the shortest/minimum-cost path of the problem by selecting only one visiting the city from each group without violating the restriction of the specified coverage range $r$ of the location of the unvisited cities. K-opt operation is applied periodically at the end of ACO operation to improve the quality of the best found solution so far by the ACO algorithm and to arrest any premature convergence. For the restricted problems paths are searched in such a manner that the total distance/travel cost of different unvisited cities of a group from the visited city of the group should not exceed a predefined upper limit. To solve the problem in an imprecise environment some approach is followed so that the tour is searched without transferring the imprecise optimisation problem into an equivalent crisp optimisation problem. Also, the simulation approaches in fuzzy and rough environments are proposed to deal with the CSPs with any type of estimation of the imprecise data set. Algorithm is tested with the standard benchmark crisp problems available in the literature. To test the algorithm in the imprecise environments, the imprecise instances are derived randomly from the standard crisp instances using a specified rule. Test results imply that the proposed algorithm is efficient enough in solving the CSPs in the crisp as well as in the imprecise environments.

Research on the Mechanism of Main Roof Advanced Breaking and Supporting Technology When Long-wall Face Passing Through Abandoned Roadways

Unlike general long-wall mining, the roof activity is more intense when long-wall face passes through the abandoned roadway. Technically, the coal pillar between the abandoned roadway and the long-wall face will suddenly fail with a certain critical value of its width, leading to the roof breaks in advance and other production-restricted problems because of the support loss, which will be a great threat to underground mining activities. In order to guarantee a safe mining condition, therefore, it is greatly necessary to uncover how the roof breaks in advance and how to cope with it. From the stability maintaining of the key block perspective, this paper took for research that the 12404-1 long-wall face of Wulanmulun coal mine, China. The critical value of the coal pillar’s width was determined to be about 5m by theoretical analysis, likely, the appropriate support force of the abandoned roadway’s roof is about 4020KN per meter. Meanwhile, a numerical simulation method was adopted to study the ground pressure when the long-wall face passing through the abandoned roadway. Correspondingly, a compound supporting technology involving the roof presplit technique, anchor cable supporting and pumping pillar supporting were proposed for the roof of the abandoned roadway, and it practically worked well.

Fine-Grained Time Complexity of Constraint Satisfaction Problems

We study the constraint satisfaction problem (CSP) parameterized by a constraint language Γ (CSPΓ) and how the choice of Γ affects its worst-case time complexity. Under the exponential-time hypothesis (ETH), we rule out the existence of subexponential algorithms for finite-domain NP-complete CSPΓ problems. This extends to certain infinite-domain CSPs and structurally restricted problems. For CSPs with finite domain D and where all unary relations are available, we identify a relation S D such that the time complexity of the NP-complete problem CSP({ S D }) is a lower bound for all NP-complete CSPs of this kind. We also prove that the time complexity of CSP({ S D }) strictly decreases when |D| increases (unless the ETH is false) and provide stronger complexity results in the special case when |D|=3.

Stable Matching with Uncertain Linear Preferences

We consider the two-sided stable matching setting in which there may be uncertainty about the agents’ preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model—for each agent, there is a probability distribution over linear preferences, (2) compact indifference model—for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model—there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

An Assembly Line Balancing Application on Oven Production Line with Hyper-Heuristics

In this study, an oven assembly line that is planning to re-establish manufacturing to increase the efficiency of the assembly process. The importance of the problem emerges from a real-world application consisting of product-oriented restrictions. These multiple restricted problems address the single model assignment restricted ALB problem with positional constraints. A cost-based objective function is used to cope with this problem. The number of platformed and non-platformed stations, the number of direction changes in a station, the number of stations in which both connector and combiner are used are the cost factors of the objective function. Also, the main objective of the problem is to minimize the total number of stations while satisfying the restrictions. A simulated annealing-based hyper-heuristic is adapted and applied to the balancing problem of oven manufacturing process with assignments and operational restrictions with multiple objectives. The results show that better solutions can be found in the current line balance level while satisfying more restrictions. It is also observed that line balance can be improved depending on the relaxation of the restrictions.