An interacting replica approach applied to the traveling salesman problem

We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with multiple extrema. Our method involves (i) coupling otherwise independent simulations of a system ("replicas") via geometrical distances as well as (ii) probabilistic inference applied to the solutions found by individual replicas. The {\it ensemble} of replicas evolves as to maximize the inter-replica correlation while simultaneously minimize the local intra-replica cost function (e.g., the total path length in the Traveling Salesman Problem within each replica). We demonstrate how our method improves the performance of rudimentary local optimization schemes long applied to the NP hard Traveling Salesman Problem. In particular, we apply our method to the well-known "$k$-opt" algorithm and examine two particular cases- $k=2$ and $k=3$. With the aid of geometrical coupling alone, we are able to determine for the optimum tour length on systems up to $280$ cities (an order of magnitude larger than the largest systems typically solved by the bare $k=3$ opt). The probabilistic replica-based inference approach improves $k-opt$ even further and determines the optimal solution of a problem with $318$ cities and find tours whose total length is close to that of the optimal solutions for other systems with a larger number of cities.Comment: To appear in SAI 2016 conference proceedings 12 pages,17 figure

Ant Colony Optimization approaches for the Sequential Ordering Problem

We present two algorithms within the framework of the Ant Colony Optimization (ACO) metaheuristic. The rst algorithm seeks to increase the exploration bias of Gambardella et al.\u27s (2012) Enhanced Ant Colony System (EACS) model, a model which heavily increases the exploitation bias of the already highly exploitative ACS model in order to gain the bene t of increased speed. Our algorithm aims to strike a balance between these two models. The second is also an extension of EACS, based on Jayadeva et al.\u27s (2013) EigenAnt algorithm. EigenAnt aims to avoid the problem of stagnation found in ACO algorithms by, among other unique properties, utilizing a selective rather than global pheromone evaporation model, and by discarding heuristics in the solution construction phase. A performance comparison between our two models, the legacy ACS model, and the EACS model is presented. The Sequential Ordering Problem (SOP), one of the main problems used to demonstrate EACS, and one still actively studied to this day, was utilized to conduct the comparison

Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure

Reactive max-min ant system: An experimental analysis of the combination with K-OPT local searches

Ant colony optimization (ACO) is a stochastic search method for solving NP-hard problems. The exploration versus exploitation dilemma rises in ACO search.Reactive max-min ant system algorithm is a recent proposition to automate the exploration and exploitation.It memorizes the search regions in terms of reactive heuristics to be harnessed after restart, which is to avoid the arbitrary exploration later.This paper examined the assumption that local heuristics are useless when combined with local search especially when it applied for combinatorial optimization problems with rugged fitness landscape.Results showed that coupling reactive heuristics with k-Opt local search algorithms produces higher quality solutions and more robust search than max-min ant system algorithm.Well-known combinatorial optimization problems are used in experiments, i.e. traveling salesman and quadratic assignment problems. The benchmarking data for both problems are taken from TSPLIB and QAPLIB respectively

Optimal dynamic operations scheduling for small-scale satellites

A satellite's operations schedule is crafted based on each subsystem/payload operational needs, while taking into account the available resources on-board. A number of operating modes are carefully designed, each one with a different operations plan that can serve emergency cases, reduced functionality cases, the nominal case, the end of mission case and so on. During the mission span, should any operations planning amendments arise, a new schedule needs to be manually developed and uplinked to the satellite during a communications' window. The current operations planning techniques over a reduced number of solutions while approaching operations scheduling in a rigid manner. Given the complexity of a satellite as a system as well as the numerous restrictions and uncertainties imposed by both environmental and technical parameters, optimising the operations scheduling in an automated fashion can over a flexible approach while enhancing the mission robustness. In this paper we present Opt-OS (Optimised Operations Scheduler), a tool loosely based on the Ant Colony System algorithm, which can solve the Dynamic Operations Scheduling Problem (DOSP). The DOSP is treated as a single-objective multiple constraint discrete optimisation problem, where the objective is to maximise the useful operation time per subsystem on-board while respecting a set of constraints such as the feasible operation timeslot per payload or maintaining the power consumption below a specific threshold. Given basic mission inputs such as the Keplerian elements of the satellite's orbit, its launch date as well as the individual subsystems' power consumption and useful operation periods, Opt-OS outputs the optimal ON/OFF state per subsystem per orbital time step, keeping each subsystem's useful operation time to a maximum while ensuring that constraints such as the power availability threshold are never violated. Opt-OS can provide the flexibility needed for designing an optimal operations schedule on the spot throughout any mission phase as well as the ability to automatically schedule operations in case of emergency. Furthermore, Opt-OS can be used in conjunction with multi-objective optimisation tools for performing full system optimisation. Based on the optimal operations schedule, subsystem design parameters are being optimised in order to achieve the maximal usage of the satellite while keeping its mass minimal

Parallelization Strategies for Ant Colony Optimisation on GPUs

Ant Colony Optimisation (ACO) is an effective population-based meta-heuristic for the solution of a wide variety of problems. As a population-based algorithm, its computation is intrinsically massively parallel, and it is there- fore theoretically well-suited for implementation on Graphics Processing Units (GPUs). The ACO algorithm comprises two main stages: Tour construction and Pheromone update. The former has been previously implemented on the GPU, using a task-based parallelism approach. However, up until now, the latter has always been implemented on the CPU. In this paper, we discuss several parallelisation strategies for both stages of the ACO algorithm on the GPU. We propose an alternative data-based parallelism scheme for Tour construction, which fits better on the GPU architecture. We also describe novel GPU programming strategies for the Pheromone update stage. Our results show a total speed-up exceeding 28x for the Tour construction stage, and 20x for Pheromone update, and suggest that ACO is a potentially fruitful area for future research in the GPU domain.Comment: Accepted by 14th International Workshop on Nature Inspired Distributed Computing (NIDISC 2011), held in conjunction with the 25th IEEE/ACM International Parallel and Distributed Processing Symposium (IPDPS 2011

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Optimal power harness routing for small-scale satellites

This paper presents an approach to optimal power harness design based on a modified ant colony optimisation algorithm. The optimisation of the harness routing topology is formulated as a constrained multi-objective optimisation problem in which the main objectives are to minimise the length (and therefore the mass) of the harness. The modified ant colony optimisation algorithm automatically routes different types of wiring, creating the optimal harness layout. During the optimisation the length, mass and bundleness of the cables are computed and used as cost functions. The optimisation algorithm works incrementally on a finite set of waypoints, forming a tree, by adding and evaluating one branch at a time, utilising a set of heuristics using the cable length and cable bundling as criteria to select the optimal path. Constraints are introduced as forbidden waypoints through which digital agents (hereafter called ants) cannot travel. The new algorithm developed will be applied to the design of the harness of a small satellite, with results highlighting the capabilities and potentialities of the code