Dual Probability Learning Based Local Search for the Task Assignment Problem

Abstract

The task assignment problem (TAP) is concerned with assigning a set of tasks to a set of agents subject to the limited processing and memory capacities of each agent. The objective to be minimized is the total assignment cost and total communication cost. TAP is a relevant model for many practical applications, yet solving the problem is computationally challenging. Most of the current metaheuristic algorithms for TAP adopt population-based search frameworks, whose search behaviors are usually difficult to analyze and understand due to their complex features. In this work, unlike previous population-based solution methods, we concentrate on a single trajectory stochastic local search model to solve TAP. Especially, we consider TAP from the perspective of a grouping problem and introduce the first probability learning-based local search algorithm for the problem. The proposed algorithm relies on a dual probability learning procedure to discover promising search regions and a gain-based neighborhood search procedure to intensively exploit a given search region. We perform extensive computational experiments on a set of 180 benchmark instances with the proposed algorithm and the general mixed integer programming solver CPLEX. We assess the composing ingredients of the proposed algorithm to shed light on their impacts on the performance of the algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the problem of program modules designing and task allocation in parallel and distribution systems. It can also be applied to deal with job (task) grouping problems in practical industrial applications. This article presents a novel and effective learning-based local search algorithm to obtain high-quality solutions for the considered problem. The results of numerical experiments and comparisons show that our algorithm can achieve good search performances on problem instances of different scales and difficulties. Afterward, we use the proposed solution method to solve a real-life open-order slab assignment problem, which is derived from the production planning of silicon steel for an iron and steel company. The learning techniques of the proposed algorithm are of general interest and can be used in search algorithms for solving other real-life optimization problems with grouping features. For future research, we will design solution methods based on these learning techniques to address other practical optimization problems.