An effective modified binary particle swarm optimization (mBPSO) algorithm for multi-objective resource allocation problem (MORAP)

Abstract

A modified binary particle swarm optimization (mBPSO) algorithm is proposed for solving the multi-objective resource allocation problem (MORAP). First, the generation mechanism for initial particles is established to guarantee that the algorithm can begin to search optimal particle in the feasible solution space. Second, we develop the update mechanism for iterative particles which includes setting up the memory array, modifying Sig function and verifying the constraint condition to assure that the regenerated particles meet the constraint and algorithm can quickly converge. Third, the selection mechanism for pbest_i and gbest is proposed which uses the dynamic neighborhood strategy to ensure that the algorithm to find Pareto optimal solutions. Through comparing the example simulation results of our mBPSO with hGA and ACO published in references, we find that proposed mBPSO outperforms hGA and ACO. Finally, the effectiveness of the different improved methods is analyzed, and the synergism effect and the convergence behavior of the mBPSO algorithm show its good performances.

Introduction

Resource allocation problem (RAP) is a process that limited resources are distributed to various projects reasonably so as to optimize a certain objective. Resources may be raw materials, capitals, machineries and equipments, labors or foods, and the objective includes profit maximization, cost minimization, quality optimization, and so on. For instance, plant distribution [1] allocates limited products among plants to minimize the total cost, and water resources allocation [2] requires that a certain amount of water be purposefully left in or released into an aquatic ecosystem to maintain it in a condition. Job shop scheduling [3] allocates time for work orders on different types of production equipment to minimize delivery time or maximize equipment utilization. In addition, software testing [4], [5] guarantees the maximum reliability by allotting testing resource to program modules, and public services resource allocation [6] achieves effective–efficient–equality goal and balances the desire needs between different management level. There are so many resource allocation problems in the world need to research.

Because the number of optimization goals is different in diverse problem scenarios, resource allocation problem includes single-objective RAP (SORAP) and multi-objective RAP. SORAP optimizes a single goal, such as benefit maximization or cost minimization, while MORAP seeks to optimize a set of goals simultaneously. In the case of multiple-objectives, the optimal solution to all objectives does not necessarily exist because of incommensurability and confliction among objectives [7]. Usually, there exists a group of solutions for the MORAP which cannot be compared with each other simply. Such solutions, called no-dominated solutions or Pareto optimal solutions, cannot make any objective value improve without deteriorating any other objective value [7].

In the past few years, there has been a boom in applying various approaches to solving many different RAP and MORAP optimization problems. The analytic hierarchy process combined with an artificial neural network algorithm [8] was proposed to put forward a reasonable budget allocation, while Ko & Lin [9] employed neural network to make portfolio selection as a resource allocation problem. The data envelopment analysis (DEA) model [10] was proposed for resource allocation, and the important advantage of using this model is that the decision makers’ preferences can be incorporated into the resource reallocation. Rachmawati & Srinivasan [11] proposed a fuzzy evolutionary algorithm (EA) employing fuzzy representation and reasoning for the student project allocation involving fuzzy objectives. Grid systems were used in [12] to consider the MORAP and scheduling problem in a grid computing environment. A memetic algorithm [13] was presented for solving project resource allocation problems, where the resource requirement of each project concerns numbers of monetary units and never exceeds the amount of capital available. Osman et al. [14] used general genetic algorithm (GA) to solve MORAP, while Lin & Gen [15] proposed a multi-objective hybrid genetic algorithm (mo-hGA) approach based on the multistage decision making model to obtain a set of Pareto solutions. On the other hand, ant colony optimization algorithm (ACO) was modified by Chaharsooghi & Kermani [16] to get Pareto solutions of the same MORAP as [15]. Yin & Wang [17] employed the particle swarm optimization (PSO) paradigm and presented a hybrid execution plan to solve the nonlinear MORAP with integer decision variable constraint.

Based on previous works, this paper intends to present a new algorithm for solving MORAP based on the binary particle swarm optimization algorithm (BPSO) which was developed by Kennedy & Eberhart [18]. The motivations of our research are threefold.

• Most existing methods based on swarm optimization for RAP and MORAP mainly include ACO [16] and PSO [17], while to the best of our knowledge there is no previous work that applied BPSO to the MORAP. Encouraged by our successful application of BPSO in [19] to solve a class of job shop scheduling problem with a single objective, we employ modified binary particle swarm optimization (mBPSO) for solving the MORAP.

• The multi-objective hybrid genetic algorithm (mo-hGA) and the modified ant colony optimization (ACO) proposed in [15] and [16] respectively are shown to be efficient for MORAP, and we hope to compare the performance of our mBPSO with them through solving the same MORAP.

• We propose several strategies for handing Pareto optimal solutions which include initial particle generation mechanism, iterative particle update mechanism and best particle selection mechanism. These techniques can ensure algorithm to search optimal particle in the feasible solution space and expedite the search. At the same time, these strategies are not only useful in our methods but also beneficial to any other problems whose solutions are “0–1” matrixes.

The remainder of this paper is organized as follows. Section 2 formulates the addressed MORAP problem. Section 3 presents the modified BPSO algorithm for tackling the MORAP in details. Section 4 reports the comparative performance of proposed mBPSO with the hybrid genetic algorithm and ant colony optimization, and also convergence analysis. Conclusions are drawn in Section 5.