## 1 Introduction  
Presently, a variety of NP-hard problems are involved in many real-world applications and AI computing. Solving specific NP-hard problems (with high performance in efficient time) for those applications is challenging. Some of the interesting NP-hard problems are the 0/1-KP (knapsack problem), the 0/1-mKP (multiple \(m\) knapsacks), etc. Formally, the 0/1-KP is defined as follows: Consider a set of \(n\) objects and a knapsack capacity \(C\), where each object \(i\)(=0, 1,..., \(n-1\)) has profit \(p_{j}\) and weight \(w_{j}\). The objective of the 0/1-KP is to select some objects for the maximum total profit kept in the knapsack that cannot exceed the knapsack capacity (\(C\)), defined in Equations (1)-(3). Recently (2018), unbiased filtering [1] was proposed (for the 0/1-KP) to select outstanding objects (from \(n\) objects) before applying the exact DP (dynamic programming) algorithm on small remaining \(n^{\prime}\) (\(\leq\)200) in efficient time for most optimal solutions (at least 95%) of regular and irregular datasets. \[\text{Maximize }\sum_{j=0}^{n-1}p_{j}x_{j} \tag{1}\]  
\[\text{Subject to }\sum_{j=0}^{n-1}w_{j}x_{j}\ \leq C \tag{2}\]  
\[\text{and }x_{j}\in\{0,1\};j=0,\,1,\,2,\,\ldots,\,n-1 \tag{3}\]  
For the complex 0/1-mKP (\(m\) knapsacks), the objective is to select some objects for multiple knapsacks (each selected object) (\(x_{ij}=1\)) in a proper knapsack \(i\)) that cannot exceed each of the knapsack capacities (\(C_{i}\); \(i=1,\,2,\,3,\,\ldots,\,m\)), see Figure 1 (one and \(m\) knapsacks), for the maximized total profit, defined in Equations(4)-(6). \[\text{Maximize }\sum_{i=1}^{m}\sum_{j=0}^{n-1}p_{j}x_{ij} \tag{4}\]  
\[\text{Subject to }\sum_{j=0}^{n-1}w_{j}x_{ij}\leq\ C_{i}\ ;\ i=1,\,2,\ldots,\ m;\ j=0,\,1,\,2,\ldots,\ n-1 \tag{5}\]  
\[\text{and }\sum_{i=1}^{m}\ x_{ij}\leq\ 1,\ xij\ \{0,\,1\};\,i,\ j \tag{6}\]  
The 0/1-KP and 0/1-mKP are constructive for science and engineering applications, such as resource allocation [2; 3], capital budgeting [4], production planning [5], multicontainer packing [6], risk balancing and assortment optimization [7], other applications in network systems [8; 9; 10], etc. However, finding the optimal solution of the 0/1-mKP is much harder than that of the 0/1-KP since each selected object (\(x_{ij}=1\)) must specify a proper knapsack (\(K_{i}\) with capacity \(C_{i}\); \(i\in\{1,\,\ldots,\,m\}\)) from the available knapsacks. In popular 0/1-KP research, two approaches are extensively studied: 1. the exact approach for optimal solutions (but in exponential time) and 2. the fast approximate approach (but the optimal solution may not be found). In theory, the optimal solution of the 0/1-KP can be computed by DP (dynamic programming) algorithms in O(\(nC\)) [11; 12; 13; 14; 15], or BnB (branch-and-bound) [16] and backtracking [17] algorithms in exponential time (O(\(2^{m}\))). In practice, approximate methods (i.e., greedy methods [18; 19], kernel search [20; 21], genetic algorithms [22; 23], swarm optimization [24; 25; 26; 27; 28], hybrid methods [29; 30; 31; 32], hyper-heuristic method [33], etc.) can find the good solutions in polynomial time. Recently, the time-space reduction algorithm [1] was proposed to solve the 0/1-KP in O(\(n+C^{\prime}\)) for large \(n\) by unbiased filtering to preselect the outstanding objects (from \(n\) objects) before applying the exact DP algorithm on remaining \(n^{\prime}\) and \(C^{\prime}\) (\(n^{\prime}\leq 200\), \(C^{\prime}<<C\), and massive \(C\) may not be a polynomial bound of \(n\)), which could find most optimal solutions (at least 95%) in experiments. In current KP-researches, a variety of 0/1-KPs have been studied, including the multiple KP (0/1-mKP) [34; 35; 36], no shared \(x_{ij}\) in \(m\) knapsacks (\(\sum_{j=0}^{n-1}w_{j}x_{ij}\leq\ C_{i}\)), the multi-dimensional KP (0/1-MKP) [37; 38; 39; 40; 41], (\(\sum_{i=1}^{m}\sum_{j=0}^{n-1}w_{j}x_{ij}\leq\ C_{i}\) shared \(x_{j}\) in \(m\) knapsacks), and the multidimensional multiple-choice KP (0/1-MMKP) [42].