## 1 Introduction
The real-time data are collected and sent to the phasor data concentrator (PDC), enabling it able to undertake applications such as monitoring, control, and network stability [1]. This measuring fact allows real-time monitoring, which is important for energy management system applications [1; 2; 3; 4; 6]. With the utilization of PMUs, the SE procedure is now able to work more accurately in large power networks, as it incorporates phasor voltage measurements at network buses and current measurements through connection lines [1; 2; 3; 4; 6; 7; 8; 9; 10; 11; 12]. In the last decade, utilities have made significant investments in enhancing the actual-time monitoring and power transmission grid control applications [1; 2; 3; 4; 6; 7; 8; 9; 10; 11]. All over the world, many utility industries have installed large numbers of PMUs to render their optimal deployment at substations [7; 8; 9; 10; 11]. The deployment of synchronized sensors is still continuing and somehow is in slow progress, mainly due to economic and technical restrictions [5]. Due to the high cost of installing a PMU at every power grid node in the WAMS implementation to attain full observability, it is significant to take into account the best PMU position sites through a solvable OPP problem [7; 8; 9; 10; 11]. Hence, the OPP problem still stands, giving a full network observation of the power grid state while the entire cost investment is minimized [7; 8; 9; 10; 11]. A PMU is placed at the installation bus and computes the phasor voltage at that bus and all the phasor current lines running from that bus with the assumption that the monitoring device has an unlimited number of channels [4; 6; 7; 8; 9; 10; 11]. Over two decades of research, a plethora of significant papers has emerged to tackle the OPP problem. They aim to ascertain the optimal PMU number needed and strategically position them to ensure the power grid achieves full observability [4; 8; 9; 10; 11; 12; 13; 14]. Many of these papers delve into various strategies for solving the OPP problem, with a primary focus on achieving full observability while satisfying zero-one constraints on a minimum objective function bound [4; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Some interesting research studies have been published recently in the OPP domain [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67]. The pioneering work is to address the OPP-based model on optimization [28; 29; 30; 31; 32] using a zero-one integer linear programming (ILP) model, and some interesting research works have been published in the OPP domain in the recent past [33; 34; 35; 36]. Mathematical algorithms are utilized in the OPP problem solving [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42], whereas heuristic algorithms are also implemented to handle the integer program's inequality to examine the solution, thereby yielding heuristically sound knowledge [39; 43; 44; 45; 46; 47; 48; 49; 55]. In the past years, the initial OPP formulation has become more and more attractive in the incorporation of intellectually demanding tasks under operating conditions [7; 8; 9; 10; 11]. These OPP models consider relative constraints to satisfy these issues without sacrificing the entire observability [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. Many research works on OPP rely on a cumulative single objective function that is minimized subject to a constraint function defined on specific decision bounds [32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. On the contrary, a two-product objective minimization model is proposed in [42; 47; 49; 51] to find those optima points with a maximum system observability index declared in [33; 37; 38; 41; 42; 51]. The optimization problem in [37; 38; 42; 43; 44; 45; 47; 49; 51] considers obtaining more than one objective product.